Calculus of Variations: An Introduction to the One-Dimensional Theory with Examples and Exercises

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Hansjörg Kielhöfer

Calculus of Variations

An Introduction to the One-Dimensional Theory with Examples and Exercises

Hansjörg Kielhöfer

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English

Springer International Publishing AG
06 June 2019

Calculus of variations; Optimisation

Series: Texts in Applied Mathematics

This clear and concise textbook provides a rigorous introduction to the calculus of variations, depending on functions of one variable and their first derivatives. It is based on a translation of a German edition of the book Variationsrechnung (Vieweg+Teubner Verlag, 2010), translated and updated by the author himself. Topics include: the Euler-Lagrange equation for one-dimensional variational problems, with and without constraints, as well as an introduction to the direct methods. The book targets students who have a solid background in calculus and linear algebra, not necessarily in functional analysis. Some advanced mathematical tools, possibly not familiar to the reader, are given along with proofs in the appendix. Numerous figures, advanced problems and proofs, examples, and exercises with solutions accompany the book, making it suitable for self-study.

The book will be particularly useful for beginning graduate students from the physical,engineering, and mathematical sciences with a rigorous theoretical background.

By: Hansjörg Kielhöfer
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: Softcover reprint of the original 1st ed. 2018
Volume: 67
Dimensions: Height: 235mm, Width: 155mm,
Weight: 454g
ISBN: 9783319890388
ISBN 10: 3319890387
Series: Texts in Applied Mathematics
Pages: 227
Publication Date: 06 June 2019
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Introduction.- The Euler-Language Equation.- Variational Problems with Constraints.- Direct Methods in the Calculus of Variations.- Appendix.- Solutions of the Exercises.

Hansjörg Kielhöfer is a Professor at the University of Augsburg, Germany.

Reviews for Calculus of Variations: An Introduction to the One-Dimensional Theory with Examples and Exercises

This is a friendly and well-written introduction to a topic of great interest in modern analysis. (M. Kunzinger, Monatshefte fur Mathematik, Vol. 193 (4), 2020) This book is an introductory textbook ... . The textbook is appropriate for students with solid background in calculus and linear algebra but without preliminary knowledge of variational analysis. ... this textbook is useful for beginning graduate students in physical, engineering, and mathematical sciences having a rigorous theoretical background. (Mihail Voicu, zbMATH 1390.49001, 2018)