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Mathematical Physics, 2nd ed. 2013
◆Springer Text Book セール開催中！：2025年8月24日(日)ご注文分まで
※上記表示の販売価格は割引適用後の価格です 出版済み 3週間でお届けいたします。 A Modern Introduction to Its Foundations Author: Hassani, Sadri Publisher: Springer ISBN: 9783319011943 Cover: HARDCOVER Date: 2013年09月 DESCRIPTION The goal of this book is to expose the reader to the indispensable role that mathematics 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, differential and integral equations, operator theory, and multi-dimensional Green's functions. The second half of the book introduces groups, manifolds, Lie groups and their representations, Clifford algebras and their representations, and fibre bundles and their applications to differential geometry and gauge theories. This second edition is a substantial revision with a complete rewriting of many chapters and the addition of new ones, including chapters on algebras, representation of Clifford algebras, fibre bundles, and gauge theories. The spirit of the first edition, namely the balance between rigour and physical application, has been maintained, as is the abundance of historical notes and worked out examples that demonstrate the "unreasonable effectiveness of mathematics" in modern physics. TABLE OF CONTENTS Mathematical Preliminaries Finite-Dimensional Vector Spaces Vectors and Linear Maps Algebras Operator Algebra Matrices Spectral Decomposition Infinite-Dimensional Vector Spaces Hilbert Spaces Classical Orthogonal Polynomials Fourier Analysis Complex Analysis Complex Calculus Calculus of Residues Advanced Topics Differential Equations Separation of Variables in Spherical Coordinates Second-Order Linear Differential Equations Complex Analysis of SOLDEs Integral Transforms and Differential Equations Operators on Hilbert Spaces Introductory Operator Theory Integral Equations Sturm-Liouville Systems Green’s Functions Green’s Functions in One Dimension Multidimensional Green’s Functions: Formalism Multidimensional Green’s Functions: Applications Groups and Their Representations Group Theory Representation of Groups Representations of the Symmetric Group Tensors and Manifolds Tensors Clifford Algebras Analysis of Tensors Lie Groups and Their Applications Lie Groups and Lie Algebras Representation of Lie Groups and Lie Algebras Representation of Clifford Algebras Lie Groups and Differential Equations Calculus of Variations, Symmetries, and Conservation Laws Fiber Bundles Fiber Bundles and Connections Gauge Theories Differential Geometry Riemannian Geometry
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