Calculus of Variations

AvBruce van Brunt

Inbunden, Engelska, 2003

Del i serien Universitext

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Beskrivning

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. More recently, the calculus of variations has found applications in other fields such as economics and electrical engineering. Much of the mathematics underlying control theory, for instance, can be regarded as part of the calculus of variations.This book is an introductory account of the calculus of variations suitable for advanced undergraduate and graduate students of mathematics, physics, or engineering. 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. The book focuses on variational problems that involve one independent variable. The fixed endpoint problem and problems with constraints are discussed in detail. 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 text contains numerous examples to illustrate key concepts along with problems to help the student consolidate the material. 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. Bruce van Brunt is Senior Lecturer at Massey University, New Zealand. He is the author of The Lebesgue-Stieltjes Integral, with Michael Carter, and has been teaching the calculus of variations to undergraduate and graduate students for several years.

Produktinformation

Utgivningsdatum:2003-09-12
Mått:155 x 235 x 23 mm
Vikt:602 g
Format:Inbunden
Språk:Engelska
Serie:Universitext
Antal sidor:292
Upplaga:2004
Förlag:Springer-Verlag New York Inc.
ISBN:9780387402475

Utforska kategorier

Läromedel: matematik inom Läromedel
Matematik inom Naturvetenskap och teknik

Recensioner i media

From the reviews: "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. g. mathematical physics). It is written with a deep pedagogical attention ... . According to my classroom experience with undergraduate physicists, the presentation of the examples in the book may be very helpful ... . It can also be appreciated that the author tries to present the results showing motivation and heuristical ideas for each crucial theorem." (L. L. Stacho, Acta Scientiarum Mathematicarum, Vol. 71, 2005) "The calculus of variations is one of the latest books in Springer's Universitext series. As such, it is intended to be a non-intimidating, introductory text ... . I enjoyed reading The calculus of variations. Brunt writes in a lucid, engaging style ... . can be used in a variety of undergraduate and beginning postgraduate courses. There is sufficient meat, both in the range of examples treated and in the development of the underlying mathematics ... that most of its intended audience will just be grateful ... ." (Nick Lord, The Mathematical Gazette, Vol. 89 (516), 2005) "The author describes this book as suitable for a one semester course for advance undergraduate students in math, physics or engineering. ... Accordingly, I chose to use this book as my primary reference for presenting the course ... . From my perspective, the book was pitched at a good level for the students I was teaching ... . Overall I enjoyed this book, and would unreservedly recommend it ... . The book really brought home to me the elegance of this subject ... ." (Matthew Roughan, The Australian Mathematical Society Gazette, Vol. 32 (1), 2005) "This text provides a friendly and ... elementary introduction to the calculus of variations. ... The emphasis is on well-chosen examples used to obtain the necessary heuristics for developing the theoretical background. ... Due to its concrete and well-organized approach, the book constitutes a valuable addition to the text book literature on the calculus of variations." (M. Kunzinger, Monatshefte fur Mathematik, Vol. 147 (1), 2006) "Bruce van Brunt shows his love of the subject in his new book The Calculus of Variations ... . Brunt gives us a nice historical introduction to the calculus of variations. ... The exercises have ... been polished and sharpened in the classroom. ... this is a well crafted, reasonably priced book that would be a fine introduction to a fascinating subject that not enough mathematicians know about." (Ed Sandifer, MathDL, May, 2004) "Professor van Brunt's Calculus of Variations is an easily understandable introductory account of the (classical) Calculus of Variations ... . This text is aimed at the beginning graduate and advanced graduate students of mathematics and physics as well as engineering. ... The references contain 75 items ... ." (R. Thiele, Zeitschrift fur Analysis und ihre Anwendungen, Vol. 24 (4), 2005)

Innehållsförteckning

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.