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1
Delaney, Christopher. "Generalized Differential and Integral Categories." Thesis, Université d'Ottawa / University of Ottawa, 2018. http://hdl.handle.net/10393/37136.
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This paper provides two generalizations of differential and integral categories: Leibniz and generalized Rota-Baxter categories, which capture certain algebraic structures, and q-categories, which capture structures of quantum calculus. In the search for new examples of differential and integral categories, it was observed that many structures were not quite examples but satisfied certain properties and not others. This leads us to the definition of Leibniz, Rota-Baxter and proto-FTC categories. In generalizing Rota-Baxter categories further to an arbitrary weight, we show that we recapture Ribenboim's generalized power series as a monad on vector spaces with a generalized integral transformation. This also subsumes the renormalization operator on Laurent series, which has applications in the quantum realm. Finally, we define quantum differential and quantum integral categories, show that they recapture the usual notions of quantum calculus on polynomials, and construct a new example to indicate their potential usefulness outside of that specific setting
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Kudreyko, Aleksey. "Multiscale wavelet analysis for integral and differential problems." Doctoral thesis, Universita degli studi di Salerno, 2011. http://hdl.handle.net/10556/176.
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2009 - 2010<br>The object of the present research is wavelet analysis of integral and differential problems
by means of harmonic and circular wavelets. It is shown that circular wavelets
constitute a complete basis for L2[0; 1] functions, and form multiresolution analysis.
Multiresolution analysis can be briefly considered as a decomposition of L2[0; 1]
into a complete set of scale depending subspaces of wavelets. Thus, integral operators,
differential operators, and L2(R) functions were investigated as scale depending
functions through their projection onto these subspaces of wavelets. In particular:
- conditions when a certain wavelet can be applied for solution of integral or
differential problem are given;
- it is shown that the accuracy of this approach exponentially grows when increasing
the number of vanishing moments and scaling parameter;
- wavelet solutions of low-dimensional nonlinear partial differential equations are
compared with other methods;
- wavelet-based approach is applied to low-dimensional Fredholm integral equations
and the Galerkin method for two-dimensional Fredholm integral equations.[edited by author]. Oggetto della seguente ricerca `e l’analisi di problemi differenziali e integrali, utilizzando
wavelet armoniche e wavelet armoniche periodiche. Si dimostra che le wavelet
periodiche costituiscono una base completa per le funzioni L2[0; 1] e formano un’analisi
multiscala. L’analisi multirisoluzione pu`o essere brevemente considerata come la decomposizione
di L2[0; 1] in un insieme completo di sottospazi di wavelet dipendenti
da un fattore di scala. Pertanto gli operatori integrali e differenziali e le funzioni
L2(R) vengono studiati come funzioni di scala mediante le corrispondenti proiezioni
in questi sottospazi di wavelet. In particolare, vengono sviluppati quattro principali
argomenti:
- sono state individuate le condizioni per applicare una data famiglia di wavelets
alla soluzione di un data problema differenziale o integrale;
- si `e dimostrato che la precisione di questo approccio cresce esponenzialmente
quando decresce il numero dei momenti nulli e del parametro di scala;
- soluzioni wavelet di equazioni differenziali a derivate parziali nonlineari di dimensione
bassa sono state confrontate con altri metodi di soluzioni;
- l’approccio basato sull’uso delle wavelet `e stato applicato anche per ricerca
di soluzioni di alcune equazioni integrali di Fredholm e insieme al metodo di
Galerkin per risolvere equazioni integrali Fredholm di dimensioni due.[a cura dell'autore]<br>IX n.s.
3
Kunzweiler, Sabrina [Verfasser]. "Models of curves and integral differential forms / Sabrina Kunzweiler." Ulm : Universität Ulm, 2021. http://d-nb.info/1228439044/34.
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Alzahrani, Faris. "A study of differential and integral operators in linear viscoelasticity." Thesis, Cardiff University, 2013. http://orca.cf.ac.uk/53333/.
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This thesis identifies and explores a link between the theory of linear viscoelasticity and the spectral theory of Sturm-Liouville problems. The thesis is divided into five chapters. Chapter 1 gives a brief account of the relevant parts of the theory of linear viscoelasticity and lays the foundation for making the link with spectral theory. Chapter 2 is concerned with the construction of approximate Dirichlet series for completely monotonic functions. The chapter introduces various connections between non-negative measures, orthogonal polynomials, moment problems, and the Stieltjes continued fraction. Several interlacing properties for discrete relaxation and retardation times are also proved. The link between linear viscoelasticity and spectral theory is studied in detail in Chapter 3. The stepwise spectral functions associated with some elementary viscoelastic models are derived and their Sturm-Liouville potentials are explicitly found by using the Gelfand-Levitan method for inverse spectral problems. Chapter 4 presents a new family of exact solutions to the nonlinear integrodifferential A-equation, which is the main equation in a recent method proposed by Barry Simon for solving inverse spectral problems. Starting from the A-amplitude A(t) = A(t, 0) which is determined by the spectral function, the solution A(t, x) of the A-equation identifies the potential q(x) as A(0, x). Finally, Chapter 5 deals with two numerical approaches for solving an inverse spectral problem with a viscoelastic continuous spectral function. In the first approach, the A-equation is solved by reducing it to a system of Riccati equations using expansions in terms of shifted Chebyshev polynomials. In the second approach, the spectral function is approximated by stepwise spectral functions whose potentials, obtained using the Gelfand-Levitan method, serve as approximations for the underlying potential
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Scapellato, Andrea. "Integral operators and partial differential equations in Morrey type spaces." Doctoral thesis, Università di Catania, 2018. http://hdl.handle.net/10761/4043.
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Lo scopo di questa tesi è lo studio della limitatezza di alcuni operatori integrali in spazi funzionali di tipo Morrey. Inoltre si studia la regolarità di soluzioni di equazioni differenziali alle derivate parziali.
6
Ma, Zhiwen. "A combined differential and integral model for high temperature fuel cells." Diss., Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/15831.
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Sipiläinen, Eeva-Maria. "Pathwise view on solutions of stochastic differential equations." Thesis, University of Edinburgh, 1993. http://hdl.handle.net/1842/8202.
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The Ito-Stratonovich theory of stochastic integration and stochastic differential equations has several shortcomings, especially when it comes to existence and consistency with the theory of Lebesque-Stieltjes integration and ordinary differential equations. An attempt is made firstly, to isolate the path property, possessed by almost all Brownian paths, that makes the stochastic theory of integration work. Secondly, to construct a new concept of solutions for differential equations, which would have the required consistency and continuity properties, within a class of deterministic noise functions, large enough to include almost all Brownian paths. The algebraic structure of iterated path integrals for smooth paths leads to a formal definition of a solution for a differential equation in terms of generalized path integrals for more general noises. This suggests a way of constructing solutions to differential equations in a large class of paths as limits of operators. The concept of the driving noise is extended to include the generalized path integrals of the noise. Less stringent conditions on the Holder continuity of the path can be compensated by giving more of its iterated integrals. Sufficient conditions for the solution to exist are proved in some special cases, and it is proved that almost all paths of Brownian motion as well as some other stochastic processes can be included in the theory.
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Hunt, Cynthia Young. "An Existence Theorem for an Integral Equation." Thesis, North Texas State University, 1985. https://digital.library.unt.edu/ark:/67531/metadc503874/.
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The principal theorem of this thesis is a theorem by Peano on the existence of a solution to a certain integral equation. The two primary notions underlying this theorem are uniform convergence and equi-continuity. Theorems related to these two topics are proved in Chapter II. In Chapter III we state and prove a classical existence and uniqueness theorem for an integral equation. In Chapter IV we consider the approximation on certain functions by means of elementary expressions involving "bent line" functions. The last chapter, Chapter V, is the proof of the theorem by Peano mentioned above. Also included in this chapter is an example in which the integral equation has more than one solution. The first chapter sets forth basic definitions and theorems with which the reader should be acquainted.
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Marques, Rafael dos Santos. "Integral equations in the sense of Kurzweil integral and applications." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-08112016-104931/.
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Being part of a research group on functional differential equations (FDEs, for short), due to my formation in non-absolute integration theory and because certain kinds of FDEs can be expressed as integral equations, I was motivated to investigate the latter. The purpose of this work, therefore, is to develop the theory of integral equations, when the integrals involved are in the sense of Kurzweil- Henstock or Kurzweil-Henstock-Stieltjes, through the correspondence between solutions of integral equations and solutions of generalized ordinary differential equations (we write generalized ODEs, for short). In order to be able to obtain results for integral equations, we propose extensions of both the Kurzweil integral and the generalized ODEs (found in [36]). We develop the fundamental properties of this new generalized ODE, such as existence and uniqueness of solutions results, and we propose stability concepts for the solutions of our new class of equations. We, then, apply these results to a class of nonlinear Volterra integral equations of the second kind. Finally, we consider a model of population growth (found in [4]) that can be expressed as an integral equation that belongs to this class of nonlinear Volterra integral equations.<br>Sendo parte de um grupo de pesquisa em equações diferenciais funcionais (escrevemos EDFs), por causa de minha formação em teoria de integração não absoluta e porque certos tipos de EDFs podem ser escritas como equações integrais, decidi estudar esse último tipo de equações. O objetivo desse trabalho, portanto, é desenvolver a teoria de equações integrais, quando as integrais envolvidas são no sentido de Kurzweil-Henstock ou Kurzweil-Henstock-Stieltjes, através da correspondência entre soluções de equações integrais e soluções de equações diferenciais ordinárias generalizadas (ou EDOs generalizadas). A fim de obter resultados para estas equações integrais, propomos extensões de ambas a integral de Kurzweil e as EDOs generalizadas (encontradas em [36]). Desenvolvemos propriedades fundamentais dessa nova EDO generalizada, como resultados de existência e unicidade de solução, e propomos conceitos de estabilidade para as soluções de nossa nova classe de equações. Nós, então, aplicamos esses resultados a uma classe de equações integrais de Volterra não lineares de segunda espécie. Finalmente, consideramos um modelo de crescimento de populações (encontrado em [4]) que pode ser escrito como uma equação integral pertencente a essa classe de equações integrais de Volterra não lineares.
