《complex variables and applications seventh edition P458》求取 ⇩
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1.Complex Numbers1
Sums and Products1
Basic Algebraic Properties3
Further Properties5
Moduli8
Complex Conjugates11
Exponential Form15
Products and Quotients in Exponential Form17
Roots of Complex Numbers22
Examples25
Regions in the Complex Plane29
2.Analytic Functions33
Functions of a Complex Variable33
Mappings36
Mappings by the Exponential Function40
Limits43
Theorems on Limits46
Limits Involving the Point at Infinity48
Continuity51
Derivatives54
Differentiation Formulas57
Cauchy-Riemann Equations60
Sufficient Conditions for Differentiability63
Polar Coordinates65
Analytic Functions70
Examples72
Harmonic Functions75
Uniquely Determined Analytic Functions80
Reflection Principle82
3.Elementary Functions87
The Exponential Function87
The Logarithmic Function90
Branches and Derivatives of Logarithms92
Some Identities Involving Logathms95
Complex Exponents97
Trigonometric Functions100
Hyperbolic Functions105
Inverse Trigonometric and Hyperbolic Functions108
4.Integrals111
Derivatives of Functions w(t)111
Definite Integrals of Functions w(t)113
Contours116
Contour Integrals122
Examples124
Upper Bounds for Moduli of Contour Integrals130
Antiderivatives135
Examples138
Cauchy-Goursat Theorem142
Proof of the Theorem144
Simply and Multiply Connected Domains149
Cauchy Integral Formula157
Derivatives of Analytic Functions158
Liouville's Theorem and the Fundamental Theorem of Algebra165
Maximum Modulus Principle167
5.Series175
Convergence of Sequences175
Convergence of Series178
Taylor Series182
Examples185
Laurent Series190
Examples195
Absolute and Uniform Convergence of Power Series200
Continuity of Sums of Power Series204
Integration and Differentiation of Power Series206
Uniqueness of Series Representations210
Multiplication and Division of Power Series215
6.Residues and Poles221
Residues221
Cauchy's Residue Theorem225
Using a Single Residue227
The Three Types of Isolated Singular Points231
Residues at Poles234
Examples236
Zeros of Analytic Functions239
Zeros and Poles242
Behavior off Near Isolated Singular Points247
7.Applications of Residues251
Evaluation of Improper Integrals251
Example254
Improper Integrals from Fourier Analysis259
Jordan's Lemma262
Indented Paths267
An Indentation Around a Branch Point270
Integration Along a Branch Cut273
Definite Integrals Involving Sines and Cosines278
Argument Principle281
Rouche's Theorem284
Inverse Laplace Transforms288
Examples291
8.Mapping by Elementa Functions299
Linear Transformations299
The Transformation w = 1/z301
Mappings by 1/z303
Linear Fractional Transformations307
An Implicit Form310
Mappings of the Upper Half Plane313
The Transformation w = sin z318
Mappings by z2 and Branches of z1/2324
Square Roots of Polynomials329
Riemann Surfaces335
Surfaces for Related Functions338
9.Conformal Mapping343
Preservation of Angles343
Scale Factors346
Local Inverses348
Harmonic Conjugates351
Transformations of Harmonic Functions353
Transformations of Boundary Conditions355
10.Applications of Conformal Mapping361
Steady Temperatures361
Steady Temperatures in a Half Plane363
A Related Problem365
Temperatures in a Quadrant368
Electrostatic Potential373
Potential in a Cylindrical Space374
Two-Dimensional Fluid Flow379
The Stream Function381
Flows Around a Corner and Around a Cylinder383
11.The Schwarz-Christoffel Transformation391
Mapping the Real Axis onto a Polygon391
Schwarz-Christoffel Transformation393
Triangles and Rectangles397
Degenerate Polygons401
Fluid Flow in a Channel Through a Slit406
Flow in a Channel with an Offset408
Electrostatic Potential about an Edge of a Conducting Plate411
12.Integral Formulas of the Poisson Type417
Poisson Integral Formula417
Dirichlet Problem for a Disk419
Related Boundary Value Problems423
Schwarz Integral Formula427
Dirichlet Problem for a Half Plane429
Neumann Problems433
Appendixes437
Bibliography437
Table of Transformations of Regions441
Index451
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高度相关资料
- SEVERAL COMPLEX VARIABLES AND COMPLEX GEOMETRY PART 2
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- PRENTICE HALL INC
- Metric rigidity theorems on Hermitian locally symmetric manifolds
- 1989 World Scientific
- Several complex variables and complex manifolds 1l
- 1982 Cambridge University Press
- Several complex variables and complex manifolds 1
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- Complex variables with applications
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- Elements of complex variables
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- Complex variables for scientists and engineers
- 1975 Macmillan
- Complex variables and applications Foruth Edition
- 1984 McGraw-Hill
- Complex variables and applications Third Edition
- 1974 McGraw-Hill
- APPLIED COMPLEX VARIABLES
- 1965 THE MACMILLAN COMPANY NEW YORK COLLIER-MACMILLAN LIMITED LONDON
- SEVERAL COMPLEX VARIABLES
- 1948 PRINCETON PRINCETON UNIVERSITY PRESS
- Serval Complex Variables and Complex Geometry
- 1991 Amercian Mathematical Society
- Several Complex Variables
- 1977 American Mathematical Society
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