Download or read book Differential Geometry Calculus of Variations and Their Applications written by George M. Rassias and published by CRC Press. This book was released on 2023-05-31 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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.
Download or read book Differential Geometry and Its Applications written by John Oprea and published by MAA. This book was released on 2007-09-06 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the differential geometry of surfaces and its relevance to engineering and the sciences.
Download or read book Differential Geometry Calculus of Variations and Their Applications written by George M. Rassias and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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.
Download or read book Differential Geometry and Its Applications written by John Oprea and published by American Mathematical Society. This book was released on 2024-07-01 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Geometry and Its Applications studies the differential geometry of surfaces with the goal of helping students make the transition from the compartmentalized courses in a standard university curriculum to a type of mathematics that is a unified whole. It mixes geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences. That mix of ideas offers students the opportunity to visualize concepts through the use of computer algebra systems such as Maple. Differential Geometry and Its Applications emphasizes that this visualization goes hand in hand with understanding the mathematics behind the computer construction. The book is rich in results and exercises that form a continuous spectrum, from those that depend on calculation to proofs that are quite abstract.
Download or read book Differential Geometry and Its Applications written by Oldřich Kowalski and published by World Scientific. This book was released on 2008 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains invited lectures and selected research papers in the fields of classical and modern differential geometry, global analysis, and geometric methods in physics, presented at the 10th International Conference on Differential Geometry and its Applications (DGA2007), held in Olomouc, Czech Republic.The book covers recent developments and the latest results in the following fields: Riemannian geometry, connections, jets, differential invariants, the calculus of variations on manifolds, differential equations, Finsler structures, and geometric methods in physics. It is also a celebration of the 300th anniversary of the birth of one of the greatest mathematicians, Leonhard Euler, and includes the Euler lecture OC Leonhard Euler OCo 300 years onOCO by R Wilson. Notable contributors include J F Cariena, M Castrilln Lpez, J Erichhorn, J-H Eschenburg, I KoliO, A P Kopylov, J Korbai, O Kowalski, B Kruglikov, D Krupka, O Krupkovi, R L(r)andre, Haizhong Li, S Maeda, M A Malakhaltsev, O I Mokhov, J Muoz Masqu(r), S Preston, V Rovenski, D J Saunders, M Sekizawa, J Slovik, J Szilasi, L Tamissy, P Walczak, and others."
Download or read book The Calculus of Variations written by Bruce van Brunt and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 295 pages. 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.
Download or read book Differential Geometry and its Applications written by D. Krupka and published by Springer. This book was released on 1987-07-31 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Inverse Problem of the Calculus of Variations written by Dmitry V. Zenkov and published by Springer. This book was released on 2015-10-15 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 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).
Download or read book Applied Calculus of Variations for Engineers written by Louis Komzsik and published by CRC Press. This book was released on 2018-09-03 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Geometric Mechanics on Riemannian Manifolds written by Ovidiu Calin and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: * 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
Download or read book Applied Calculus of Variations for Engineers written by Louis Komzsik and published by CRC Press. This book was released on 2008-10-27 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of calculus of variations is to find optimal solutions to engineering problems where the optimum may be a certain quantity, a shape, or a function. Applied Calculus of Variations for Engineers addresses this very important mathematical area applicable to many engineering disciplines. Its unique, application-oriented approach sets it apart from the theoretical treatises of most texts. It is aimed at enhancing the engineer’s understanding of the topic as well as aiding in the application of the concepts in a variety of engineering disciplines. The first part of the book presents the fundamental variational problem and its solution via the Euler–Lagrange equation. It also discusses variational problems subject to constraints, the inverse problem of variational calculus, and the direct solution techniques of variational problems, such as the Ritz, Galerkin, and Kantorovich methods. With an emphasis on applications, the second part details the geodesic concept of differential geometry and its extensions to higher order spaces. It covers the variational origin of natural splines and the variational formulation of B-splines under various constraints. This section also focuses on analytic and computational mechanics, explaining classical mechanical problems and Lagrange’s equations of motion.
Download or read book Variational Methods written by Michael Struwe and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert'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.
Download or read book The Shapes of Things written by Shawn W. Walker and published by SIAM. This book was released on 2015-06-25 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many things around us have properties that depend on their shape--for example, the drag characteristics of a rigid body in a flow. This self-contained overview of differential geometry explains how to differentiate a function (in the calculus sense) with respect to a "shape variable." This approach, which is useful for understanding mathematical models containing geometric partial differential equations (PDEs), allows readers to obtain formulas for geometric quantities (such as curvature) that are clearer than those usually offered in differential geometry texts. Readers will learn how to compute sensitivities with respect to geometry by developing basic calculus tools on surfaces and combining them with the calculus of variations. Several applications that utilize shape derivatives and many illustrations that help build intuition are included.
Download or read book Differential Geometry and Calculus of Variations written by American Mathematical Society and published by . This book was released on 1962 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Variational Problems in Differential Geometry written by Roger Bielawski and published by Cambridge University Press. This book was released on 2011-10-20 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a mix of expository and original papers this volume is an excellent reference for experienced researchers in geometric variational problems, as well as an ideal introduction for graduate students. It presents all the varied methods and techniques used in attacking geometric variational problems and includes many up-to-date results.
Download or read book Differential Geometry and Calculus of Variations written by and published by . This book was released on 1987 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Calculus of Variations and Harmonic Maps written by Hajime Urakawa and published by American Mathematical Soc.. This book was released on 1993-01-01 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a wide view of the calculus of variations as it plays an essential role in various areas of mathematics and science. Containing many examples, open problems, and exercises with complete solutions, the book would be suitable as a text for graduate courses in differential geometry, partial differential equations, and variational methods. The first part of the book is devoted to explaining the notion of (infinite-dimensional) manifolds and contains many examples. An introduction to Morse theory of Banach manifolds is provided, along with a proof of the existence of a minimizer under the Palais-Smale condition. The second part, which may be read independently of the first, presents the theory of harmonic maps, with a careful calculation of the first and second variations of the energy. Several applications of the second variation and classification theories of harmonic maps are given.
