Applied Mathematics

Front Cover
Springer Science & Business Media, Dec 31, 2001 - Mathematics - 368 pages
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.
 

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Contents

Determinants
1
11 Cramers Rules
3
12 Gaussian Elimination
4
13 Special Determinants
7
Matrices
13
21 Several Theorems
14
22 Linear Equations
15
23 Inverse of a Matrix
17
653 Mapping
172
Markov Averaging
177
72 Speckle
183
73 Inhomogeneous Broadening
188
Fourier Transforms
195
812 Half Space
197
813 Finite Systems in 1D
199
82 Laplace Transforms
202

24 Eigenvalues and Eigenvectors
18
25 Unitary Transformations
23
26 NonHermitian Matrices
25
27 A Special Matrix
32
28 GramSchmidt
34
29 Chains
38
Group Theory
47
32 Group Representations
51
33 Characters
54
34 Direct Product Groups
58
35 Basis Functions
60
36 Angular Momentum
61
37 Products of Representations
64
382 Representations
65
383 Matrix Elements
67
39 Double Groups
68
Complex Variables
73
42 Analytic Functions
75
43 Multivalued Functions
80
44 Contour Integrals
84
45 Meromorphic Functions
99
46 Higher Poles
100
47 Integrals Involving Branch Cuts
101
48 Approximate Evaluation of Integrals
108
481 Steepest Descent
109
482 Saddle Point Integrals
110
Series
119
52 Convergence
121
53 Laurent Series
126
54 Meromorphic Functions
128
55 Asymptotic Series
129
56 Summing Series
132
57 Fade Approximants
135
Conformal Mapping
141
62 Mapping
144
63 Examples
149
64 SchwartzChristoffel Transformations
157
65 van der Pauw
167
651 Currents
168
652 Resistance
170
83 Wavelets
205
831 Continuous Wavelet Transform
207
832 Discrete Transforms
210
Equations of Physics
217
91 Boundary and Initial Conditions
218
921 Moment Equations
219
922 Diffusion Equations
223
93 Solving Differential Equations
225
932 Inhomogeneous Linear Equations
227
933 Nonlinear Equations
229
94 Elliptic Integrals
235
One Dimension
237
102 Diffusion Equation
240
103 Wave Equation
252
Two Dimensions
265
1112 Diffusion Equation
268
1113 Wave Equation
272
112 Polar Coordinates
273
1121 Laplaces Equation
274
1122 Helmholtz Equation
279
1123 Hankel Transforms
286
Three Dimensions
297
122 Cylindrical Coordinates
299
123 Spherical Coordinates
305
1231 Laplaces Equation
306
1232 Diffusion and Wave Equations
309
124 Problems Inside a Sphere
315
125 Vector Wave Equation
319
1252 Boundary Conditions
320
Odds and Ends
333
1311 Continued Fractions
337
1312 Solving Equations With Series
339
132 Orthogonal Polynomials
343
1321 Parabolic Cylinder Functions
344
1323 Laguerre Polynomial
346
133 SturmLiouville Theory
347
134 Greens Functions
352
135 Singular Integral Equations
357
Index
365
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