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Geigant, Edith. "Nichtlineare Integro-Differential-Gleichungen zur Modellierung interaktiver Musterbildungsprozesse auf S¹." Bonn : Rheinische Friedrich-Wilhelms-Universität, 1999. http://catalog.hathitrust.org/api/volumes/oclc/45517690.html.
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Caillé, Jean. "New integral and differential computational procedures for incompressible wall-bounded turbulent flows." Diss., Virginia Tech, 1992. http://hdl.handle.net/10919/37425.
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Three new computational procedures are presented for the simulation of incompressible wall-bounded turbulent flows. First, an integral method based on the strip integral method has been developed for the solution of three-dimensional turbulent boundary-layer flows. The integral equations written in a general form using non-orthogonal streamline coordinates include the turbulent shear stress at the upper limit of an inner strip inside the boundary-layer. The shear stress components are modeled using the Boussinesq assumption, and the eddy viscosity is defined explicitly as in differential methods. The turbulence modeling is not hidden in opaque empirical correlations as in conventional integral methods. A practical four-parameter velocity profile has been established based on the Johnston Law of the Wall using a triangular model for the crosswise velocity. Two strips are used to solve for the four unknowns: skin friction coefficient, wall crossflow angle, boundary-layer thickness, and location of maximum crosswise velocity. The location of maximum crosswise velocity proves to be a natural and adequate parameter in the formulation, but it is numerically sensitive and has a strong influence on the wall crossflow angle. Good results were obtained when compared to predictions of other integral or differential methods.
Secondly, two computational procedures solving the Reynolds Averaged Navier-Stokes equations for 20 and 3D flows respectively have also been developed using a new treatment of the near-wall region. The flow is solved down to the wall with a slip velocity based on Clauser's idea of a pseudolaminar velocity profile. The present idea is different from the wall-function methods and does not require a multi-layer eddy viscosity model. The solution of the equations of motion is obtained by the Finite Element Method using the wall shear stress as a boundary condition along solid surfaces, and using the Clauser outer region model for the eddy viscosity. The wall shear stress distribution is updated by solving integral equations obtained from the enforcement of conservation of mass and momentum over an inner strip in the near-wall region. The Navier-Stokes solution provides the necessary information to the inner strip integral formulation in order to evaluate the skin friction coefficient for 2D flows, or the skin friction coefficient and the wall crossflow angle for 3D flows. The procedures converge to the numerically "exact" solution in a few iterations depending on the accuracy of the initial guess for the wall shear stress. A small number of nodes is required in the boundary-layer to represent adequately the physics of the flow, which proves especially useful for 3D calculations. Excellent results were obtained for the 2D simulations with a simple eddy viscosity model. 3D calculations gave good results for the turbulent boundary-layer flows considered here.
The present methods were validated using well-known experiments chosen for the STANFORD conferences and EUROVISC workshop. The 2D numerical predictions are compared with the experimental measurements obtained by Wieghardt-Tillmann, Samuel-Joubert, and Schubauer-Klebanoff. For the 3D analyses, the numerical predictions obtained by the strip-integral method and the Finite Element Navier-Stokes Integral Equation procedure are validated using the Van den Berg-Elsenaar and Müller-Krause experiments.<br>Ph. D.
12
Ngounda, Edgard. "Efficient numerical methods based on integral transforms to solve option pricing problems." Thesis, University of the Western Cape, 2012. http://hdl.handle.net/11394/4223.
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Philosophiae Doctor - PhD<br>In this thesis, we design and implement a class of numerical methods (based on integral transforms) to solve PDEs for pricing a variety of financial derivatives. Our approach is based on spectral discretization of the spatial (asset) derivatives and the use of inverse Laplace transforms to solve the resulting problem in time. The conventional spectral methods are further modified by using piecewise high order rational interpolants on the Chebyshev mesh within each sub-domain with the boundary domain placed at the strike price where the discontinuity is located. The resulting system is then solved by applying Laplace transform method through deformation of a contour integral. Firstly, we use this approach to price plain vanilla options and then extend it to price options described by a jump-diffusion model, barrier options and the Heston’s volatility model. To approximate the integral part in the jump-diffusion model, we use the Gauss-Legendre quadrature method. Finally, we carry out extensive numerical simulations to value these options and associated Greeks (the measures of sensitivity). The results presented in this thesis demonstrate the spectral accuracy and efficiency of our approach, which can therefore be considered as an alternative approach to price these class of options.
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Jacyntho, Luiz Antonio. "Uso de episodios historicos e de geometria dinamica para desenvolvimento de coneitos de integral de Riemann e do teorema fundamental do calculo para funções reais de variavel real." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/305871.
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Orientador: Luiz Mariano Paes de Carvalho Filho<br>Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação<br>Made available in DSpace on 2018-08-11T14:58:23Z (GMT). No. of bitstreams: 1
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Previous issue date: 2008<br>Resumo: Este trabalho tem como objetivos estudar algumas realizações de Arquimedes (287 a.C. - 212 a.C., Grécia) e de Isaac Barrow (1630-1677, Inglaterra), e, também, desenvolver atividades no Geogebra para auxiliar no ensino do Cálculo Diferencial e Integral. Apresentamos a construção do conjunto dos números reais, definições e teoremas atuais que antecedem, logicamente, o Teorema Fundamental do Cálculo. Tratamos de algumas das realizações de Arquimedes: a demonstração da medida da área do círculo, utilizando o Método de Eudoxo, o "método mecânico", pelo qual ele descobriu a medida da área do segmento parabólico e a demonstração rigorosa desta medida. São discutidas algumas realizações de Isaac Barrow: o método por ele utilizado para encontrar retas tangentes a uma curva, um estudo sobre o conteúdo da Conferência I e sobre algumas proposições da Conferência X. Nesta última, será dada atenção especial à Proposição 11, que demonstra casos particulares do Teorema Fundamental do Cálculo. O trabalho termina com um conjunto de atividades baseadas no programa Geogebra. Cada atividade tem a sua função numa seqüência didática e aborda os seguintes temas: a representação do conjunto dos números reais, a proposição de Arquimedes sobre a medida da área do círculo, o cálculo de áreas, a construção da função área, o cálculo de primitivas, a interpretação de Barrow para casos particulares do Teorema fundamental do Cálculo e algumas aplicações do Teorema Fundamental do Cálculo<br>Abstract: This work has as objectives study some realizations of Archimedes (287 BC - 212 BC, Greece) and of Isaac Barrow (1630-1677, UK), and, also, develop activities in Geogebra to aid in the teaching of Differential and Integral Calculus. We present the construction of the set of the real numbers, definitions and actual theorems that precede, logically, the Fundamental Theorem of Calculus. We deal with some of Archimedes' realizations: the demonstration of the measure of the circle's area, using the Eudoxus' Method, the "mechanical method", by which he discovered the measure of the area of the parabolic segment and the rigorous demonstration of it. There are discussed some realizations of Isaac Barrow: the method used by him to find tangent straights to a curve, a study about the content of the Lecture I and about some prepositions of the Lecture X. In this last one, main attention will be given to Proposition 11, which demonstrates particular cases of the Fundamental Theorem of Calculus. The word ends with a group of activities based in the Geogebra. Each activity has its function in a didactic sequence and they are about the following themes: the representation of the set of the real numbers, the proposition of Archimedes about the measure of the area of the circle, the calculation of areas, the construction of the area function, the calculation of primitives, the interpretation of Barrow to particular cases of the Fundamental Theorem of Calculus and some applications of the Fundamental Theorem of Calculus<br>Mestrado<br>Geometria<br>Mestre em Matemática
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Kalinin, Alexander [Verfasser], and Alexander [Akademischer Betreuer] Schied. "Markovian Integral Equations and Path-Dependent Partial Differential Equations / Alexander Kalinin ; Betreuer: Alexander Schied." Mannheim : Universitätsbibliothek Mannheim, 2017. http://d-nb.info/1137158220/34.
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Cerezo, Graciela M. "Solution Representation and Indentification for Singular neutral Functional Differential Equations." Diss., Virginia Tech, 1996. http://hdl.handle.net/10919/30365.
