A Course In The Calculus Of Variations PDF Download
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Author | : Mark Kot |
Publisher | : American Mathematical Society |
Total Pages | : 311 |
Release | : 2014-10-06 |
Genre | : Mathematics |
ISBN | : 1470414953 |
Download A First Course in the Calculus of Variations Book in PDF, ePub and Kindle
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.
Author | : Mark Kot |
Publisher | : |
Total Pages | : 0 |
Release | : 2017 |
Genre | : |
ISBN | : 9781470437398 |
Download A First Course in the Calculus of Variations Book in PDF, ePub and Kindle
Author | : |
Publisher | : |
Total Pages | : |
Release | : 2014 |
Genre | : MATHEMATICS |
ISBN | : 9781470419615 |
Download A First Course in the Calculus of Variations Book in PDF, ePub and Kindle
Author | : Filippo Santambrogio |
Publisher | : Springer Nature |
Total Pages | : 354 |
Release | : 2024-01-18 |
Genre | : Mathematics |
ISBN | : 3031450361 |
Download A Course in the Calculus of Variations Book in PDF, ePub and Kindle
This book provides an introduction to the broad topic of the calculus of variations. It addresses the most natural questions on variational problems and the mathematical complexities they present. Beginning with the scientific modeling that motivates the subject, the book then tackles mathematical questions such as the existence and uniqueness of solutions, their characterization in terms of partial differential equations, and their regularity. It includes both classical and recent results on one-dimensional variational problems, as well as the adaptation to the multi-dimensional case. Here, convexity plays an important role in establishing semi-continuity results and connections with techniques from optimization, and convex duality is even used to produce regularity results. This is then followed by the more classical Hölder regularity theory for elliptic PDEs and some geometric variational problems on sets, including the isoperimetric inequality and the Steiner tree problem. The book concludes with a chapter on the limits of sequences of variational problems, expressed in terms of Γ-convergence. While primarily designed for master's-level and advanced courses, this textbook, based on its author's instructional experience, also offers original insights that may be of interest to PhD students and researchers. A foundational understanding of measure theory and functional analysis is required, but all the essential concepts are reiterated throughout the book using special memo-boxes.
Author | : L.A. Pars |
Publisher | : Courier Corporation |
Total Pages | : 358 |
Release | : 2013-12-10 |
Genre | : Mathematics |
ISBN | : 0486165957 |
Download An Introduction to the Calculus of Variations Book in PDF, ePub and Kindle
Clear, rigorous introductory treatment covers applications to geometry, dynamics, and physics. It focuses upon problems with one independent variable, connecting abstract theory with its use in concrete problems. 1962 edition.
Author | : I. M. Gelfand |
Publisher | : Courier Corporation |
Total Pages | : 260 |
Release | : 2012-04-26 |
Genre | : Mathematics |
ISBN | : 0486135012 |
Download Calculus of Variations Book in PDF, ePub and Kindle
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.
Author | : Filip Rindler |
Publisher | : Springer |
Total Pages | : 446 |
Release | : 2018-06-20 |
Genre | : Mathematics |
ISBN | : 3319776371 |
Download Calculus of Variations Book in PDF, ePub and Kindle
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.
Author | : Bruce van Brunt |
Publisher | : Springer Science & Business Media |
Total Pages | : 295 |
Release | : 2006-04-18 |
Genre | : Mathematics |
ISBN | : 0387216979 |
Download The Calculus of Variations Book in PDF, ePub and Kindle
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.
Author | : Charles R. MacCluer |
Publisher | : Courier Corporation |
Total Pages | : 274 |
Release | : 2013-05-20 |
Genre | : Mathematics |
ISBN | : 0486278301 |
Download Calculus of Variations Book in PDF, ePub and Kindle
First truly up-to-date treatment offers a simple introduction to optimal control, linear-quadratic control design, and more. Broad perspective features numerous exercises, hints, outlines, and appendixes, including a practical discussion of MATLAB. 2005 edition.
Author | : Hans Sagan |
Publisher | : Courier Corporation |
Total Pages | : 484 |
Release | : 2012-04-26 |
Genre | : Mathematics |
ISBN | : 048613802X |
Download Introduction to the Calculus of Variations Book in PDF, ePub and Kindle
Provides a thorough understanding of calculus of variations and prepares readers for the study of modern optimal control theory. Selected variational problems and over 400 exercises. Bibliography. 1969 edition.