Mathematical Physics A Modern Introduction to Its Foundations /
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,...
| Κύριος συγγραφέας: | |
|---|---|
| Συγγραφή απο Οργανισμό/Αρχή: | |
| Μορφή: | Ηλεκτρονική πηγή Ηλ. βιβλίο |
| Γλώσσα: | English |
| Έκδοση: |
Cham :
Springer International Publishing : Imprint: Springer,
2013.
|
| Έκδοση: | 2nd ed. 2013. |
| Θέματα: | |
| Διαθέσιμο Online: | Full Text via HEAL-Link |
Πίνακας περιεχομένων:
- 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.
