Variational Calculus With Elementary Convexity PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Variational Calculus With Elementary Convexity PDF full book. Access full book title Variational Calculus With Elementary Convexity.
| Author | : J.L. Troutman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 373 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1468401580 |
Download Variational Calculus with Elementary Convexity Book in PDF, ePub and Kindle
The calculus of variations, whose origins can be traced to the works of Aristotle and Zenodoros, is now Ii vast repository supplying fundamental tools of exploration not only to the mathematician, but-as evidenced by current literature-also to those in most branches of science in which mathematics is applied. (Indeed, the macroscopic statements afforded by variational principles may provide the only valid mathematical formulation of many physical laws. ) As such, it retains the spirit of natural philosophy common to most mathematical investigations prior to this century. How ever, it is a discipline in which a single symbol (b) has at times been assigned almost mystical powers of operation and discernment, not readily subsumed into the formal structures of modern mathematics. And it is a field for which it is generally supposed that most questions motivating interest in the subject will probably not be answerable at the introductory level of their formulation. In earlier articles,1,2 it was shown through several examples that a complete characterization of the solution of optimization problems may be available by elementary methods, and it is the purpose of this work to explore further the convexity which underlay these individual successes in the context of a full introductory treatment of the theory of the variational calculus. The required convexity is that determined through Gateaux variations, which can be defined in any real linear space and which provide an unambiguous foundation for the theory.
| Author | : W. Hrusa |
| Publisher | : |
| Total Pages | : 384 |
| Release | : 1983-04-15 |
| Genre | : |
| ISBN | : 9781468401592 |
Download Variational Calculus with Elementary Convexity Book in PDF, ePub and Kindle
| Author | : John L. Troutman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 471 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461207371 |
Download Variational Calculus and Optimal Control Book in PDF, ePub and Kindle
An introduction to the variational methods used to formulate and solve mathematical and physical problems, allowing the reader an insight into the systematic use of elementary (partial) convexity of differentiable functions in Euclidian space. By helping students directly characterize the solutions for many minimization problems, the text serves as a prelude to the field theory for sufficiency, laying as it does the groundwork for further explorations in mathematics, physics, mechanical and electrical engineering, as well as computer science.
| Author | : John L. Troutman |
| Publisher | : |
| Total Pages | : 364 |
| Release | : 1983 |
| Genre | : Calculus of variations |
| ISBN | : |
Download Introduction to the Variational Calculus with Elementary Convexity Book in PDF, ePub and Kindle
| Author | : R. Tyrrell Rockafellar |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 747 |
| Release | : 2009-06-26 |
| Genre | : Mathematics |
| ISBN | : 3642024319 |
Download Variational Analysis Book in PDF, ePub and Kindle
From its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control. This book develops a unified framework and provides a detailed exposition of variational geometry and subdifferential calculus in their current forms beyond classical and convex analysis. Also covered are set-convergence, set-valued mappings, epi-convergence, duality, and normal integrands.
| Author | : Frederic Wan |
| Publisher | : Routledge |
| Total Pages | : 660 |
| Release | : 2017-10-19 |
| Genre | : Mathematics |
| ISBN | : 1351436511 |
Download Introduction To The Calculus of Variations And Its Applications Book in PDF, ePub and Kindle
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.
| Author | : Daniel Liberzon |
| Publisher | : Princeton University Press |
| Total Pages | : 255 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 0691151873 |
Download Calculus of Variations and Optimal Control Theory Book in PDF, ePub and Kindle
This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the historical development of the subject Solutions manual (available only to teachers) Leading universities that have adopted this book include: University of Illinois at Urbana-Champaign ECE 553: Optimum Control Systems Georgia Institute of Technology ECE 6553: Optimal Control and Optimization University of Pennsylvania ESE 680: Optimal Control Theory University of Notre Dame EE 60565: Optimal Control
| Author | : Naveen Kumar |
| Publisher | : Alpha Science Int'l Ltd. |
| Total Pages | : 144 |
| Release | : 2005 |
| Genre | : Computers |
| ISBN | : 9781842651957 |
Download An Elementary Course on Variational Problems in Calculus Book in PDF, ePub and Kindle
"The book covers topics in detail supported by figures and exercises and also lists some direct (approximate) methods to solve boundary value problems containing ordinary/partial differential equations by variational and residue methods, some of them being of immense importance in the treatment of finite element numerical methods. Variety of disciplines being used in the subject, are given in brief, in respective appendices."--BOOK JACKET.
| Author | : Constantin Udriste |
| Publisher | : John Wiley & Sons |
| Total Pages | : 228 |
| Release | : 2023-02-13 |
| Genre | : Mathematics |
| ISBN | : 1119944368 |
Download Variational Calculus with Engineering Applications Book in PDF, ePub and Kindle
A comprehensive overview of foundational variational methods for problems in engineering Variational calculus is a field in which small alterations in functions and functionals are used to find their relevant maxima and minima. It is a potent tool for addressing a range of dynamic problems with otherwise counter-intuitive solutions, particularly ones incorporating multiple confounding variables. Its value in engineering fields, where materials and geometric configurations can produce highly specific problems with unconventional or unintuitive solutions, is considerable. Variational Calculus with Engineering Applications provides a comprehensive survey of this toolkit and its engineering applications. Balancing theory and practice, it offers a thorough and accessible introduction to the field pioneered by Euler, Lagrange and Hamilton, offering tools that can be every bit as powerful as the better-known Newtonian mechanics. It is an indispensable resource for those looking for engineering-oriented overview of a subject whose capacity to provide engineering solutions is only increasing. Variational Calculus with Engineering Applications readers will also find: Discussion of subjects including variational principles, levitation, geometric dynamics, and more Examples and instructional problems in every Chapter, along with MAPLE codes for performing the simulations described in each Engineering applications based on simple, curvilinear, and multiple integral functionals Variational Calculus with Engineering Applications is ideal for advanced students, researchers, and instructors in engineering and materials science.
| 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.
