Texts in Applied Mathematics

Calculus of Variations

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

Authors: Kielhöfer, Hansjörg

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  • Provides examples and exercises with solutions, allowing for self-studyIncludes numerous figures to help aid the reader
  • Includes advances problems and proofs in the appendix
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  • ISBN 978-3-319-71123-2
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About this Textbook

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. 


About the authors

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

Reviews

“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)

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Buy this book

eBook n/a
  • ISBN 978-3-319-71123-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
Hardcover n/a
  • ISBN 978-3-319-71122-5
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Calculus of Variations
Book Subtitle
An Introduction to the One-Dimensional Theory with Examples and Exercises
Authors
Series Title
Texts in Applied Mathematics
Series Volume
67
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-71123-2
DOI
10.1007/978-3-319-71123-2
Hardcover ISBN
978-3-319-71122-5
Series ISSN
0939-2475
Edition Number
1
Number of Pages
XVI, 227
Number of Illustrations
59 b/w illustrations
Topics