Methods of Mathematical PhysicsThis 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. |
Contents
Preface page | 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 | 574 |
Applications of Bessel Functions | 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 |
Conformal Representation | 409 |
Fouriers Theorem | 429 |
The Factorial and Related Functions | 462 |
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Common terms and phrases
absolutely convergent analytic function apply approximation asymptotic asymptotic expansion axes axis B₁ boundary bounded variation circle circle of convergence coefficients complex components condition consider constant continuous continuous function convergent series coordinates corresponding cosh curve defined definition denote derivatives differential equation displacement distance equal essential singularity exists expansion expressed factor finite number formula Fourier Fourier series give given harmonic Heine-Borel theorem Hence infinite integral interpolation interval Laplace's equation lemma limit linear matrix method modulus motion multiple negative notation orthogonal particle path plane poles polynomial positive potential power series prove real numbers region relations Riemann integral rotation satisfied scalar Similarly single-valued singularity sinh solution sphere suffix surface tend to zero tensor theorem transformation uniformly convergent values vanish variable vector velocity waves y₁