It is written with a deep pedagogical attention …. "I find this book a very useful supplementary reading for undergraduate students and a good teaching aid for lecturers of topics involving traditional variational calculus (as e. The student can thus learn the main results in each chapter and return as needed to the proofs for a deeper understanding. The technical details for many of the results can be skipped on the initial reading. More importantly, the book is written on two levels. In addition, topics such as Hamilton’s Principle, eigenvalue approximations, conservation laws, and nonholonomic constraints in mechanics are discussed. For the reader interested mainly in techniques and applications of the calculus of variations, I leavened the book with numerous examples mostly from physics. I have made “passive use” of functional analysis (in particular normed vector spaces) to place certain results in context and reassure the mathematician that a suitable framework is available for a more rigorous study. I have paused at times to develop the proofs of some of these results, and discuss briefly various topics not normally found in an introductory book on this subject such as the existence and uniqueness of solutions to boundary-value problems, the inverse problem, and Morse theory. The reader interested primarily in mathematics will find results of interest in geometry and differential equations. This book is an introduction to the calculus of variations for mathematicians and scientists. Much of the mathematics underlying control theory, for instance, can be regarded as part of the calculus of variations. More recently, the calculus of variations has found applications in other fields such as economics and electrical engineering. Bruce van Brunt is Senior Lecturer at Massey University, New Zealand.The calculus of variations has a long history of interaction with other branches of mathematics such as geometry and differential equations, and with physics, particularly mechanics. The book can be used as a textbook for a one semester course on the calculus of variations, or as a book to supplement a course on applied mathematics or classical mechanics. The text contains numerous examples to illustrate key concepts along with problems to help the student consolidate the material. In addition, more advanced topics such as the inverse problem, eigenvalue problems, separability conditions for the Hamilton-Jacobi equation, and Noether's theorem are discussed. The fixed endpoint problem and problems with constraints are discussed in detail. The book focuses on variational problems that involve one independent variable. The mathematical background assumed of the reader is a course in multivariable calculus, and some familiarity with the elements of real analysis and ordinary differential equations. This book is an introductory account of the calculus of variations suitable for advanced undergraduate and graduate students of mathematics, physics, or engineering. The calculus of variations has a long history of interaction with other branches of mathematics, such as geometry and differential equations, and with physics, particularly mechanics. Preface - Introduction - The First Variation - Some Generalizations - Isoperimetric Problems - Applications to Eigenvalue Problems - Holonomic and Nonholonomic Constraints - Problems with Variable Endpoints - The Hamiltonian Formulation - Noether's Theorem - The Second Variation - Appendix A: Some Results from Analysis and Differential Equations - Appendix B: Function Spaces - References - Index Includes bibliographical references (pages 283-285) and index
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