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Books on the topic 'Numerical differentiation'

Author: Grafiati
Published: 4 June 2021
Last updated: 30 July 2024

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1

Owolabi, Kolade M., and Abdon Atangana. Numerical Methods for Fractional Differentiation. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-15-0098-5.

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2

Bitterlich, Walter. Numerische Methoden für technische Berechnungen. Aachen: Shaker Verlag, 2004.

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3

Kai, Diethelm, Luchko Yury, and NASA Glenn Research Center, eds. Fractional-order viscoelasticity (FOV): Constitutive development using the fractional calculus : first annual report. [Cleveland, Ohio]: National Aeronautics and Space Administration, Glenn Research Center, 2002.

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4

Kai, Diethelm, Luchko Yury, and NASA Glenn Research Center, eds. Fractional-order viscoelasticity (FOV): Constitutive development using the fractional calculus : first annual report. [Cleveland, Ohio]: National Aeronautics and Space Administration, Glenn Research Center, 2002.

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5

Freed, Alan. Fractional-order viscoelasticity (FOV): Constitutive development using the fractional calculus : first annual report. [Cleveland, Ohio]: National Aeronautics and Space Administration, Glenn Research Center, 2002.

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6

Skeel, Robert D. Global error estimation and the backward differentiation formulas. Urbana, IL (1304 W. Springfield Ave., Urbana 61801): Dept. of Computer Science, University of Illinois at Urbana-Champaign, 1986.

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7

Treanţă, Savin. Variational analysis with applications in optimisation and control. Newcastle upon Tyne, UK: Cambridge Scholars Publishing, 2019.

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8

Verma, Arun. On the efficient methods to solve ODEs and BVPs using automatic differentiation. Ithaca, N.Y: Cornell Theory Center, Cornell University, 1996.

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9

Glovackaya, Alevtina. Computational model. ru: INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1013723.

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The textbook covers the basics of classical numerical methods of computational mathematics used for solving linear and nonlinear equations and systems; interpolation and approximation of functions; numerical integration and differentiation; solutions of ordinary differential equations by methods of one-dimensional and multidimensional optimization. Meets the requirements of the Federal state educational standards of higher education of the latest generation. It is intended for students of higher educational institutions studying in the discipline "Numerical methods".
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10

Dolgov, I., Mihail Volovik, and Andrey Mahnovskiy. Thermographic signs of certain diseases of the respiratory system (acute sinusitis, pneumonia) Thermography Atlas. ru: INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/textbook_61b1ab7de6b1f9.69203696.

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The present issue focuses on the practice of medical thermal imaging in patients with paranasal sinusitis and pneumonia. The description of thermograms is based on a quantitative analysis of temperature gradients and trends in temperature of different body regions (Projection «head front» for paranasal sinusitis, «breast front» and «back», in a defined layout formed in «cloud» thermograms analysis program "Tvision" of «Dignosis», Russia) with values of thermographic markers that demonstrated their differentiating capabilities when compared with reference methods. Thus, the thermographic conclusion is formed not simply by thermal phenomenon «hot-cold», but on the basis of numerical values of markers, which indicate hypothetical nosological diagnosis and significantly simplifies the algorithm for those physicians who use this method as an additional. The publication is intended for doctors of any speciality who, in their daily clinical practice, treat the patients with suspicions disease of respiratory system
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11

Benton, D. James. Numerical Calculus: Differentiation and Integration. Independently Published, 2018.

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12

Owolabi, Kolade M., and Abdon Atangana. Numerical Methods for Fractional Differentiation. Springer, 2019.

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13

Owolabi, Kolade M., and Abdon Atangana. Numerical Methods for Fractional Differentiation. Springer Singapore Pte. Limited, 2020.

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14

Numerical Methods for Fractional Differentiation. Springer Nature, 2019.

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15

Bolton, W. Differentiation and Integration (Mathematics for Engineers). Addison Wesley Publishing Company, 1996.

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16

Bolton, W. Differentiation and Integration. CRC Press LLC, 2016.

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17

Bolton, W. Differentiation and Integration. CRC Press LLC, 2016.

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18

Bolton, W. Differentiation and Integration. CRC Press LLC, 2016.

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19

Bolton, W. Differentiation and Integration. CRC Press LLC, 2016.

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20

Differentiation and Integration. Taylor & Francis Group, 2017.

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21

Numerical analysis: An introduction. Boston: Birkhäuser, 1997.

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22

Mordukhovich, Boris S. Variational Analysis and Generalized Differentiation II: Applications. Springer, 2010.

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23

Fractional-order viscoelasticity (FOV): Constitutive development using the fractional calculus : first annual report. [Cleveland, Ohio]: National Aeronautics and Space Administration, Glenn Research Center, 2002.

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24

Mordukhovich, Boris S. Variational Analysis and Generalized Differentiation I. Springer, 2009.

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25

Forth, Shaun, Paul Hovland, and Eric Phipps. Recent Advances in Algorithmic Differentiation. Springer, 2012.

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26

Forth, Shaun, Paul Hovland, Eric Phipps, Jean Utke, and Andrea Walther. Recent Advances in Algorithmic Differentiation. Springer, 2014.

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27

Variational Analysis and Generalized Differentiation I: Basic Theory. Springer London, Limited, 2006.

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28

Mordukhovich, Boris S. Variational Analysis and Generalized Differentiation I: Basic Theory. Springer, 2010.

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29

Mordukhovich, Boris S. Variational Analysis and Generalized Differentiation II. Springer, 2009.

