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.

“This is a friendly and well-written introduction to a topic of great interest in modern analysis.” (M. Kunzinger, Monatshefte für 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)

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