Mathematical Physics A Modern Introduction to Its Foundations /

• Main Author: Hassani, Sadri. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2013.
• Edition: 2nd ed. 2013.
• Subjects: Physics.; Mathematics.; Mathematical physics.; Theoretical, Mathematical and Computational Physics.; Mathematical Methods in Physics.; Numerical and Computational Physics.; Applications of Mathematics.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-319-01195-0

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,...

Table of Contents:

• Mathematical Preliminaries
• I Finite-Dimensional Vector Spaces
• 1 Vectors and Linear Maps
• 2 Algebras
• 3 Operator Algebra
• 4 Matrices
• 5 Spectral Decomposition
• II Infinite-Dimensional Vector Spaces
• 6 Hilbert Spaces.-�7 Classical Orthogonal Polynomials
• 8 Fourier Analysis
• III Complex Analysis
• 9 Complex Calculus
• 10 Calculus of Residues
• 11 Advanced Topics
• IV Differential Equations
• 12 Separation of Variables in Spherical Coordinates
• 13 Second-Order Linear Differential Equations
• 14 Complex Analysis of SOLDEs
• 15 Integral Transforms and Differential Equations.-�V Operators on Hilbert Spaces
• 16 Introductory Operator Theory
• 17 Integral Equations.-�18 Sturm-Liouville Systems
• VI Green's Functions
• 19 Green's Functions in One Dimension
• 20 Multidimensional Green's Functions: Formalism
• 21 Multidimensional Green's Functions: Applications
• VII Groups and Their Representations
• 22 Group Theory
• 23 Representation of Groups
• 24 Representations of the Symmetric Group
• VIII Tensors and Manifolds
• 25 Tensors
• 26 Clifford Algebras
• 27 Analysis of Tensors
• IX Lie Groups and Their Applications
• 28 Lie Groups and Lie Algebras
• 28.2 An Outline of Lie Algebra Theory.-�29 Representation of Lie Groups and Lie Algebras
• 30 Representation of Clifford Algebras
• 31 Lie Groups and Differential Equations
• 32 Calculus of Variations, Symmetries, and Conservation Laws
• X Fiber Bundles
• 33 Fiber Bundles and Connections
• 34 Gauge Theories
• 35 Differential Geometry
• 36 Riemannian Geometry.