Methods of Mathematical PhysicsCambridge University Press, 18/11/1999 - 561 páginas This well-known text and reference contains an account of those parts of mathematics that are most frequently needed in physics. As a working rule, it includes methods which have applications in at least two branches of physics. The authors have aimed at a high standard of rigour and have not accepted the often-quoted opinion that 'any argument is good enough if it is intended to be used by scientists'. At the same time, they have not attempted to achieve greater generality than is required for the physical applications: this often leads to considerable simplification of the mathematics. Particular attention is also paid to the conditions under which theorems hold. Examples of the practical use of the methods developed are given in the text: these are taken from a wide range of physics, including dynamics, hydrodynamics, elasticity, electromagnetism, heat conduction, wave motion and quantum theory. Exercises accompany each chapter. |
Índice
1 | |
Scalars and Vectors | 57 |
Tensors | 86 |
Matrices | 114 |
Multiple Integrals | 171 |
Potential Theory | 199 |
Operational Methods | 228 |
Physical Applications of the Operational Method | 244 |
Solution of Linear Differential Equations of the Second Order | 474 |
Asymptotic Expansions | 498 |
The Equations of Potential Waves and Heat Conduction | 529 |
Waves in One Dimension and Waves with Spherical Symmetry | 546 |
Conduction of Heat in One and Three Dimensions | 563 |
Bessel Functions 674 | 574 |
Applications of Bessel Functions 695 | 595 |
The Confluent Hypergeometric Function | 606 |
Numerical Methods | 261 |
Calculus of Variations | 314 |
Functions of a Complex Variable | 333 |
Contour Integration and Bromwichs Integral | 375 |
Confonnal Representation | 409 |
Fouriers Theorem | 429 |
The Factorial and Related Functions | 462 |
Legendre Functions and Associated Functions | 628 |
Elliptic Functions | 667 |
Notes | 691 |
Appendix on Notation | 706 |
711 | |
Outras edições - Ver tudo
Methods of Mathematical Physics, Volume 1 Richard Courant,David Hilbert Visualização de excertos - 1953 |
Palavras e frases frequentes
absolutely convergent analytic function angle apply approximation asymptotic asymptotic expansion axes axis boundary bounded variation circle circle of convergence coefficients complex components condition consider constant continuous continuous function contour convergent series coordinates corresponding curve defined definition denote derivatives determinant differential equation displacement distance equal essential singularity exists expansion expressed factor finite number follows formula Fourier Fourier series give given harmonic Heine-Borel theorem Hence infinite integer integral interpolation interval Laplace's equation lemma limit linear matrix method modulus motion multiple negative notation origin orthogonal particle path plane poles polynomial positive potential power series prove radius real numbers region relations Riemann integral roots rotation satisfied scalar Similarly single-valued singularity solution sphere Stieltjes integral suffix surface tend to zero tensor theorem theory transformation uniformly convergent values vanish variable vector velocity waves