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Books on the topic 'Calculus of variations. Multiple integrals'

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Published: 4 June 2021
Last updated: 8 February 2022

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1

service), SpringerLink (Online, ed. Multiple Integrals in the Calculus of Variations. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg, 2008.

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2

Giaquinta, Mariano. Cartesian Currents in the Calculus of Variations II: Variational Integrals. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998.

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3

Spandagos, Vaggelēs. Oloklērōtikos logismos: Theōria-methodologia, 1600 lymenes askēseis. Athēna: Aithra, 1988.

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4

1947-, Guzman Alberto. Derivatives and integrals of multivariable functions. Boston, MA: Birkhauser, 2003.

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5

Muldowney, P. A modern theory of random variation: With applications in stochastic calculus, financial mathematics, and Feynman integration. Hoboken, N.J: Wiley, 2012.

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6

Muldowney, P. A modern theory of random variation: With applications in stochastic calculus, financial mathematics, and Feynman integration. Hoboken, N.J: Wiley, 2012.

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7

Zhukova, Galina, and Margarita Rushaylo. The mathematical analysis. Volume 2. ru: INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1072172.

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The aim of the tutorial is to help students to master the basic concepts and methods of the study of calculus. In volume 2 we study analytic geometry in space; differential calculus of functions of several variables; local, conditional, global extrema of functions of several variables; multiple, curvilinear and surface integrals; elements of field theory; numerical, power series, Taylor series and Maclaurin, and Fourier series; applications to the analysis and solution of applied problems. Great attention is paid to comparison of these methods, the proper choice of study design tasks, analyze complex situations that arise in the study of these branches of mathematical analysis. For self-training and quality control knowledge given test questions. For teachers, students and postgraduate students studying mathematical analysis.
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Zhukova, Galina, and Margarita Rushaylo. Mathematical analysis in examples and tasks. Part 2. ru: INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1072162.

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The purpose of the textbook is to help students to master basic concepts and research methods used in mathematical analysis. In part 2 of the proposed cycle of workshops on the following topics: analytic geometry in space; differential calculus of functions of several variables; local, conditional, global extrema of functions of several variables; multiple, curvilinear and surface integrals; elements of field theory; numerical, power series, Fourier series; applications to the analysis and solution of applied problems. These topics are studied in universities, usually in the second semester in the discipline "Mathematical analysis" or the course "Higher mathematics", "Mathematics". For the development of each topic the necessary theoretical and background material, reviewed a large number of examples with detailed analysis and solutions, the options for independent work. For self-training and quality control of the acquired knowledge in each section designed exercises and tasks with answers and guidance. It is recommended that teachers, students and graduate students studying advanced mathematics.
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9

Giaquinta, Mariano. Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105. Princeton University Press, 2016.

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10

Dedecker, Paul. Foundations of the Multiple Integrals Calculus of Variations: The Hamilton-Jacobi-E. Cartan Approach (Hadronic Press Monographs in Mathematics, No 2). Hadronic Press, 1985.

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11

Chapter 13: Multiple Integrals From Multivariable Calculus 3rd Edition. I.T.P. Custom Publishing, 1997.

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12

Morse, Marston. Global Variational Analysis: Weierstrass Integrals on a Riemannian Manifold. Princeton University Press, 2015.

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13

Global Variational Analysis: Weierstrass Integrals on a Riemannian Manifold. Princeton University Press, 2016.

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14

Morse, Marston. Global Variational Analysis: Weierstrass Integrals on a Riemannian Manifold. Princeton University Press, 2015.

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15

Morse, Marston. Global Variational Analysis: Weierstrass Integrals on a Riemannian Manifold. Princeton University Press, 2015.

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16

Muldowney, Patrick. Modern Theory of Random Variation: With Applications in Stochastic Calculus, Financial Mathematics, and Feynman Integration. Wiley & Sons, Incorporated, John, 2013.

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17

Muldowney, Patrick. Modern Theory of Random Variation: With Applications in Stochastic Calculus, Financial Mathematics, and Feynman Integration. Wiley & Sons, Incorporated, John, 2012.

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18

Muldowney, Patrick. Modern Theory of Random Variation: With Applications in Stochastic Calculus, Financial Mathematics, and Feynman Integration. Wiley & Sons, Incorporated, John, 2013.

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19

Johnson, Claes, Donald Estep, and Kenneth Eriksson. Applied Mathematics Body and Soul, Volume 2: Integrals and Geometry in Rn. Springer, 2003.

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20

Mann, Peter. Differential Equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0035.

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This chapter presents the general formulation of the calculus of variations as applied to mechanics, relativity and field theories. The calculus of variations is a common mathematical technique used throughout classical mechanics. First developed by Euler to determine the shortest paths between fixed points along a surface, it was applied by Lagrange to mechanical problems in analytical mechanics. The variational problems in the chapter have been simplified for ease of understanding upon first introduction, in order to give a general mathematical framework. This chapter takes a relaxed approach to explain how the Euler–Lagrange equation is derived using this method. It also discusses first integrals. The chapter closes by defining the functional derivative, which is used in classical field theory.
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