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The Calculus of Variations

2006-04-18 Mathematics
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Release : 2006-04-18
Genre : Mathematics
Kind : eBook
Book Rating : 979/5 ( reviews)

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Book Synopsis The Calculus of Variations by : Bruce van Brunt

Download or read book The Calculus of Variations written by Bruce van Brunt. This book was released on 2006-04-18. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for advanced undergraduate and graduate students of mathematics, physics, or engineering, this introduction to the calculus of variations focuses on variational problems involving one independent variable. It also discusses more advanced topics such as the inverse problem, eigenvalue problems, and Noether’s theorem. The text includes numerous examples along with problems to help students consolidate the material.

Calculus of Variations

2012-04-26 Mathematics
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Release : 2012-04-26
Genre : Mathematics
Kind : eBook
Book Rating : 012/5 ( reviews)

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Book Synopsis Calculus of Variations by : I. M. Gelfand

Download or read book Calculus of Variations written by I. M. Gelfand. This book was released on 2012-04-26. Available in PDF, EPUB and Kindle. Book excerpt: Fresh, lively text serves as a modern introduction to the subject, with applications to the mechanics of systems with a finite number of degrees of freedom. Ideal for math and physics students.

A First Course in the Calculus of Variations

2014-10-06 Mathematics
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Release : 2014-10-06
Genre : Mathematics
Kind : eBook
Book Rating : 953/5 ( reviews)

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Book Synopsis A First Course in the Calculus of Variations by : Mark Kot

Download or read book A First Course in the Calculus of Variations written by Mark Kot. This book was released on 2014-10-06. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for a first course in the calculus of variations, at the senior or beginning graduate level. The reader will learn methods for finding functions that maximize or minimize integrals. The text lays out important necessary and sufficient conditions for extrema in historical order, and it illustrates these conditions with numerous worked-out examples from mechanics, optics, geometry, and other fields. The exposition starts with simple integrals containing a single independent variable, a single dependent variable, and a single derivative, subject to weak variations, but steadily moves on to more advanced topics, including multivariate problems, constrained extrema, homogeneous problems, problems with variable endpoints, broken extremals, strong variations, and sufficiency conditions. Numerous line drawings clarify the mathematics. Each chapter ends with recommended readings that introduce the student to the relevant scientific literature and with exercises that consolidate understanding.

Calculus of Variations

2018-06-20 Mathematics
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Release : 2018-06-20
Genre : Mathematics
Kind : eBook
Book Rating : 371/5 ( reviews)

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Book Synopsis Calculus of Variations by : Filip Rindler

Download or read book Calculus of Variations written by Filip Rindler. This book was released on 2018-06-20. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a comprehensive introduction to the classical and modern calculus of variations, serving as a useful reference to advanced undergraduate and graduate students as well as researchers in the field. Starting from ten motivational examples, the book begins with the most important aspects of the classical theory, including the Direct Method, the Euler-Lagrange equation, Lagrange multipliers, Noether’s Theorem and some regularity theory. Based on the efficient Young measure approach, the author then discusses the vectorial theory of integral functionals, including quasiconvexity, polyconvexity, and relaxation. In the second part, more recent material such as rigidity in differential inclusions, microstructure, convex integration, singularities in measures, functionals defined on functions of bounded variation (BV), and Γ-convergence for phase transitions and homogenization are explored. While predominantly designed as a textbook for lecture courses on the calculus of variations, this book can also serve as the basis for a reading seminar or as a companion for self-study. The reader is assumed to be familiar with basic vector analysis, functional analysis, Sobolev spaces, and measure theory, though most of the preliminaries are also recalled in the appendix.

Modern Methods in the Calculus of Variations

2007-08-22 Science
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Release : 2007-08-22
Genre : Science
Kind : eBook
Book Rating : 069/5 ( reviews)

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Book Synopsis Modern Methods in the Calculus of Variations by : Irene Fonseca

Download or read book Modern Methods in the Calculus of Variations written by Irene Fonseca. This book was released on 2007-08-22. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of two books on methods and techniques in the calculus of variations. Contemporary arguments are used throughout the text to streamline and present in a unified way classical results, and to provide novel contributions at the forefront of the theory. This book addresses fundamental questions related to lower semicontinuity and relaxation of functionals within the unconstrained setting, mainly in L^p spaces. It prepares the ground for the second volume where the variational treatment of functionals involving fields and their derivatives will be undertaken within the framework of Sobolev spaces. This book is self-contained. All the statements are fully justified and proved, with the exception of basic results in measure theory, which may be found in any good textbook on the subject. It also contains several exercises. Therefore,it may be used both as a graduate textbook as well as a reference text for researchers in the field. Irene Fonseca is the Mellon College of Science Professor of Mathematics and is currently the Director of the Center for Nonlinear Analysis in the Department of Mathematical Sciences at Carnegie Mellon University. Her research interests lie in the areas of continuum mechanics, calculus of variations, geometric measure theory and partial differential equations. Giovanni Leoni is also a professor in the Department of Mathematical Sciences at Carnegie Mellon University. He focuses his research on calculus of variations, partial differential equations and geometric measure theory with special emphasis on applications to problems in continuum mechanics and in materials science.

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