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Author: George M. Rassias
Publisher: CRC Press
Published: 1985-10-01
Total Pages: 550
ISBN-13: 9780824772673
DOWNLOAD EBOOKThis book contains a series of papers on some of the longstanding research problems of geometry, calculus of variations, and their applications. It is suitable for advanced graduate students, teachers, research mathematicians, and other professionals in mathematics.
Author: John Oprea
Publisher: MAA
Published: 2007-09-06
Total Pages: 508
ISBN-13: 9780883857489
DOWNLOAD EBOOKThis book studies the differential geometry of surfaces and its relevance to engineering and the sciences.
Author: George M. Rassias
Publisher: CRC Press
Published: 2023-05-31
Total Pages: 550
ISBN-13: 1000950727
DOWNLOAD EBOOKThis book contains a series of papers on some of the longstanding research problems of geometry, calculus of variations, and their applications. It is suitable for advanced graduate students, teachers, research mathematicians, and other professionals in mathematics.
Author: Bruce van Brunt
Publisher: Springer Science & Business Media
Published: 2006-04-18
Total Pages: 295
ISBN-13: 0387216979
DOWNLOAD EBOOKSuitable 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: Dmitry V. Zenkov
Publisher: Springer
Published: 2015-10-15
Total Pages: 296
ISBN-13: 9462391092
DOWNLOAD EBOOKThe aim of the present book is to give a systematic treatment of the inverse problem of the calculus of variations, i.e. how to recognize whether a system of differential equations can be treated as a system for extremals of a variational functional (the Euler-Lagrange equations), using contemporary geometric methods. Selected applications in geometry, physics, optimal control, and general relativity are also considered. The book includes the following chapters: - Helmholtz conditions and the method of controlled Lagrangians (Bloch, Krupka, Zenkov) - The Sonin-Douglas's problem (Krupka) - Inverse variational problem and symmetry in action: The Ostrogradskyj relativistic third order dynamics (Matsyuk.) - Source forms and their variational completion (Voicu) - First-order variational sequences and the inverse problem of the calculus of variations (Urban, Volna) - The inverse problem of the calculus of variations on Grassmann fibrations (Urban).
Author: Bernard Dacorogna
Publisher: Imperial College Press
Published: 2009
Total Pages: 241
ISBN-13: 1848163339
DOWNLOAD EBOOKThe calculus of variations is one of the oldest subjects in mathematics, yet is very much alive and is still evolving. Besides its mathematical importance and its links to other branches of mathematics, such as geometry or differential equations, it is widely used in physics, engineering, economics and biology.This book serves both as a guide to the expansive existing literature and as an aid to the non-specialist ? mathematicians, physicists, engineers, students or researchers ? in discovering the subject's most important problems, results and techniques. Despite the aim of addressing non-specialists, mathematical rigor has not been sacrificed; most of the theorems are either fully proved or proved under more stringent conditions.In this new edition, the chapter on regularity has been significantly expanded and 27 new exercises have been added. The book, containing a total of 103 exercises with detailed solutions, is well designed for a course at both undergraduate and graduate levels.
Author: Michael Struwe
Publisher: Springer Science & Business Media
Published: 2013-04-17
Total Pages: 288
ISBN-13: 3662032120
DOWNLOAD EBOOKHilbert's talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateau's problem by Douglas and Radò. The book gives a concise introduction to variational methods and presents an overview of areas of current research in this field. This new edition has been substantially enlarged, a new chapter on the Yamabe problem has been added and the references have been updated. All topics are illustrated by carefully chosen examples, representing the current state of the art in their field.
Author: I. M. Gelfand
Publisher: Courier Corporation
Published: 2012-04-26
Total Pages: 260
ISBN-13: 0486135012
DOWNLOAD EBOOKFresh, 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: Oskar Bolza
Publisher: University of Michigan Library
Published: 1904
Total Pages: 306
ISBN-13:
DOWNLOAD EBOOKAuthor: Ovidiu Calin
Publisher: Springer Science & Business Media
Published: 2006-03-15
Total Pages: 285
ISBN-13: 0817644210
DOWNLOAD EBOOK* A geometric approach to problems in physics, many of which cannot be solved by any other methods * Text is enriched with good examples and exercises at the end of every chapter * Fine for a course or seminar directed at grad and adv. undergrad students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics