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The solutions for a class of Neutral Functional Di erential Equations (NFDE) with weakly singular kernels are studied. Using singular expansion techniques, a representation of the solution of the NFDE is obtained by studing an associated Volterra Integral Equation. We study the Collocation Method as a projection method for the approximation of solutions for Volterra Integral Equations. Particulary, the possibility of achieving higher order ap- proximations is discussed. Special attention is given to the choice of the projection space and its relation to the smoothness of the approximated solution. Finally, we study the identification problem for a parameter appearing in the weakly singular operator of the NFDE.<br>Ph. D.
16
Hao, Han. "Traveling Wave Solutions of Integro-differential Equations of One-dimensional Neuronal Networks." Thèse, Université d'Ottawa / University of Ottawa, 2013. http://hdl.handle.net/10393/24244.
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Traveling wave solutions of integro-differential equations for modeling one-dimensional neuronal networks, are studied. Under moderate continuity assumptions, necessary and sufficient conditions for the existence and uniqueness of monotone increasing (decreasing) traveling wave solutions are established. Some faults in previous studies are corrected.
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Aksoy, Umit. "Schwarz Problem For Complex Partial Differential Equations." Phd thesis, METU, 2006. http://etd.lib.metu.edu.tr/upload/3/12607977/index.pdf.
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This study consists of four chapters. In the first chapter we
give some historical background of the problem, basic definitions
and properties. Basic integral operators of complex analysis and
and Schwarz problem for model equations are presented in Chapter
2. Chapter 3 is devoted to the investigation of the properties of
a class of strongly singular integral operators. In the last
chapter we consider the Schwarz boundary value problem for the
general partial complex differential equations of higher order.
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Ozimba, Peter A. "A study of small angle differential and integral cross sections for k 4s-4p transition." DigitalCommons@Robert W. Woodruff Library, Atlanta University Center, 1994. http://digitalcommons.auctr.edu/dissertations/3056.
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Measured and calculated differential cross sections(DCS) are contrasted through the generalized ocsillator strength for impact energies of 16, 20, 40, 54.4, 60, 75, 100 and 200 eV. The recently constructed universal formula by Msezane and Sakmar is used to compare these results. Most of the results require renormalization and also show inaccuracy at small scattering angles. By also using the cubic spline function and the constructed formula from the universal formula, for the integral cross section by Chen and Msezane, total cross sections are calculated. These integral cross sections which serve as a good check to the measured and calculated DCS indicated the importance and need for the integral cross section formula for small scattering angles as contribution from this region ranges from to of the total contribution. The need for the universal extrapolation formula is thus found to be crucially important for accurate extrapolation.
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Paneah, Boris. "On a new problem in integral geometry related to boundary problems for partial differential equations." Universität Potsdam, 2001. http://opus.kobv.de/ubp/volltexte/2008/2608/.
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Contents:
1 Introduction
2 Statement of the problem and definitions
3 The main results
4 Proof of theorem 2
4.1 Reduction of problem (2) to functional - integral equations
4.2 The uniqueness of a solution of equation (2)
4.3 The existence of a solution of equation (2)
5 Proof of theorem 1
6 Proof of theorem 3
7 First boundary problem for hyperbolic differential equations
7.1 Statement of the problem
7.2 The formulation of the result and a sketch of the proof
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Jin, Chao. "Parallel domain decomposition methods for stochastic partial differential equations and analysis of nonlinear integral equations." Connect to online resource, 2007. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3256468.
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Santos, Fábio Lima. "Dicotomias em equações diferenciais ordinárias generalizadas e aplicações." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-24032017-102955/.
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Neste trabalho, estabelecemos a teoria de dicotomias para equações diferenciais ordinárias generalizadas, introduzindo os conceitos de dicotomias para essas equações generalizadas, estudando as suas propriedades e propondo resultados novos. Investigamos condições para a existência de soluções limitadas e condições para a existência de dicotomia exponencial. Utilizando teoremas de correspondência entre equações diferenciais ordinárias generalizadas e outras equações, traduzimos os resultados obtidos para os casos particulares de dicotomias para equações diferenciais em medida e para equações diferenciais com impulsos. O fato de trabalharmos no ambiente das equações diferenciais ordinárias generalizadas faz com que os resultados obtidos para os casos particulares possam envolver funções com muitas descontinuidades e de variação ilimitada.<br>In this work we establish the theory of dichotomies for generalized ordinary dierential equations, introducing the concepts of dichotomies for these equations, studying their properties and proposing new results. We investigate conditions of existence of exponential dichotomies and bounded solutions. Using correspondence theorems between generalized ordinary dierential equations and other equations, we translate the obtained results to the particular cases of dichotomies for measure dierential equations and for impulsive dierential equations. The fact that we work in the framework of generalized ordinary dierential equations allows us to obtain results for the particular cases where the functions involved can have many discontinuities and be of unbounded variation.
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Kastickaitė, Joana. "Diferencialinio ir integralinio skaičiavimo pradmenų mokymas Lietuvos mokykloje XX a. 3 – 4 dešimtmetyje." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2008. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2008~D_20080924_174749-11849.
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Temos „Diferencialinio ir integralinio skaičiavimo pradmenų mokymas Lietuvos mokykloje XX a. 3 – 4 dešimtmetyje“ svarbumas grindžiamas tuo, kad išanalizavus diferencialinio ir integralinio skaičiavimo mokymą tarpukario Lietuvoje (1918 – 1940), faktiškai būtų galima geriau suprasti ir dabartinės Lietuvos mokyklos diferencialinio ir integralinio skaičiavimo mokymo privalumus ir trūkumus. Darbas dar svarbus ir tuo, kad jame nuodugniai išnagrinėta diferencialinio ir integralinio skaičiavimo mokymas (programos, vadovėliai) iki matematikos mokymo reformos (1918 – 1928) ir po jos (1929 – 1940).
Atskirai tema specialiai nebuvo nagrinėta, tik paliečiama Algirdo Ažubalio „Matematika lietuviškoje mokykloje (XIX a. pr. – 1940)“, Juozo Banionio „Matematinė mintis Lietuvoje (istorinė apžvalga 1832 – 1990 m.)“ knygose. Be to, vadovėliai: J. Stoukaus „Begalinių mažybių analizio pagrindai“ (1925), A. Juškos „Matematinės analizės pagrindai“ (1934), B. Godvaišos ir J. Šinkūno „Matematika“ antra dalis (1996) nebuvo lyginti.
Darbo tikslai:
• apžvelgti, išanalizuoti ir palyginti diferencialinio ir integralinio skaičiavimo pradmenų mokymą Lietuvos mokykloje iki matematikos mokymo reformos, po reformos ir dabar;
• nustatyti diferencialinio ir integralinio skaičiavimo pradmenų mokymo privalumus ir trūkumus minėtais laikotarpiais.
Matematikos mokymas Lietuvoje 1918 – 1940 metais: buvo organizuotas, modernėjo, remtasi Vakarų Europos pavyzdžiu. Tai liudija: nepriklausomybės metais tobulintos... [toliau žr. visą tekstą]<br>The relevance of the topic “Teaching of Differential and Integral Calculation Basics in Lithuanian Schools in 3 – 4 Decades of the XXth Century” is based on the assumption that analysis of teaching of differential and integral calculation in the interwar Lithuania (1918-1940) would actually enable better understanding of advantages and drawbacks of teaching differential and integral calculation in Lithuanian schools nowadays. The final thesis is important for it thoroughly analyses teaching of differential and integral calculation (curricula, textbooks) before the teaching reform in mathematics (in 1918 – 1928) and after the reform (in 1929 – 1940).
Separately the topic was not analysed but only mentioned in the following books: Algirdas Ažubalis “Matematika lietuviškoje mokykloje (XIX a. pr. - 1940)” (Mathematics in Lithuanian School (Beginning of XIX Century – 1940)), Juozas Banionis “Matematinė mintis Lietuvoje (istorinė apžvalga 1832 – 1990 m.)” (Mathematical Thought in Lithuania (Historical Survey 1832 – 1990). Moreover, the following textbooks: J. Stoukus “Begalinių mažybių analizio pagrindai” (Basics of Infinite Least Analysis) (1925), A. Juška “Matematinės analizės pagrindai” (Basics of Mathematical Analysis) (1934), B. Godvaiša and J. Šinkūnas “Matematika” (Mathematics) Volume II (1996) were not compared.
Aims of the final thesis shall be the following:
• To make an overview, analysis and comparison of teaching differential and integral calculation basics in... [to full text]
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Silva, Fernanda Andrade da. "Controlabilidade e observabilidade em equações diferenciais ordinárias generalizadas e aplicações." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-08022018-100936/.
