Introduction to Mathematical Physics: Methods & ConceptsMathematical physics provides physical theories with their logical basis and the tools for drawing conclusions from hypotheses. Introduction to Mathematical Physics explains to the reader why and how mathematics is needed in the description of physical events in space. For undergraduates in physics, it is a classroom-tested textbook on vector analysis, linear operators, Fourier series and integrals, differential equations, special functions and functions of a complex variable. Strongly correlated with core undergraduate courses on classical and quantum mechanics and electromagnetism, it helps the student master these necessary mathematical skills. It contains advanced topics of interest to graduate students on relativistic square-root spaces and nonlinear systems. It contains many tables of mathematical formulas and references to useful materials on the Internet. It includes short tutorials on basic mathematical topics to help readers refresh their mathematical knowledge. An appendix on Mathematica encourages the reader to use computer-aided algebra to solve problems in mathematical physics. A free Instructor's Solutions Manual is available to instructors who order the book for course adoption. |
Contents
| 1 | |
2 Transformations matrices and operators | 76 |
3 Relativistic squareroot spacessup | 138 |
4 Fourier series and Fourier transforms | 244 |
5 Differential equations in physics | 319 |
6 Nonlinear systemssup | 373 |
7 Special functions | 458 |
8 Functions of a complex variable | 502 |
Tutorials | 620 |
Mathematica and other computer algebra systems | 670 |
Computer algebra CA with Mathematica | 677 |
Resources for students | 688 |
| 694 | |
Name index | 699 |
| 702 | |
Other editions - View all
Common terms and phrases
algebra analytic appear asymptotic attractor axes axis bifurcation branch cut calculated called Cartesian tensors coefficients complex numbers components constant contour convergence coordinate system curve defined derivative described differential equation differential operator dimension Dirac Dirac equation direction eigenvalues eigenvectors example expansion exponential expression finite formula Fourier series Fourier transform frame gives Green function Hence Hermitian infinite series integral inverse irreps kink Laplace Legendre linear linearly independent Lorentz mathematical matrix nonlinear notation obtained orthogonal parameters parity particle Pauli matrices permutation physical plane polynomials positive Problem properties quantum quaternion relations result Riemann surface rotation satisfies scalar product Show shown in Fig singularity ſº soliton solution space spacetime spherical spin spinors square symbol symmetry Taylor series tensor theorem vanishes variable vector field velocity Verify wave equation wave function