Introduction To The Calculus Of Variations 3rd Edition
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| Author | : Hansjörg Kielhöfer |
| Publisher | : Springer |
| Total Pages | : 242 |
| Release | : 2018-01-25 |
| Genre | : Mathematics |
| ISBN | : 3319711237 |
This clear and concise textbook provides a rigorous introduction to the calculus of variations, depending on functions of one variable and their first derivatives. It is based on a translation of a German edition of the book Variationsrechnung (Vieweg+Teubner Verlag, 2010), translated and updated by the author himself. Topics include: the Euler-Lagrange equation for one-dimensional variational problems, with and without constraints, as well as an introduction to the direct methods. The book targets students who have a solid background in calculus and linear algebra, not necessarily in functional analysis. Some advanced mathematical tools, possibly not familiar to the reader, are given along with proofs in the appendix. Numerous figures, advanced problems and proofs, examples, and exercises with solutions accompany the book, making it suitable for self-study. The book will be particularly useful for beginning graduate students from the physical, engineering, and mathematical sciences with a rigorous theoretical background.
| Author | : Bernard Dacorogna |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 322 |
| Release | : 2014-08-13 |
| Genre | : Mathematics |
| ISBN | : 178326554X |
The calculus of variations is one of the oldest subjects in mathematics, and it is very much alive and 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, several new exercises have been added. The book, containing a total of 119 exercises with detailed solutions, is well designed for a course at both undergraduate and graduate levels.
| Author | : Hans Sagan |
| Publisher | : Courier Corporation |
| Total Pages | : 484 |
| Release | : 2012-04-26 |
| Genre | : Mathematics |
| ISBN | : 048613802X |
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.
| Author | : John A. Burns |
| Publisher | : CRC Press |
| Total Pages | : 562 |
| Release | : 2013-08-28 |
| Genre | : Mathematics |
| ISBN | : 1466571403 |
Introduction to the Calculus of Variations and Control with Modern Applications provides the fundamental background required to develop rigorous necessary conditions that are the starting points for theoretical and numerical approaches to modern variational calculus and control problems. The book also presents some classical sufficient conditions a
| Author | : Bruce van Brunt |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 295 |
| Release | : 2006-04-18 |
| Genre | : Mathematics |
| ISBN | : 0387216979 |
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 | : Louis Komzsik |
| Publisher | : CRC Press |
| Total Pages | : 234 |
| Release | : 2018-09-03 |
| Genre | : Mathematics |
| ISBN | : 1482253607 |
The purpose of the calculus of variations is to find optimal solutions to engineering problems whose optimum may be a certain quantity, shape, or function. Applied Calculus of Variations for Engineers addresses this important mathematical area applicable to many engineering disciplines. Its unique, application-oriented approach sets it apart from the theoretical treatises of most texts, as it is aimed at enhancing the engineer’s understanding of the topic. This Second Edition text: Contains new chapters discussing analytic solutions of variational problems and Lagrange-Hamilton equations of motion in depth Provides new sections detailing the boundary integral and finite element methods and their calculation techniques Includes enlightening new examples, such as the compression of a beam, the optimal cross section of beam under bending force, the solution of Laplace’s equation, and Poisson’s equation with various methods Applied Calculus of Variations for Engineers, Second Edition extends the collection of techniques aiding the engineer in the application of the concepts of the calculus of variations.
| Author | : I. M. Gelfand |
| Publisher | : Courier Corporation |
| Total Pages | : 260 |
| Release | : 2012-04-26 |
| Genre | : Mathematics |
| ISBN | : 0486135012 |
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 | : Charles Fox |
| Publisher | : Courier Corporation |
| Total Pages | : 308 |
| Release | : 1987-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780486654997 |
In this highly regarded text for advanced undergraduate and graduate students, the author develops the calculus of variations both for its intrinsic interest and for its powerful applications to modern mathematical physics. Topics include first and second variations of an integral, generalizations, isoperimetrical problems, least action, special relativity, elasticity, more. 1963 edition.
| Author | : Charles R. MacCluer |
| Publisher | : Courier Corporation |
| Total Pages | : 274 |
| Release | : 2013-05-20 |
| Genre | : Mathematics |
| ISBN | : 0486278301 |
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 | : Frederic Wan |
| Publisher | : Routledge |
| Total Pages | : 640 |
| Release | : 2017-10-19 |
| Genre | : Mathematics |
| ISBN | : 135143652X |
This comprehensive text provides all information necessary for an introductory course on the calculus of variations and optimal control theory. Following a thorough discussion of the basic problem, including sufficient conditions for optimality, the theory and techniques are extended to problems with a free end point, a free boundary, auxiliary and inequality constraints, leading to a study of optimal control theory.