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Neste trabalho, introduzimos os conceitos de controlabilidade e de observabilidade para equações diferenciais ordinárias generalizadas, apresentamos resultados inéditos sobre condições suficientes e necessárias para controlabilidade e para observabilidade para estas equações e também apresentaremos uma aplicação. Utilizando teoremas de correspondência entre equações diferenciais ordinárias generalizadas e outras equações diferenciais, traduzimos os resultados obtidos para os casos particulares de controlabilidade e observabilidade para equações diferenciais em medida e equações diferencias com impulsos. O fato de trabalharmos no ambiente das equações diferenciais ordinárias generalizadas permitiu que os resultados obtidos pudessem envolver funções com muitas descontinuidades e muito oscilantes, ou seja, de variação ilimitada. Os resultados novos apresentados aqui estão contidos no artigo [21] que se encontra em fase final de redação e será submetido à publicação em breve.<br>In this work, we introduce concepts of controllability and observability for generalized ordinary differential equations, we present new results on necessary and sufficient conditions for controllability and observability for these equations and we also present an application. Using theorems of correspondence between generalized ordinary differential equations and other differential equations, we translate the results obtained for the particular cases of controllability and observability for measure differential equations and differential equations with impulses. The fact that we work in the framework of generalized ordinary differential equations allows us to obtain results where the functions involved can have many discontinuities and be highly oscillating, that is, of unbounded variation. The new results presented here are contained in the preprint [21] which is under final revision and will soon be submitted for publication.
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Shu, Chang. "Generalized differential-integral quadrature and application to the simulation of incompressible viscous flows including parallel computation." Thesis, University of Glasgow, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.361006.
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Sobes, Vladimir. "Coupled differential and integral data analysis for improved uncertainty quantification of the ⁶³,⁶⁵Cu cross section evaluations." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/87491.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Nuclear Science and Engineering, 2014.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 191-193).<br>A new methodology has been developed that couples differential cross section data evaluation with integral benchmark analysis for improved uncertainty quantification. The new methodology was applied to the two new copper evaluations and resulted in an improved evaluation with smaller covariance data. Copper is a structural material in many nuclear applications, particularly those dealing with criticality safety. The current standard for the resonance evaluation of the two copper isotopes, ⁶³,⁶⁵Cu, has been determined to result in poor modeling performance. Therefore a new resonance evaluation of the two copper isotopes is vital to nuclear criticality safety applications. Performing a new resolved resonance region evaluation for copper has served as a backdrop to this work on developing new techniques for resolved resonance region evaluation. For the new evaluations, experimental cross section measurements have been carried out in the thermal energy region where no experimental data had previously been measured. Along the way, an automated routine was developed to aid with the determination of the quantum angular momentum of newly identified resonances. The impact of differential scattering cross sections with respect to angle was determined in the benchmarking process. The implications of the study of the impact of differential cross sections on criticality suggest a necessity for detailed treatment of the angular distributions during the evaluation process, as well as temperature broadening of the angular distributions for simulation applications. The formalism for temperature broadening of angular distributions has been derived and tested. The new evaluations were compared against the current ENDF/B-VII.1 standard on a set of 23 criticality safety benchmark models and displayed improved performance. In the new methodology developed for coupling of the differential and integral data evaluation, resonance parameters are directly and systematically adjusted based on feedback from integral benchmark experiments. Coupling this feedback directly to the resonance parameters gives the new method the advantage of implicitly adjusting all of the cross sections simultaneously, including the double differential cross sections. Based on integral feedback, the new methodology provides a way of updating the reported covariance of the resolved resonance region to reflect true state of knowledge.<br>by Vladimir Sobes.<br>Ph. D.
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Ito, Yu. "Rough path theory via fractional calculus." 京都大学 (Kyoto University), 2015. http://hdl.handle.net/2433/199445.
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Valente, Maria Serra. "Stability of non-trivial solutions of stochastic differential equations driven by the fractional Brownian motion." Master's thesis, Instituto Superior de Economia e Gestão, 2019. http://hdl.handle.net/10400.5/18993.
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Mestrado em Mathematical Finance<br>O objectivo desta dissertação é o de generalizar um resultado sobre a estabilidade exponencial de soluções triviais de equações diferenciais estocásticas com movimento Browniano fraccionário, desenvolvido por Garrido-Atienza et al., para soluções não-triviais. São apresentadas noções de cálculo fraccionário, assim como a definição e principias propriedades do movimento Browniano fraccionário. De seguida, um framework para equações diferenciais estocásticas com movimento Browniano fraccionário é definido juntamente com resultados de existência e unicidade de soluções. O resultado, original desta dissertação, é aplicado a um modelo Vasicek fraccionário de taxas de juro.<br>This dissertation aims to generalize a result on the exponential stability of trivial solutions of stochastic differential equations driven by the fractional Brownian motion by Garrido-Atienza et al. to non-trivial solutions in the scalar case. Notions on fractional calculus are presented, as well as the definition and main properties of the fractional Brownian motion. Subsequently the framework for SDEs driven by fractional Brownian motion with a pathwise approach is characterized along with some existence and uniqueness results. The result on stability is then applied to the fractional Vasicek model for interest rates.<br>info:eu-repo/semantics/publishedVersion
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Silva, Armando Paulo da. "A modalidade EaD semipresencial e a disciplina de Cálculo Diferencial e Integral /." Bauru, 2017. http://hdl.handle.net/11449/148813.
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Orientador: Wilson Massashiro Yonezawa<br>Banca: Patrícia Sandalo Pereira<br>Banca: João Coelho Neto<br>Banca: Luiz Antonio da Silva Vasconcellos<br>Banca: Andrea Carla Gonçalves Vianna<br>Resumo: O intuito desta pesquisa é investigar as formas que a disciplina de Cálculo Diferencial e Integral 1 na modalidade educação a distância (EaD) semipresencial pode auxiliar alunos em regime de dependência. Esta disciplina nos cursos de Engenharia é um ramo importante da matemática, porém com alta taxa de evasão. Em algumas universidades, chega a 55% dos ingressantes. Uma das ações realizada em uma Universidade Federal brasileira para flexibilizar a vida dos alunos que ficam em dependência nesta disciplina é sua oferta na modalidade EaD semipresencial. A execução do projeto, bem como a realização desta pesquisa só foi possível porque a legislação brasileira permite que os cursos superiores presenciais tenham até 20% de sua carga horária total na modalidade de educação a distância. Na fundamentação teórica abordamos as pesquisas sobre os problemas no ensino de Cálculo Diferencial e Integral 1, a educação a distância e suas possibilidades, as tecnologias na educação a distância, os ambientes virtuais de ensino e aprendizagem; o perfil esperado para os alunos da EaD e a aprendizagem colaborativa. A Análise Textual Discursiva foi a opção metodológica e apresentamos uma nova possibilidade de utilizar esta metodologia associada ao Software de análise qualitativa ATLAS.ti ®. Os resultados obtidos nesta pesquisa dão indícios de que os seus participantes se beneficiaram com esta proposta de utilizar as contribuições e as características da Modalidade EaD semipresencial, bem como os recur... (Resumo completo, clicar acesso eletrônico abaixo)<br>Abstract: The purpose of this research is to investigate the forms that the subject of Differential and Integral Calculus 1 in the blended distance education modality can help students in a dependency regime. in Engineering courses such a subject in an important branch of mathematics, but with a high dropout rate. In some universities, it reaches 55% of the students. One of the actions which has been carried out in a Brazilian Federal University to make life flexible for the students who are dependent on the subject is its offering in the blended distance education modality. The execution of the project, as well as the realization of this research, was only possible because the Brazilian law allows the upper-level courses to have up to 20% of their total workload in the distance education modality. For the theoretical basis it was approached the researches on the problems in the teaching of Differential and Integral the researches on the problems in the teaching of Differential and Integral Calculus 1, the distance education and its possibilities, the technologies in the distance education, the virtual environments of teaching and learning, the expected profile for EaD (Distance Education) students and collaborative learning. The discursive textual analysis was the methodological option and it was presented a new possibility to use such a methodology associated to the qualitative analysis software ATLAD.ti. The results obtained in this research indicate that its participants have been benefited from the proposal to use the contributions and characteristics of the blended distance education modality, as well as the technological resources that have been available or aggregated by the students themselves. Furthermore, communicability as well as the sharing were of a great importance since the collaborative learning became one of the strong factors: In conclusion, it was emphasized that the... (Complete abstract electronic access below)<br>Doutor
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Zangeneh, Bijan Z. "Semilinear stochastic evolution equations." Thesis, University of British Columbia, 1990. http://hdl.handle.net/2429/31117.
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Let H be a separable Hilbert space. Suppose (Ω, F, Ft, P) is a complete stochastic basis with a right continuous filtration and {Wt,t ∈ R} is an H-valued cylindrical Brownian motion with respect to {Ω, F, Ft, P). U(t, s) denotes an almost strong evolution operator generated by a family of unbounded closed linear operators on H. Consider the semilinear stochastic integral equation
[formula omitted]
where
• f is of monotone type, i.e., ft(.) = f(t, w,.) : H → H is semimonotone, demicon-tinuous, uniformly bounded, and for each x ∈ H, ft(x) is a stochastic process which satisfies certain measurability conditions.
• gs(.) is a uniformly-Lipschitz predictable functional with values in the space of Hilbert-Schmidt operators on H.
• Vt is a cadlag adapted process with values in H.
• X₀ is a random variable.
We obtain existence, uniqueness, boundedness of the solution of this equation. We show the solution of this equation changes continuously when one or all of X₀, f, g, and V are varied. We apply this result to find stationary solutions of certain equations, and to study the associated large deviation principles.
Let {Zt,t ∈ R} be an H-valued semimartingale. We prove an Ito-type inequality and a Burkholder-type inequality for stochastic convolution [formula omitted]. These are the main tools for our study of the above stochastic integral equation.<br>Science, Faculty of<br>Mathematics, Department of<br>Graduate
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Misturini, Ricardo. "Movimento browniano, integral de Itô e introdução às equações diferenciais estocásticas." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2010. http://hdl.handle.net/10183/24926.
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Este texto apresenta alguns dos elementos básicos envolvidos em um estudo introdutório das equações diferencias estocásticas. Tais equações modelam problemas a tempo contínuo em que as grandezas de interesse estão sujeitas a certos tipos de perturbações aleatórias. Em nosso estudo, a aleatoriedade nessas equações será representada por um termo que envolve o processo estocástico conhecido como Movimento Browniano. Para um tratamento matematicamente rigoroso dessas equações, faremos uso da Integral Estocástica de Itô. A construção dessa integral é um dos principais objetivos do texto. Depois de desenvolver os conceitos necessários, apresentaremos alguns exemplos e provaremos existência e unicidade de solução para equações diferenciais estocásticas satisfazendo certas hipóteses.<br>This text presents some of the basic elements involved in an introductory study of stochastic differential equations. Such equations describe certain kinds of random perturbations on continuous time models. In our study, the randomness in these equations will be represented by a term involving the stochastic process known as Brownian Motion. For a mathematically rigorous treatment of these equations, we use the Itô Stochastic Integral. The construction of this integral is one of the main goals of the text. After developing the necessary concepts, we present some examples and prove existence and uniqueness of solution of stochastic differential equations satisfying some hypothesis.
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Monteiro, Giselle Antunes. "Generalized linear differential equations in a Banach space: continuous dependence on parameters and applications." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-30032012-105214/.
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The purpose of this work is to investigate continuous dependence on parameters for generalized linear differential equations in a Banach space- valued setting. More precisely, we establish a theorem inspired by the clas- sical continuous dependence result due to Z. Opial. In addition, our second outcome extends, to Banach spaces, the result proved by M. Ashordia in the framework of finite dimensional generalized linear differential equations. Roughly speaking, the continuous dependence derives from assumptions of uniform convergence of the functions in the right-hand side of the equations, together with the uniform boundedness of variation of the linear terms. Fur- thermore, applications of these results to dynamic equations on time scales and also to functional differential equations are proposed. Besides these results on continuous dependence, we complete the theory of abstract Kurzweil-Stieltjes integration so that it is well applicable for our purposes in generalized linear differential equations. In view of this, our contributions are related not only to differential equations but also to the abstract Kurzweil-Stieltjes integration theory itself. The new results presented in this work are contained in the papers [26] and [27], both accepted for publication<br>O objetivo deste trabalho é investigar a dependência contínua de soluções em relação a parâmetros para equações diferenciais lineares generalizadas no contexto de espaços de Banach. Mais precisamente, apresentamos um teo- rema inspirado no resultado clássico de dependência contínua obtido por Z. Opial. Nosso segundo resultado estende, para espaços de Banach, o provado por M. Ashordia no contexto de equações diferenciais lineares gen- eralizadas em dimensão finita. Em linhas gerais, a dependência contínua decorre da convergência uniforme das funções à direita das equações, junta- mente com a limitação uniforme da variação dos termos lineares. No mais, são propostas aplicações desses resultados em equações dinâmicas em escalas temporais e também em equações diferenciais funcionais. Além dos resultados em dependência contínua, completamos à teoria de integração abstrata de Kurzweil-Stieltjes de modo que esta se adeque aos nossos propósitos em equações diferenciais lineares generalizadas. Assim, nossas contribuições dizem respeito não apenas a equações diferenciais, mas também a teoria de integração abstrata de Kurzweil-Stieltjes em si. Os resultados originais apresentados neste trabalho estão contidos nos artigos [26] e [27], ambos aceitos para publicação
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Al-Jawary, Majeed Ahmed Weli. "The radial integration boundary integral and integro-differential equation methods for numerical solution of problems with variable coefficients." Thesis, Brunel University, 2012. http://bura.brunel.ac.uk/handle/2438/6449.
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The boundary element method (BEM) has become a powerful method for the numerical solution of boundary-value problems (BVPs), due to its ability (at least for problems with constant coefficients) of reducing a BVP for a linear partial differential equation (PDE) defined in a domain to an integral equation defined on the boundary, leading to a simplified discretisation process with boundary elements only. On the other hand, the coefficients in the mathematical model of a physical problem typically correspond to the material parameters of the problem. In many physical problems, the governing equation is likely to involve variable coefficients. The application of the BEM to these equations is hampered by the difficulty of finding a fundamental solution. The first part of this thesis will focus on the derivation of the boundary integral equation (BIE) for the Laplace equation, and numerical results are presented for some examples using constant elements. Then, the formulations of the boundary-domain integral or integro-differential equation (BDIE or BDIDE) for heat conduction problems with variable coefficients are presented using a parametrix (Levi function), which is usually available. The second part of this thesis deals with the extension of the BDIE and BDIDE formulations to the treatment of the two-dimensional Helmholtz equation with variable coefficients. Four possible cases are investigated, first of all when both material parameters and wave number are constant, in which case the zero-order Bessel function of the second kind is used as fundamental solution. Moreover, when the material parameters are variable (with constant or variable wave number), a parametrix is adopted to reduce the Helmholtz equation to a BDIE or a BDIDE. Finally, when material parameters are constant (with variable wave number), the standard fundamental solution for the Laplace equation is used in the formulation. In the third part, the radial integration method (RIM) is introduced and discussed in detail. Modifications are introduced to the RIM, particularly the fact that the radial integral is calculated by using a pure boundary-only integral which relaxes the “star-shaped” requirement of the RIM. Then, the RIM is used to convert the domain integrals appearing in both BDIE and BDIDE for heat conduction and Helmholtz equations to equivalent boundary integrals. For domain integrals consisting of known functions the transformation is straightforward, while for domain integrals that include unknown variables the transformation is accomplished with the use of augmented radial basis functions (RBFs). The most attractive feature of the method is that the transformations are very simple and have similar forms for both 2D and 3D problems. Finally, the application of the RIM is discussed for the diffusion equation, in which the parabolic PDE is initially reformulated as a BDIE or a BDIDE and the RIM is used to convert the resulting domain integrals to equivalent boundary integrals. Three cases have been investigated, for homogenous, non-homogeneous and variable coefficient diffusion problems.
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Wilkinson, Joan Christina. "Stability in the numerical treatment of Volterra integral and integro-differential equations with emphasis on finite recurrence relations." Thesis, Open University, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.290222.
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Johan, Filip Rindler Johan Filip. "Lower Semicontinuity and Young Measures for Integral Functionals with Linear Growth." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:c4736fa2-ab51-4cb7-b1d9-cbab0ede274b.
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Baysal, Arzu. "Inverse Problems For Parabolic Equations." Master's thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/12605623/index.pdf.
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In this thesis, we study inverse problems of restoration of the unknown function in a boundary condition, where on the boundary of the domain there is a convective heat exchange with the environment. Besides the temperature of the domain, we seek either the temperature of the environment in Problem I and II, or the coefficient of external boundary heat emission in Problem III and IV. An additional information is given, which is the overdetermination condition, either on the boundary of the domain (in Problem III and IV) or on a time interval (in
Problem I and II). If solution of inverse problem exists, then the temperature can be defined everywhere on the domain at all instants.
The thesis consists of six chapters. In the first chapter, there is the introduction where the definition and applications of inverse problems are given and definition of the four inverse problems, that we will analyze in this thesis, are stated. In the second chapter, some definitions and theorems which we will use to obtain some conclusions about the corresponding direct problem of our four inverse problems are stated, and the conclusions about direct problem are obtained.
In the third, fourth, fifth and sixth chapters we have the analysis of inverse problems I, II, III and IV, respectively.
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Silva, Marielle Aparecida. "Teoria de oscilações para equações diferenciais em medida." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-27092017-140627/.
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Neste trabalho, apresentamos novos critérios para a existência de soluções oscilatórias e não oscilatórias de equações diferenciais funcionais em medida com impulsos, separando-as em duas classes: equações diferenciais funcionais retardadas e equações diferenciais funcionais com argumento avançado. Tratamos das formas integrais destas equações diferenciais usando as integrais de Perron e Perron-Stieltjes. Assim, as funções envolvidas podem ter muitas descontinuidades e/ou podem ser de variação ilimitada.<br>In this work, we present new criteria for the existence of oscillatory and nonoscillatory solutions of measure functional differential equations with impulses, separating them into two classes: delay differential equations and functional differential equations with advanced argument. We deal with the integral forms of the differential equations using the Perron and the Perron-Stieltjes integrals. Thus the functions involved can have many discontinuities and/or they can be of unbounded variation.
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Paranhos, Marcos de Miranda. "Geometria dinâmica e o cálculo diferencial e integral." Pontifícia Universidade Católica de São Paulo, 2009. https://tede2.pucsp.br/handle/handle/11408.
