Overview
- Provides examples and exercises with solutions, allowing for self-study
- Includes numerous figures to help aid the reader
- Includes advances problems and proofs in the appendix
Part of the book series: Texts in Applied Mathematics (TAM, volume 67)
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Table of contents (3 chapters)
Keywords
About this book
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.
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)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Calculus of Variations
Book Subtitle: An Introduction to the One-Dimensional Theory with Examples and Exercises
Authors: Hansjörg Kielhöfer
Series Title: Texts in Applied Mathematics
DOI: https://doi.org/10.1007/978-3-319-71123-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2018
Hardcover ISBN: 978-3-319-71122-5Published: 08 February 2018
Softcover ISBN: 978-3-319-89038-8Published: 06 June 2019
eBook ISBN: 978-3-319-71123-2Published: 25 January 2018
Series ISSN: 0939-2475
Series E-ISSN: 2196-9949
Edition Number: 1
Number of Pages: XVI, 227
Number of Illustrations: 59 b/w illustrations
Topics: Calculus of Variations and Optimal Control; Optimization