Physical MathematicsCambridge University Press, 2019. 8. 7. Unique in its clarity, examples, and range, Physical Mathematics explains simply and succinctly the mathematics that graduate students and professional physicists need to succeed in their courses and research. The book illustrates the mathematics with numerous physical examples drawn from contemporary research. This second edition has new chapters on vector calculus, special relativity and artificial intelligence and many new sections and examples. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations, Bessel functions, and spherical harmonics, the book explains topics such as the singular value decomposition, Lie algebras and group theory, tensors and general relativity, the central limit theorem and Kolmogorov's theorems, Monte Carlo methods of experimental and theoretical physics, Feynman's path integrals, and the standard model of cosmology. |
목차
1 Linear Algebra | 1 |
2 Vector Calculus | 84 |
3 Fourier Series | 93 |
4 Fourier and Laplace Transforms | 128 |
5 Infinite Series | 158 |
6 ComplexVariable Theory | 185 |
7 Differential Equations | 248 |
8 Integral Equations | 334 |
14 Forms | 536 |
15 Probability and Statistics | 564 |
16 Monte Carlo Methods | 632 |
17 Artificial Intelligence | 643 |
18 Order Chaos and Fractals | 647 |
19 Functional Derivatives | 661 |
20 Path Integrals | 669 |
21 Renormalization Group | 718 |
9 Legendre Polynomials and Spherical Harmonics | 343 |
10 Bessel Functions | 365 |
11 Group Theory | 390 |
12 Special Relativity | 451 |
13 General Relativity | 466 |
22 Strings | 727 |
| 737 | |
| 744 | |
자주 나오는 단어 및 구문
action analytic basis boundary conditions called charge closed coefficients combination commutation complex constant continuous contour converges coordinates covariant defined definition density derivative determinant differential equation dimensions eigenvalues eigenvectors elements energy Example Exercise exponential exterior derivative factor field Figure follows formula Fourier series Fourier transform function function f(x gauge given gives hermitian homogeneous identity implies independent inner product integral interval invariant inverse limit linear Lorentz maps mass matrix mean momentum multiplied normal obey operator orthogonal orthonormal particle path physical positive potential probability distribution quantum quantum mechanics relation represent representation rotation satisfy scalar Show ſº solution space square Suppose symmetric tensor theorem theory transform unitary vanishes variables variance vector wave write zero