[PDF] Interdisciplinary Mathematics Topics In Physical Geometry eBook

Author : Robert Hermann
Publisher : Math Science Press
Page : 363 pages
File Size : 44,88 MB
Release : 1991
Category : Mathematics
ISBN : 9780915692422

GET BOOK

VOLUME 26 of INTERDISCIPLINARY MATHEMATICS, series expounding mathematical methodology in Physics & Engineering. TOPICS: Differential & Riemannian Geometry; Theories of Vorticity Dynamics, Einstein-Hilbert Gravitation, Colobeau-Rosinger Generalized Function Algebra, Deformations & Quantum Mechanics of Particles & Fields. Ultimate goal is to develop mathematical framework for reconciling Quantum Mechanics & concept of Point Particle. New ideas for researchers & students. Order: Math Sci Press, 53 Jordan Road, Brookline, MA 02146. (617) 738-0307.

Author : Georg Glaeser
Publisher : Walter de Gruyter GmbH & Co KG
Page : 248 pages
File Size : 12,89 MB
Release : 2023-11-20
Category : Mathematics
ISBN : 3111365786

GET BOOK

Understanding geometry, physics, and biology This is a highly informative and richly illustrated nonfiction book that conveys scientific content in a clear and understandable way. Drawing on numerous examples, it explains topics from geometry, physics, and biology and points out commonalities between the disciplines. The book contains approx. 300 links to video animations and is accompanied by a freely accessible interactive software that allows readers to delve even deeper into the content covered in the book. The content, videos, and software were developed by the Department of Geometry at the University of Applied Arts Vienna. Georg Glaeser’s research focuses particularly on interdisciplinary mathematical and biological issues, and he worked for many years with Franz Gruber, who was highly adept at visualizing complex issues. Includes links to around 300 video animations, accessible via QR codes Compact, informative, and easy-to-understand explanations of scientific issues in the disciplines of geometry, physics, and biology With numerous images and illustrations

Author : Heinz Schättler
Publisher : Springer Science & Business Media
Page : 652 pages
File Size : 38,13 MB
Release : 2012-06-26
Category : Mathematics
ISBN : 1461438349

GET BOOK

This book gives a comprehensive treatment of the fundamental necessary and sufficient conditions for optimality for finite-dimensional, deterministic, optimal control problems. The emphasis is on the geometric aspects of the theory and on illustrating how these methods can be used to solve optimal control problems. It provides tools and techniques that go well beyond standard procedures and can be used to obtain a full understanding of the global structure of solutions for the underlying problem. The text includes a large number and variety of fully worked out examples that range from the classical problem of minimum surfaces of revolution to cancer treatment for novel therapy approaches. All these examples, in one way or the other, illustrate the power of geometric techniques and methods. The versatile text contains material on different levels ranging from the introductory and elementary to the advanced. Parts of the text can be viewed as a comprehensive textbook for both advanced undergraduate and all level graduate courses on optimal control in both mathematics and engineering departments. The text moves smoothly from the more introductory topics to those parts that are in a monograph style were advanced topics are presented. While the presentation is mathematically rigorous, it is carried out in a tutorial style that makes the text accessible to a wide audience of researchers and students from various fields, including the mathematical sciences and engineering. Heinz Schättler is an Associate Professor at Washington University in St. Louis in the Department of Electrical and Systems Engineering, Urszula Ledzewicz is a Distinguished Research Professor at Southern Illinois University Edwardsville in the Department of Mathematics and Statistics.

Author : M. D. Maia
Publisher : Springer Science & Business Media
Page : 182 pages
File Size : 23,26 MB
Release : 2011-06-14
Category : Science
ISBN : 1441982736

GET BOOK

The Yang-Mills theory of gauge interactions is a prime example of interdisciplinary mathematics and advanced physics. Its historical development is a fascinating window into the ongoing struggle of mankind to understand nature. The discovery of gauge fields and their properties is the most formidable landmark of modern physics. The expression of the gauge field strength as the curvature associated to a given connection, places quantum field theory in the same geometrical footing as the gravitational field of general relativity which is naturally written in geometrical terms. The understanding of such geometrical property may help one day to write a unified field theory starting from symmetry principles. Of course, there are remarkable differences between the standard gauge fields and the gravitational field, which must be understood by mathematicians and physicists before attempting such unification. In particular, it is important to understand why gravitation is not a standard gauge field. This book presents an account of the geometrical properties of gauge field theory, while trying to keep the equilibrium between mathematics and physics. At the end we will introduce a similar approach to the gravitational field.