Mathematical Physics: A Modern Introduction to Its Foundations / Edition 1

Mathematical Physics: A Modern Introduction to Its Foundations / Edition 1

by Sadri Hassani, S. Hassani
     
 

This book is for physics students interested in the mathematics they use and for mathematics students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation tries to strike a balance between formalism and application, between abstract and concrete. The interconnections among the various topics are… See more details below

Overview

This book is for physics students interested in the mathematics they use and for mathematics students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation tries to strike a balance between formalism and application, between abstract and concrete. The interconnections among the various topics are clarified both by the use of vector spaces as a central unifying theme, recurring throughout the book, and by putting ideas into their historical context. Enough of the essential formalism is included to make the presentation self-contained. Intended for advanced undergraduate or beginning graduate students, this comprehensive guide should also prove useful as a refresher or reference for physicists and applied mathematicians. Over 300 worked-out examples and more than 800 problems provide valuable learning aids.

Product Details

ISBN-13:
9780387985794
Publisher:
Springer New York
Publication date:
02/28/2002
Edition description:
1st ed. 1999. Corr. 3rd printing 2002
Pages:
1026
Sales rank:
1,197,095
Product dimensions:
6.70(w) x 9.80(h) x 2.00(d)

Table of Contents

Preface
Note to the Reader
Mathematical Preliminaries
IFinite-Dimensional Vector Spaces
1Vectors and Transformations
2Operator Algebra
3Matrices: Operator Representations
4Spectral Decomposition
IIInfinite-Dimensional Vector Spaces
5Hilbert Spaces
6Generalized Functions
7Classical Orthogonal Polynomials
8Fourier Analysis
IIIComplex Analysis
9Complex Calculus
10Calculus of Residues
11Complex Analysis: Advanced Topics
IVDifferential Equations
12Separation of Variables in Spherical Coordinates
13Second-Order Linear Differential Equations
14Complex Analysis of SOLDEs
15Integral Transforms and Differential Equations
VOperators on Hilbert Spaces
16An Introduction to Operator Theory
17Integral Equations
18Sturm-Liouville Systems: Formalism
19Sturm-Liouville Systems: Examples
VIGreen's Functions
20Green's Functions in One Dimension
21Multidimensional Green's Functions: Formalism
22Multidimensional Green's Functions: Applications
VIIGroups and Manifolds
23Group Theory
24Group Representation Theory
25Algebra of Tensors
26Analysis of Tensors
VIIILie Groups and Their Applications
27Lie Groups and Lie Algebras
28Differential Geometry
29Lie Groups and Differential Equations
30Calculus of Variations, Symmetries, and Conservation Laws
Bibliography
Index

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