Applied Mathematics

AvGerald D. Mahan

Inbunden, Engelska, 2001

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Beskrivning

This is a textbook for a two-semester graduate course in mathematical methods in physics. Most universities give this course, which is often taught jointly with the engineering or mathematics departments. General topics include: group theory; linear equations; matrices; series; functions of complex variables; conformal mapping; special functions; and partial differential equations. Each chapter has numerous homework problems. The section on transforms includes those on Fourier and Laplace, as well as the modern topic of wavelets. The chapters on partial differential equations include: Laplace's; Poisson's; Helmholtz; diffusion; and wave equations. Problems are treated in one, two, and three dimensions.

Produktinformation

Utgivningsdatum:2001-12-31
Mått:178 x 254 x 27 mm
Vikt:916 g
Format:Inbunden
Språk:Engelska
Antal sidor:368
Upplaga:2002
Förlag:Springer Science+Business Media
ISBN:9780306466830

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Recensioner i media

'...the treatment is user-friendly. [...] The printing is excellent and the publishers are to be thanked for producing a hard back volume for what is, these days, a reasonable price. I have no hesitation giving a warm recommendation for this book.' Mathematical Reviews, 2003

Innehållsförteckning

1. Determinants.- 1.1. Cramer’s Rule.- 1.2. Gaussian Elimination.- 1.3. Special Determinants.- 2. Matrices.- 2.1. Several Theorems.- 2.2. Linear Equations.- 2.3. Inverse of a Matrix.- 2.4. Eigenvalues and Eigenvectors.- 2.5. Unitary Transformations.- 2.6. Hon-Hermitian Matrices.- 2.7. A Special Matrix.- 2.8. Gram-Schmidt.- 2.9. Chains.- 3. Group Theory.- 3.1. Basic Properties of Groups.- 3.2. Group Representations.- 3.3. Characters.- 3.4. Direct Product Groups.- 3.5. Basis Functions.- 3.6. Angular Momentum.- 3.7. Products of Representations.- 3.8. Quantum Mechanics.- 3.9. Double Groups.- 4. Complex Variables.- 4.1. Introduction.- 4.2. Analytic Functions.- 4.3. Multivalued Functions.- 4.4. Contour Integrals.- 4.5. Meromorphic Functions.- 4.6. Higher Poles.- 4.7. Integrals Involving Branch Cuts.- 4.8. Approximate Evaluation of Integrals.- 5. Series.- 5.1. Taylor Series.- 5.2. Convergence.- 5.3. Laurent Series.- 5.4. Meromorphic Functions.- 5.5. Asymptotic Series.- 5.6. Summing Series.- 5.7. Padé Approximants.- 6. Conformal Mapping.- 6.1. Laplace’s Equation.- 6.2. Mapping.- 6.3. Examples.- 6.4. Schwartz-Christoffel Transformations.- 6.5. van der Pauw.- 7. Markov Averaging.- 7.1. Random Walk.- 7.2. Speckle.- 7.3. Inhomogeneous Broadening.- 8. Fourier Transforms.- 8.1. Fourier Transforms.- 8.2. Laplace Transforms.- 8.3. Wavelets.- 9. Equations of Physics.- 9.1. Boundary and Initial Conditions.- 9.2. Boltzmann Equation.- 9.3. Solving Differential Equations.- 9.4. Elliptic Integrals.- 10. One Dimension.- 10.1. Introduction.- 10.2. Diffusion Equation.- 10.3. Wave Equation.- 11. Two Dimensions.- 11.1. Rectangular Coordinates.- 11.2. Polar Coordinates.- 12. Three Dimensions.- 12.1. Cartesian Coordinates.- 12.2. Cylindrical Coordinates.- 12.3. Spherical Coordinates.- 12.4.Problems Inside a Sphere.- 12.5. Vector Wave Equation.- 13. Odds and Ends.- 13.1. Hypergeometric Functions.- 13.2. Orthogonal Polynomials.- 13.3. Sturm-Liouville.- 13.4. Green’s Functions.- 13.5. Singular Integral Equations.