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Previous issue date: 2009-09-23<br>The aim of this work is to present fundamental ideas of differential and
integral calculus and its applications in solving problems. As a teacher of calculus,
I see my trajectory and by exchanging experiences with other professionals, a
common sense about the mechanization of techniques and low student
achievement in relation to the ideas and applications so significant that the
calculation might provide. Reflecting, experiencing and informing me about this
issue, I think much of this problem in a limited way with which we have presented
these ideas in our classes.
Every teacher develops along its trajectory ways to represent the ideas you
want to convey and that is the essence of pedagogical reasoning. In that sense, I
understood that every idea must be transformed to be taught and it was this
aspect that directed this work.
Inspired by the possibility of using software in the teaching of Mathematics
and didactically based on "Dialectic Tool-Object" and "Game Tables" by Régine
Douady, I performed this work that consists of a sequence of activities, divided into
six modules, where basic ideas about derivative, integral and optimization
functions are presented by means of software and GeoGebra Winplot. The strings
are made to functions with one and two variables, can be developed along with the
student or be provided only by the teacher. I hope with this work is expanding the
size that most students have the Calculus and its applications, besides stimulating
the use of technological resources as tools for large capacity in interpreting and
solving problems<br>O objetivo deste trabalho é apresentar idéias fundamentais do Cálculo
Diferencial e Integral e suas aplicações na resolução de problemas. Como
professor de Cálculo, constato pela minha trajetória e pela troca de experiências
com outros profissionais da área, um senso comum a respeito da mecanização de
técnicas e do baixo aproveitamento dos alunos com relação às idéias e
aplicações tão significativas que o Cálculo poderia lhes proporcionar. Refletindo,
experimentando e me informando sobre essa questão, penso que grande parte
dessa problemática está na forma limitada com que temos apresentado essas
idéias em nossas aulas.
Todo professor desenvolve ao longo de sua trajetória formas de
representar as idéias que deseja transmitir e essa é a essência do raciocínio
pedagógico. Nesse sentido, acredito que toda idéia compreendida deve ser
transformada para ser ensinada e foi esse aspecto da questão que direcionou
esse trabalho.
Inspirado pela possibilidade do uso de softwares no ensino do Cálculo e
fundamentado didaticamente na Dialética Ferramenta-Objeto e o Jogo de
Quadros de Régine Douady, realizei este trabalho que consiste de uma
seqüência de atividades, divididas em seis módulos, em que as idéias básicas
sobre derivada, integral e otimização de funções são apresentadas por meio dos
softwares Geogebra e Winplot. As seqüências são feitas para funções com uma e
duas variáveis, podendo ser desenvolvidas juntamente com o aluno ou ser
apenas apresentadas pelo professor. Espero com esse trabalho estar ampliando
a dimensão que a maioria dos estudantes tem do Cálculo e de suas aplicações,
além de estimular o uso de recursos tecnológicos como ferramentas de larga
capacidade na interpretação e resolução de problemas
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Santos, Janice Valia de Los. "Formação básica em engenharia: a articulação das disciplinas pelo cálculo diferencial e integral." Pontifícia Universidade Católica de São Paulo, 2009. https://tede2.pucsp.br/handle/handle/10170.
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Previous issue date: 2009-10-29<br>The present research aimed at studying the articulation of the basic formation
subjects of the Engineering courses through the Differential and Integral
Calculus. Thus, in this study, it was proposed a methodology which could guide
the calculus activities and could be constituted as integrative experiences in the
course. In order to accomplish the goals, it was also necessary to study the
teachers role so as the learning process could be built. For this reason, a field
research with the Differential and Integral Calculus subject, which is part of the
basic formation of the Engineering course of Cruzeiro do Sul University, was
developed. After accomplishing the activities, it was noticed that using
integrative activities such as the ones suggested in the research by the
proposed methodology is viable for the results showed the students have
acquired scientific knowledge, have developed their creativity as well as basic
concepts for problem solving in their specific formation<br>A pesquisa desenvolvida teve por objetivo estudar a articulação das disciplinas
de formação básica nos cursos de engenharia por meio do Cálculo Diferencial
e Integral. Desta forma, propomos, neste trabalho, uma metodologia que
oriente as atividades de cálculo e que se constituam como experiências
integrativas no curso. Para que atinjamos o objetivo, foi necessário estudar,
também a postura do professor para que possa ser construída a aprendizagem
junto ao aluno.
Desse modo, desenvolvemos uma pesquisa de campo com a disciplina Cálculo
Diferencial e Integral, que pertence à formação básica dos cursos de
engenharia, junto aos alunos da Universidade cruzeiro do Sul.
Após a realização das atividades, percebemos que é viável a utilização de
atividades integrativas utilizadas na pesquisa pela metodologia proposta, visto
que o aluno adquiriu conhecimento científico, desenvolveu criatividade como
também conceitos básicos para a resolução de problemas em sua formação
específica
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O'Neale, Dion Robert James. "Preservation of phase space structure in symplectic integration : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Palmerston North, New Zealand." Massey University, 2009. http://hdl.handle.net/10179/1127.
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This thesis concerns the study of geometric numerical integrators and how they preserve phase space structures of Hamiltonian ordinary differential equations. We examine the invariant sets of differential equations and investigate which numerical integrators preserve these sets, and under what conditions. We prove that when periodic orbits of Hamiltonian differential equations are discretized by a symplectic integrator they are preserved in the numerical solution when the integrator step size is not resonant with the frequency of the periodic orbit. The preservation of periodic orbits is the result of a more general theorem which proves preservation of lower dimensional invariant tori from dimension zero (fixed points) up to full dimension (the same as the number of degrees of freedom for the differential equation). The proof involves first embedding the numerical trajectory in a non-autonomous flow and then applying a KAM type theorem for flows to achieve the result. This avoids having to prove a KAM type theorem directly for the symplectic map which is generally difficult to do. We also numerically investigate the break up of periodic orbits when the integrator's step size is resonant with the frequency of the orbit. We study the performance of trigonometric integrators applied to highly oscillatory Hamiltonian differential equations with constant frequency. We show that such integrators may not be as practical as was first thought since they suffer from higher order resonances and can perform poorly at preserving various properties of the di fferential equation. We show that, despite not being intended for such systems, the midpoint rule performs no worse than many of the trigonometric integrators, and indeed, better than some. Lastly, we present a numerical study of a Hamiltonian system consisting of two magnetic moments in an applied magnetic field. We investigate the effect of both the choice of integrator and the choice of coordinate system on the numerical solutions of the system. We show that by a good choice of integrator (in this case the generalised leapfrog method) one can preserve phase space structures of the system without having to resort to a change of coordinates that introduce a coordinate singularity.
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Menezes, Daniel BrandÃo. "O ensino do cÃlculo diferencial e integral na perspectiva da SequÃncia Fedathi: caracterizaÃÃo do comportamento de um bom professor." Universidade Federal do CearÃ, 2017. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=20559.
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nÃo hÃ<br>Os cursos da Ãrea de CiÃncias Exatas, em particular, as licenciaturas em MatemÃtica no CearÃ
possuem ainda muitos desafios com a disciplina CÃlculo Diferencial e Integral, no tocante aos
aspectos metodolÃgicos desenvolvidos nas sessÃes didÃticas que ainda representam alguns
pontos de insatisfaÃÃo, motivo de desistÃncia e reprovaÃÃo por parte dos alunos. Ante esse
problema, esta Tese trata de uma pesquisa expressa na metodologia de pesquisa e ensino
SequÃncia Fedathi (SF) cuja finalidade foi investigar como sua relaÃÃo com a Teoria do
Pensamento MatemÃtico AvanÃado (PMA) pode alicerÃar os processos de ensino de CÃlculo
Diferencial e Integral (CDI) dos alunos de um grupo de estudos da Universidade Estadual Vale
do AcaraÃ, respondendo de que maneira isso contribui para a aprendizagem de conceitos e
procedimentos nessa disciplina, em particular, do conteÃdo de Taxas de VariaÃÃo, e como pode
ser feita a caracterizaÃÃo do docente em amparo nesses conceitos. Como suporte teÃrico
preliminar, foram utilizados estudos da SequÃncia Fedathi, Teoria do Pensamento MatemÃtico
AvanÃado e do recurso computacional (Geogebra) para contribuir com a melhoria do processo
de ensino-aprendizagem. EntÃo, para alcanÃar os objetivos, as sessÃes didÃticas foram
trabalhadas com a SequÃncia Fedathi como metodologia para elaboraÃÃo e conduÃÃo no ensino
do conteÃdo. A pesquisa à de natureza qualitativa, delineada como participante e, alÃm disso,
seguiu o mÃtodo cientÃfico SequÃncia Fedathi, descrito e estudado no decorrer do trabalho;
como campo e sujeitos da investigaÃÃo, o ensaio delineou-se num grupo de estudos criados no
curso de MatemÃtica da Universidade Estadual Vale do Acaraà e os sujeitos foram os alunos
inscritos e o professor que mediou os encontros. No decorrer da experimentaÃÃo, as perguntas
da pesquisa foram respondidas e colhidos resultados que serviram como embasamento para a
classificaÃÃo de bons professores e bons alunos. A metodologia de pesquisa mostrou-se como
um rÃgido mÃtodo a ser promovido cientificamente, direcionando corretamente cada etapa do
experimento e os instrumentos metodolÃgicos necessÃrios para a obtenÃÃo e coleta de dados.
