Applied Mathematics

By: Gerald D. Mahan

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Hardcover | 31 December 2001

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Hardcover
384 Pages

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24.77 x 17.78 x 1.91

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This volume is a textbook for a year-long graduate level course in All research universities have applied mathematics for scientists and engineers. such a course, which could be taught in different departments, such as mathematics, physics, or engineering. I volunteered to teach this course when I realized that my own research students did not learn much in this course at my university. Then I learned that the available textbooks were too introduc tory. While teaching this course without an assigned text, I wrote up my lecture notes and gave them to the students. This textbook is a result of that endeavor. When I took this course many, many, years ago, the primary references were the two volumes of P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, 1953). The present text returns the contents to a similar level, although the syllabus is quite different than given in this venerable pair of books.

Industry Reviews

`...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

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Determinants	p. 1
Cramer's Rule	p. 3
Gaussian Elimination	p. 4
Special Determinants	p. 7
Matrices	p. 13
Several Theorems	p. 14
Linear Equations	p. 15
Inverse of a Matrix	p. 17
Eigenvalues and Eigenvectors	p. 18
Unitary Transformations	p. 23
Hon-Hermitian Matrices	p. 25
A Special Matrix	p. 32
Gram-Schmidt	p. 34
Chains	p. 38
Group Theory	p. 47
Basic Properties of Groups	p. 47
Group Representations	p. 51
Characters	p. 54
Direct Product Groups	p. 58
Basis Functions	p. 60
Angular Momentum	p. 61
Products of Representations	p. 64
Quantum Mechanics	p. 64
Double Groups	p. 68
Complex Variables	p. 73
Introduction	p. 73
Analytic Functions	p. 75
Multivalued Functions	p. 80
Contour Integrals	p. 84
Meromorphic Functions	p. 99
Higher Poles	p. 101
Integrals Involving Branch Cuts	p. 102
Approximate Evaluation of Integrals	p. 109
Series	p. 119
Taylor Series	p. 119
Convergence	p. 121
Laurent Series	p. 126
Meromorphic Functions	p. 128
Asymptotic Series	p. 129
Summing Series	p. 132
Pade Approximants	p. 135
Conformal Mapping	p. 141
Laplace's Equation	p. 141
Mapping	p. 144
Examples	p. 149
Schwartz-Christoffel Transformations	p. 157
van der Pauw	p. 167
Markov Averaging	p. 177
Random Walk	p. 177
Speckle	p. 183
Inhomogeneous Broadening	p. 188
Fourier Transforms	p. 195
Fourier Transforms	p. 195
Laplace Transforms	p. 202
Wavelets	p. 205
Equations of Physics	p. 217
Boundary and Initial Conditions	p. 218
Boltzmann Equation	p. 218
Solving Differential Equations	p. 225
Elliptic Integrals	p. 235
One Dimension	p. 237
Introduction	p. 237
Diffusion Equation	p. 240
Wave Equation	p. 252
Two Dimensions	p. 265
Rectangular Coordinates	p. 265
Polar Coordinates	p. 273
Three Dimensions	p. 297
Cartesian Coordinates	p. 297
Cylindrical Coordinates	p. 299
Spherical Coordinates	p. 305
Problems Inside a Sphere	p. 315
Vector Wave Equation	p. 319
Odds and Ends	p. 333
Hypergeometric Functions	p. 333
Orthogonal Polynomials	p. 343
Sturm-Liouville	p. 347
Green's Functions	p. 352
Singular Integral Equations	p. 357
Index	p. 365
Table of Contents provided by Blackwell. All Rights Reserved.

Applied Mathematics

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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Paperback

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