Springer-Verlag,1992,420 p. This textbook is a comprehensive introduction to variational methods. Its unifying aspect, based on appropriate concepts of compactness, is the study of critical points of functionals via direct methods. It shows the interactions between linear and nonlinear functional analysis. Addressing in particular the interests of physicists, the authors treat in detail the variational problems of mechanics and classical field theories, writing on local linear and nonlinear boundary and eigenvalue problems of important classes of nonlinear partial differential equations, and giving more recent results on Thomas-Fermi theory and on problems involving critical nonlinearities. This book is an excellent introduction for students in mathematics and mathematical physics
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John Wiley & Sons Inc., 2011, 301 p. This book aims to disseminate geometric algebra as a straightforward mathematical tool set for working with and understanding classical electromagnetic theory. It's target readership is anyone who has some knowledge of electromagnetic theory, predominantly ordinary scientists and engineers who use it in the course of their work, or postgraduate...
Wiley, 2010. — 318 pages. The importance of partial differential equations (PDEs) in modeling phenomena in engineering as well as in the physical, natural, and social sciences is well known by students and practitioners in these fields. Striking a balance between theory and applications, Fourier Series and Numerical Methods for Partial Differential Equations presents an...
Springer, 2013. — 1198 p. — 2nd ed. — ISBN: 9783319011943
The goal of this book is to expose the reader to the indispensable role that mathematics-often very abstract-plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics as diverse as algebras, classical orthogonal polynomials, Fourier analysis, complex analysis,...
Cambridge University Press, 2007. — 1262 p. Authors: William H. Press - Raymer Chair in Computer Sciences and Integrative Biology The University of Texas at Austin Saul A. Teukolsky - Hans A. Bethe Professor of Physics and Astrophysics Cornell University William T. Vetterling - Research Fellow and Director of Image Science ZINK Imaging, LLC Brian P. Flannery - Science, Strategy...
Springer, 2008. — xiv, 218 p. — (Undergraduate Texts in Mathematics). — ISBN 978-0-387-78214-0, 978-0-387-78215-7. In this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates. In order to achieve this, he focuses on the so-called "classical groups'' that capture the symmetries of real,...
Springer, 2003. — 302 p. The calculus of variations has a long history of interaction with other branches of mathematics, such as geometry and differential equations, and with physics, particularly mechanics. More recently, the calculus of variations has found applications in other fields such as economics and electrical engineering. Much of the mathematics underlying control...