No decorrer das prÃticas e consequente anÃlise, foi possÃvel estabelecer relaÃÃo entre a SF e o
PMA nos testes que foram aplicados com os alunos. AlÃm disso, concluiu-se, o quÃo benÃfico
foi para a compreensÃo dos conteÃdos o uso do recurso computacional, com as questÃes
contextualizadas utilizadas como problemas na vivÃncia da Tomada de PosiÃÃo, ou seja,
contribuiu para demandar compreensÃes para o ensino do CÃlculo Diferencial e Integral, alÃm
de desenvolver avanÃos para as pesquisas em EducaÃÃo MatemÃtica e, acima de tudo, como o
comportamento docente influenciou nas emoÃÃes dos alunos em relaÃÃo à MatemÃtica e na
conduÃÃo da vivÃncia da SequÃncia Fedathi.
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Nguyen, Cu Ngoc. "Stochastic differential equations with long-memory input." Thesis, Queensland University of Technology, 2001.
Find full text
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Одарченко, Наталія Іванівна, Наталия Ивановна Одарченко, Nataliia Ivanivna Odarchenko, С. Мошна та В. В. Власенко. "Узагальнення при розв`язанні задач за допомогою диференціального та інтегрального числення". Thesis, Вид-во СумДУ, 2010. http://essuir.sumdu.edu.ua/handle/123456789/6152.
Full textAbstract:
При розв’язанні практичних задач за допомогою диференціального та інтегрального числення
студентами застосовуються аналогії, узагальнення. Уміння проводити раціональні міркування – важливий
компонент загальної інтелектуальної культури сучасної людини, а його формування є значним резервом
посилення прикладної спрямованості навчання математичних дисциплін.
При цитуванні документа, використовуйте посилання http://essuir.sumdu.edu.ua/handle/123456789/6152
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Беда, Іван Микитович, Иван Никитич Беда, Ivan Mykytovych Beda та А. С. Гатцук. "Побудова графіка функції, заданої параметрично". Thesis, Вид-во СумДУ, 2010. http://essuir.sumdu.edu.ua/handle/123456789/6129.
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LY, KIM HA. "ON TWO APPROACHES FOR PARTIAL DIFFERENTIAL EQUATIONS IN SEVERAL COMPLEX VARIABLES." Doctoral thesis, Università degli studi di Padova, 2014. http://hdl.handle.net/11577/3423534.
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The aim of this thesis is to present influence of notations of ''type" on partial differential equations in several complex variables. The notations of "type" here include the finite and the infinite type in the sense of Hormander, and D'Angelo. In particular, in the first part, under the finite type condition, we will consider the existence and uniqueness of solutions for the initial value problem associated to the heat operator δs+□b on CR manifolds. The finite type m is the critical condition to provide pointwise estimates of the heat kernel via theory of singular integral operators developed by E. Stein and A. Nagel, D.H. Phong and E. Stein. Next, in the second part, we will introduce a new method to investigate the Cauchy-Riemann equations δu = φ. The solutions are constructed via the integral representation method. Moreover, we will show that the new method here is also applied well to the complex Monge-Ampère operator (ddc)n inCn. The main point is that our method can pass some well-known results from the case of finite type to infinite type.<br>Lo scopo di questa tesi è quello di presentare l'influenza di notazioni di " tipo'' su equazioni differenziali alle derivate parziali in più variabili complesse. Le notazioni di "tipo" qui includono il finito e il tipo di infinito, nel senso di Hormander, e D'Angelo. In particolare, nella prima parte, a condizione tipo finito, prenderemo in considerazione l'esistenza e l'unicità delle soluzioni per il problema del valore iniziale associato ai operatore calore δs+□b su varietà CR. Il tipo finito m è la condizione fondamentale per fornire stime puntuali del nucleo del calore attraverso la teoria degli operatori integrali singolari sviluppate da E. Stein e A. Nagel, D.H. Phong e E. Stein. Prossimo, nella seconda parte, introdurremo un nuovo metodo per indagare la equazioni Cauchy-Riemann δu = φ. Le soluzioni sono costruite con via metodo rappresentazione integrale. Inoltre, mostreremo che il nuovo metodo qui viene applicato anche ben al complesso operatore Monge-Ampère (ddc)n inCn. Il punto principale è che il nostro metodo può passare alcuni risultati noti dal caso di tipo finito al tipo di infinito.
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Richit, Andriceli [UNESP]. "Aspectos conceituais e instrumentais do conhecimento da prática do professor de cálculo diferencial e integral no contexto das tecnologias digitais." Universidade Estadual Paulista (UNESP), 2010. http://hdl.handle.net/11449/91111.
Full textAbstract:
Made available in DSpace on 2014-06-11T19:24:54Z (GMT). No. of bitstreams: 0
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richit_a_me_rcla.pdf: 2407245 bytes, checksum: 1a7f37548de362cd3fb478d4d62b3f1b (MD5)<br>A presente investigação tem como objetivo identificar e compreender os aspectos conceituais e instrumentais do conhecimento da prática docente em um curso à distância de formação de professores de Cálculo Diferencial e Integral no contexto das tecnologias digitais. Assim, a pesquisa é conduzida pela seguinte questão diretriz: “Quais são os aspectos conceituais e instrumentais do conhecimento da prática docente do professor de Cálculo Diferencial e Integral no contexto das tecnologias digitais?” Esta pesquisa está pautada nos pressupostos da pesquisa qualitativa, de caráter interpretativo. O cenário para investigação e constituição dos dados foi um Curso de Extensão, totalmente a distância, viabilizado por meio da plataforma de ensino à distância TelEduc, e contou com professores de diferentes estados do Brasil e do Exterior, atuantes no ensino superior e ministrantes da disciplina Cálculo Diferencial e Integral (CDI). No decorrer do Curso, os participantes discutiram textos atinentes ao uso das tecnologias digitais nas práticas de sala de aula, além de refletir sobre as possibilidades didático-pedagógicas de uso das tecnologias digitais nos processos de ensinar e aprender conceitos de CDI. Além disso, os professores também desenvolveram competências para uso do software educacional GeoGebra, o qual subsidiou as discussões relacionadas aos principais conceitos de Cálculo: Funções, Limites, Derivadas e Integrais. Sendo assim, os dados gerados nesta pesquisa são oriundos das Fichas de Inscrição, Ferramentas Perfil, Bate- Papo, Fóruns de Discussão do ambiente TelEduc, Formulário de Avaliação do Curso, Projeto Final e Questionário. Desta forma, a análise dos dados possibilitou o levantamento de algumas categorias as quais foram divididas em dois Eixos: Eixo 1 compreende as categorias referentes aos aspectos conceituais do conhecimento da prática:...<br>This study aim is to identify and understand the conceptual and instrumental aspects of teachers’ knowledge of practice in a distance course involving in-service (practising) Differential and Integral Calculus teachers in the context of digital technologies. This research is conducted by the following research question: What are the conceptual and instrumental aspects of Differential and Integral Calculus teachers’ knowledge of practice in the context of digital technologies? In this sense, the thesis is based on the assumptions of qualitative research, highlighting an interpretative design. The scenario for the investigation and construction of data is an academic distance course, conducted through the online learning platform called TelEduc. The participants are in-service (practising) teachers from several states of Brazil (and from other countries as well). They work in higher education as teachers (instructors) of Differential and Integral Calculus (DIC) courses. During the online distance course, participants discussed articles related to the use of digital technologies in higher education classrooms’ practices, reflecting on didactical-pedagogical possibilities for the use of digital technologies in the process of teaching and learning DIC concepts. In addition, teachers also developed skills to use the educational software called GeoGebra, which worked as an engaging technology for investigations related to Calculus concepts such as Functions, Limits, Derivatives and Integrals. The data were produced from Teachers’ Application Forms, Tools, Profile, Chats, and Discussion Forums of TelEduc platform, and Teachers’ Course Evaluation Form, Final Assignment, and Surveys. The analysis of the data enabled a categorization in two axes. Axis 1 includes the following categories on the conceptual knowledge of practice: Processes of teacher education for use of ICT and ... (Complete abstract click electronic access below)
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Richit, Andriceli. "Aspectos conceituais e instrumentais do conhecimento da prática do professor de cálculo diferencial e integral no contexto das tecnologias digitais /." Rio Claro : [s.n.], 2010. http://hdl.handle.net/11449/91111.