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30

Variational Analysis and Generalized Differentiation II: Applications. Springer London, Limited, 2006.

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31

Mordukhovich, Boris S. Variational Analysis and Generalized Differentiation I: Basic Theory (Grundlehren der mathematischen Wissenschaften). Springer, 2005.

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32

Mordukhovich, Boris S. Variational Analysis and Generalized Differentiation II: Applications (Grundlehren der mathematischen Wissenschaften). Springer, 2005.

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33

Advances in Automatic Differentiation (Lecture Notes in Computational Science and Engineering Book 64). Springer, 2008.

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34

Automatic Differentiation: Applications, Theory, and Implementations: Applications, Theory and Implementations (Lecture Notes in Computational Science and Engineering Book 50). Springer, 2006.

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35

Topolnik, Michaela, and Julia Schmidmayer. Evaluation of Austrian Research and Technology Policies. A Summary of Austrian Evaluation Studies from 2003 to 2007. Edited by Klaus Zinöcker and Wolfgang Neurath. Austrian Council for Research and Technology Development, 2007. http://dx.doi.org/10.22163/fteval.2007.560.

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Over the past decade, the number of public interventions in R&D has risen considerably; the growth has not just been in a numerical sense – about 60 different programmes were launched during the last years – but also in terms of differentiation. These interventions address structural flaccidities as well as market and system failures, basic instruments were strengthened and funding gaps closed. Facing this rise of complexity, policy makers and stakeholders are calling for more evidence, for more accountability and for more impact measurement – a necessary and desirable call for a better, evidence based policy. Evaluation is the key instrument for providing such information, independent assessments and recommendations on how to improve. This book gives an overview about evaluations compiled in the field of research and technology policy in Austria over the past few years. The editors’ motivation was to contribute to the evaluation culture in our country by making recent evaluation reports accessible and transparent.
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36

Bartkowicz, Leszek. Tekstura drzewostanów naturalnych w polskich parkach narodowych na tle teorii dynamiki lasu. Publishing House of the University of Agriculture in Krakow, 2021. http://dx.doi.org/10.15576/978-83-66602-20-5.

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The aim of the study was to compare a patch-mosaic pattern in the old-growth forest stands developed in various climate and soil conditions occurring in different regions of Poland. Based on the assumption, that the patch-mosaic pattern in the forest reflect the dynamic processes taking place in it, and that each type of forest ecosystem is characterized by a specific regime of natural disturbances, the following hypotheses were formulated: (i) the patches with a complex structure in stands composed of latesuccessional, shade-tolerant tree species are more common than those composed of early-successional, light-demanding ones, (ii) the patch-mosaic pattern is more heterogeneous in optimal forest site conditions than in extreme ones, (iii) in similar site conditions differentiation of the stand structure in distinguished patches is determined by the successional status of the tree species forming a given patch, (iv) the successional trends leading to changes of species composition foster diversification of the patch structure, (v) differentiation of the stand structure is negatively related to their local basal area, especially in patches with a high level of its accumulation. Among the best-preserved old-growth forest remaining under strict protection in the Polish national parks, nineteen research plots of around 10 ha each were selected. In each plot, a grid (50 × 50 m) of circular sample subplots (with radius 12,62 m) was established. In the sample subplots, species and diameter at breast height of living trees (dbh ≥ 7 cm) were determined. Subsequently, for each sample subplot, several numerical indices were calculated: local basal area (G), dbh structure differentiation index (STR), climax index (CL) and successional index (MS). Statistical tests of Kruskal- Wallis, Levene and Generalized Additive Models (GAM) were used to verify the hypotheses. All examined forests were characterized by a large diversity of stand structure. A particularly high frequency of highly differentiated patches (STR > 0,6) was recorded in the alder swamp forest. The patch mosaic in the examined plots was different – apart from the stands with a strongly pronounced mosaic character (especially subalpine spruce forests), there were also stands with high spatial homogeneity (mainly fir forests). The stand structure in the distinguished patches was generally poorly related to the other studied features. Consequently, all hypotheses were rejected. These results indicate a very complex, mixed pattern of forest natural dynamics regardless of site conditions. In beech forests and lowland multi-species deciduous forests, small-scale disturbances of the gap dynamics type dominate, which are overlapped with less frequent medium-scale disturbances. In more difficult site conditions, large-scale catastrophic disturbances, which occasionally appear in communities formed under the influence of gap dynamics (mainly spruce forests) or cohort dynamics (mainly pine forests), gain importance.
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37

Evtushenko, Yury, Vladimir Zubov, and Anna Albu. Optimal control of thermal processes with phase transitions. LCC MAKS Press, 2021. http://dx.doi.org/10.29003/m2449.978-5-317-06677-2.

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The optimal control of the metal solidification process in casting is considered. Quality of the obtained detail greatly depends on how the crystallization process proceeds. It is known that to obtain a model of a good quality it is desirable that the phase interface would be as close as possible to a plane and that the speed of its motion would be close to prescribed. The proposed mathematical model of the crystallization process is based on a three dimensional two phase initial-boundary value problem of the Stefan type. The velocity of the mold in the furnace is used as the control. The control satisfying the technological requirements is determined by solving the posed optimal control problem. The optimal control problem was solved numerically using gradient optimization methods. The effective method is proposed for calculation of the cost functional gradient. It is based on the fast automatic differentiation technique and produces the exact gradient for the chosen approximation of the optimal control problem.
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