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Schaum's Outlines-Problem Solved.
Author(s): Murray Spiegel, Seymour Lipschutz, John Schiller, Dennis Spellman
Series: Schaum's Outline Series
Edition: 2
Publisher: McGraw-Hill
Year: 2009
Language: English
Pages: 385
Contents......Page 8
1.2 Graphical Representation of Real Numbers......Page 12
1.4 Fundamental Operations with Complex Numbers......Page 13
1.7 Graphical Representation of Complex Numbers......Page 14
1.9 De Moivre’s Theorem......Page 15
1.12 Polynomial Equations......Page 16
1.15 Stereographic Projection......Page 17
1.18 Point Sets......Page 18
2.3 Inverse Functions......Page 52
2.5 Curvilinear Coordinates......Page 53
2.6 The Elementary Functions......Page 54
2.7 Branch Points and Branch Lines......Page 56
2.10 Theorems on Limits......Page 57
2.12 Continuity......Page 58
2.15 Sequences......Page 59
2.18 Infinite Series......Page 60
3.3 Cauchy–Riemann Equations......Page 88
3.5 Geometric Interpretation of the Derivative......Page 89
3.7 Rules for Differentiation......Page 90
3.8 Derivatives of Elementary Functions......Page 91
3.11 Singular Points......Page 92
3.12 Orthogonal Families......Page 93
3.14 Applications to Geometry and Mechanics......Page 94
3.16 Gradient, Divergence, Curl, and Laplacian......Page 95
4.1 Complex Line Integrals......Page 122
4.4 Properties of Integrals......Page 123
4.6 Simply and Multiply Connected Regions......Page 124
4.10 Complex Form of Green’s Theorem......Page 125
4.14 Integrals of Special Functions......Page 126
4.15 Some Consequences of Cauchy’s Theorem......Page 128
5.1 Cauchy’s Integral Formulas......Page 155
5.2 Some Important Theorems......Page 156
6.2 Series of Functions......Page 180
6.5 Power Series......Page 181
6.6 Some Important Theorems......Page 182
6.8 Some Special Series......Page 184
6.9 Laurent’s Theorem......Page 185
6.10 Classification of Singularities......Page 186
6.14 Analytic Continuation......Page 187
7.2 Calculation of Residues......Page 216
7.3 The Residue Theorem......Page 217
7.5 Special Theorems Used in Evaluating Integrals......Page 218
7.7 Differentiation Under the Integral Sign. Leibnitz’s Rule......Page 219
7.10 Some Special Expansions......Page 220
8.2 Jacobian of a Transformation......Page 253
8.5 Riemann’s Mapping Theorem......Page 254
8.7 Some General Transformations......Page 255
8.10 The Bilinear or Fractional Transformation......Page 256
8.12 The Schwarz–Christoffel Transformation......Page 257
8.14 Some Special Mappings......Page 258
9.3 Dirichlet and Neumann Problems......Page 291
9.5 The Dirichlet Problem for the Half Plane......Page 292
9.7 Basic Assumptions......Page 293
9.8 The Complex Potential......Page 294
9.11 Some Special Flows......Page 295
9.14 Theorems of Blasius......Page 297
9.16 Electric Field Intensity. Electrostatic Potential......Page 298
9.19 Line Charges......Page 299
9.23 The Complex Temperature......Page 300
10.1 Analytic Continuation......Page 330
10.4 Absolute, Conditional and Uniform Convergence of Infinite Products......Page 331
10.8 The Gamma Function......Page 332
10.9 Properties of the Gamma Function......Page 333
10.11 Differential Equations......Page 334
10.13 Bessel Functions......Page 336
10.14 Legendre Functions......Page 338
10.16 The Zeta Function......Page 339
10.17 Asymptotic Series......Page 340
10.19 Special Asymptotic Expansions......Page 341
10.20 Elliptic Functions......Page 342
C......Page 380
E......Page 381
J......Page 382
P......Page 383
S......Page 384
Z......Page 385