Full textAbstract:
Orientador: Rosana Giaretta Sguerra Miskulin<br>Banca: Miriam Godoy Penteado<br>Banca: Regina Célia Grando<br>Resumo: A presente investigação tem como objetivo identificar e compreender os aspectos conceituais e instrumentais do conhecimento da prática docente em um curso à distância de formação de professores de Cálculo Diferencial e Integral no contexto das tecnologias digitais. Assim, a pesquisa é conduzida pela seguinte questão diretriz: "Quais são os aspectos conceituais e instrumentais do conhecimento da prática docente do professor de Cálculo Diferencial e Integral no contexto das tecnologias digitais?" Esta pesquisa está pautada nos pressupostos da pesquisa qualitativa, de caráter interpretativo. O cenário para investigação e constituição dos dados foi um Curso de Extensão, totalmente a distância, viabilizado por meio da plataforma de ensino à distância TelEduc, e contou com professores de diferentes estados do Brasil e do Exterior, atuantes no ensino superior e ministrantes da disciplina Cálculo Diferencial e Integral (CDI). No decorrer do Curso, os participantes discutiram textos atinentes ao uso das tecnologias digitais nas práticas de sala de aula, além de refletir sobre as possibilidades didático-pedagógicas de uso das tecnologias digitais nos processos de ensinar e aprender conceitos de CDI. Além disso, os professores também desenvolveram competências para uso do software educacional GeoGebra, o qual subsidiou as discussões relacionadas aos principais conceitos de Cálculo: Funções, Limites, Derivadas e Integrais. Sendo assim, os dados gerados nesta pesquisa são oriundos das Fichas de Inscrição, Ferramentas Perfil, Bate- Papo, Fóruns de Discussão do ambiente TelEduc, Formulário de Avaliação do Curso, Projeto Final e Questionário. Desta forma, a análise dos dados possibilitou o levantamento de algumas categorias as quais foram divididas em dois Eixos: Eixo 1 compreende as categorias referentes aos aspectos conceituais do conhecimento da prática: ... (Resumo completo, clicar acesso eletrônico abaixo)<br>Abstract: This study aim is to identify and understand the conceptual and instrumental aspects of teachers' knowledge of practice in a distance course involving in-service (practising) Differential and Integral Calculus teachers in the context of digital technologies. This research is conducted by the following research question: "What are the conceptual and instrumental aspects of Differential and Integral Calculus teachers' knowledge of practice in the context of digital technologies?" In this sense, the thesis is based on the assumptions of qualitative research, highlighting an interpretative design. The scenario for the investigation and construction of data is an academic distance course, conducted through the online learning platform called TelEduc. The participants are in-service (practising) teachers from several states of Brazil (and from other countries as well). They work in higher education as teachers (instructors) of Differential and Integral Calculus (DIC) courses. During the online distance course, participants discussed articles related to the use of digital technologies in higher education classrooms' practices, reflecting on didactical-pedagogical possibilities for the use of digital technologies in the process of teaching and learning DIC concepts. In addition, teachers also developed skills to use the educational software called GeoGebra, which worked as an engaging technology for investigations related to Calculus concepts such as Functions, Limits, Derivatives and Integrals. The data were produced from Teachers' Application Forms, Tools, Profile, Chats, and Discussion Forums of TelEduc platform, and Teachers' Course Evaluation Form, Final Assignment, and Surveys. The analysis of the data enabled a categorization in two axes. Axis 1 includes the following categories on the conceptual knowledge of practice: "Processes of teacher education for use of ICT" and ... (Complete abstract click electronic access below)<br>Mestre
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Floret, Rejane Teixeira de Souza. "Uma proposta para introdução de noções de Cálculo no ensino médio." Universidade do Estado do Rio de Janeiro, 2014. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=7803.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>A presente dissertação tem o objetivo de propor a reinclusão de elementos de Cálculo no ensino médio, pois no passado o Cálculo fazia parte do currículo e foi abolido após uma reforma no ensino da matemática. O trabalho apresenta os resultados de um levantamento estatístico sobre os índices de reprovação na disciplina Cálculo Diferencial e Integral I nos períodos mais recentes da Universidade do Estado do Rio de Janeiro (UERJ) e, também, uma pesquisa quantitativa com quarenta professores de matemática com o objetivo de analisar a viabilidade do projeto e os problemas a serem enfrentados. Por fim, a dissertação conta com uma série de atividades comentadas sobre o tema de limites, que é o foco do trabalho. Tais atividades podem ser incluídas já no 1 ano do ensino médio, paralelamente ao conteúdo de funções, e visam proporcionar aos estudantes o contato com elementos de Cálculo em uma linguagem acessível, e orientar o professor nesta tarefa<br>This dissertation has the objective of proposing the reinclusion of Calculus elements in high school, because in the past Calculus was part of the curriculum and it was abolished after a reform in mathematics teaching. This paper presents the results of a statistical return about the rates of fails in the subject Differential and integral Calculus I in recent terms at Universidade do Estado do Rio de Janeiro (UERJ) and also a quantitative research with forty mathematics teachers, which has the objective of analyzing the viability of the project and the problems to be faced. Finally, the dissertation has a series of discussed activities about the theme of limits, which is the focus of this paper. These activities can be included in the first year of high school, at the same time as functions content. They aim to offer students a contact with Calculus elements in an accessible language and also to orientate the teacher in this task.
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Bahník, Michal. "Stochastické obyčejné diferenciálni rovnice." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2015. http://www.nusl.cz/ntk/nusl-232074.
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Diplomová práce se zabývá problematikou obyčejných stochastických diferenciálních rovnic. Po souhrnu teorie stochastických procesů, zejména tzv. Brownova pohybu je zaveden stochastický Itôův integrál, diferenciál a tzv. Itôova formule. Poté je definováno řešení počáteční úlohy stochastické diferenciální rovnice a uvedena věta o existenci a jednoznačnosti řešení. Pro případ lineární rovnice je odvozen tvar řešení a rovnice pro jeho střední hodnotu a rozptzyl. Závěr tvoří rozbor vybraných rovnic.
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Ferrão, Naíma Soltau. "Mapas conceituais digitais como elemento sinalizador da aprendizagem de cálculo diferencial e integral." Pontifícia Universidade Católica de São Paulo, 2013. https://tede2.pucsp.br/handle/handle/10965.
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Naima Soltau Ferrao.pdf: 5983579 bytes, checksum: 7f051481a31774e2e673e8290f1ba5f2 (MD5)
Previous issue date: 2013-06-07<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>The present study aims to analyze the use of digital concept maps in Higher Education, drawing with CmapTools software, as an indicator of meaning learning in students that finished Differential and Integral Calculus, concerning derivative as mathematical object. This is a qualitative approach, situated in the area of mathematics education, based on Ausubel's Theory of Meaningful Learning and on technique of Novak's Concept Mapping. As data acquisition instruments, use of classroom observations, mixed questionnaire, brainstorming and digital conceptual mapping, made by an undergraduate physics course. To analyze we defined four aspects to be observed in the maps constructed by students: (i) validity of propositions formed with concepts, (ii) hierarchization, (iii) cross-links between the propositions, and (vi) the presence of applications. The identification of these elements, taken as reference to analyze the maps, allowed the collection of information about how each student has structured and correlated the set of concepts learned on the derivative of a function along their course. Based on the results, we have identified in the digital conceptual maps effective tools to evaluate the students in terms of meaningful learning about specific contents of Differential and Integral Calculus by the hierarchy of concepts, progressive differentiation and integrative reconciliation as defined in the Theory of Meaningful Learning<br>O presente estudo tem por objetivo analisar o uso de mapas conceituais digitais no Ensino Superior, construídos com o software CmapTools, como elemento sinalizador da aprendizagem significativa de estudantes que já cursaram Cálculo Diferencial e Integral em relação ao objeto matemático derivada. Trata-se de uma abordagem qualitativa, situada no campo da Educação Matemática, fundamentada na Teoria da Aprendizagem Significativa de Ausubel e na técnica de Mapeamento Conceitual de Novak. Como instrumentos de aquisição de dados, utilizamos observações de sala de aula, questionário misto, brainstorming e mapas conceituais digitais, produzidos por licenciandos de um curso de Física. Para a análise definimos quatro aspectos a serem observados nos mapas construídos pelos estudantes: (i) validade das proposições formadas com os conceitos; (ii) hierarquização; (iii) ligações cruzadas entre as proposições; e (vi) presença de aplicações. A identificação desses elementos, que tomamos como referência para analisar os mapas, possibilitou a obtenção de informações a respeito do modo como cada estudante estruturou e correlacionou o conjunto de conceitos aprendidos sobre a derivada de uma função ao longo de seu curso. Com base nos resultados obtidos, identificamos nos mapas conceituais digitais instrumentos eficazes para avaliar a aprendizagem significativa dos estudantes em conteúdos específicos do Cálculo Diferencial e Integral a partir dos conceitos de hierarquização, diferenciação progressiva e reconciliação integrativa definidos na Teoria da Aprendizagem Significativa
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Sinicyna, Natalja. "Paprastųjų diferencilainių lygčių integravimo metodų konstravimas remiantis silpnąja Galiorkino formuluote." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2008. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2008~D_20080811_151442-11770.
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Remiantis silpnąja Galiorkino formuluote darbe sukonstruoti trys paprastųjų diferencialinių lygčių integravimo metodai. Tyrinėtas metodų konvergavimas remiantis skaitiniais integravimo rezultatais, bei metodų tikslumas lyginant rezultatus su tiksliuoju sprendinių ir kitų integratorių rezultatais.<br>Three integrators of ordinary diferential equations based on Galiorkin's weak formulation were constructed in this work. The precision of ontegrators is evaluated numerically,by comparing the result with exact first integral and the solution got using Runge-Kutto method.