Mathematical Physics [E-Book] : A Modern Introduction to Its Foundations / by Sadri Hassani.
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,...
Saved in:
|
Full text |
|
| Personal Name(s): | Hassani, Sadri, author |
| Edition: |
2nd ed. 2013. |
| Imprint: |
Cham :
Springer,
2013
|
| Physical Description: |
XXXI, 1205 pages 160 illustrations (online resource) |
| Note: |
englisch |
| ISBN: |
9783319011950 |
| DOI: |
10.1007/978-3-319-01195-0 |
| Subject (LOC): |
- 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.