Catálogo de la biblioteca Antonio Monteiro - INMABB

Incluye referencias bibliográficas (p. 203-204) e índice.

TABLE OF CONTENTS --
PREFACE v --
Chapter I --
COMPLEX NUMBERS [1] --
Definition. --
Fundamental Operations. --
Laws of Algebra. --
Geometric Representation. --
Complex Conjugates. --
Absolute Values. --
The Polar Form. --
Products, Powers, and Quotients. --
Extraction of Roots. --
The nth Roots of Unity. --
Regions in the Complex Plane. --
Chapter II --
ANALYTIG FUNCTIONS [18] --
Functions of a Complex Variable. --
Limits. --
Theorems on Limits. --
Continuity. --
The Derivative. --
Differentiation Formulas. --
The Cauchy-Riemann Conditions. --
Sufficient Conditions. --
Analytic Functions. --
Algebraic Functions. --
Harmonic Functions. --
Chapter III --
ELEMENTARY FUNCTIONS [37] --
The Exponential Function. --
Other Properties of the Exponential Function. --
The Trigonometric Functions. --
Further Properties of the Trigonometric Functions. --
The Hyperbolic Functions. --
The Logarithmic Function. --
The Inverse Trigonometric Functions. --
Chapter IV --
THE GEOMETRY OF ELEMENTARY FUNCTIONS [50] --
Mapping. --
Linear Functions. --
Powers of z. --
The Function 1/z. --
The Point - -at Infinity. --
The Linear Fractional Transformation. --
Further Properties of the Linear Fractional Transformation. --
Special Linear Fractional Transformations. --
The Function, z1/2 --
Other Irrational Functions. --
The Transformation w = exp z. --
The Transformation w = sin z. --
Successive Transformations. --
Table of Transformations of Regions. --
Chapter V --
INTEGRALS [74] --
Line Integrals. --
Examples. --
Properties of Integrals. --
The Cauchy-Goursat Theorem. --
A Preliminary Theorem. --
Proof of the Cauchy-Goursat Theorem. --
Multiply Connected Regions. --
Indefinite Integrals. --
The Cauchy Integral Formula. --
Derivatives of Analytic Functions. --
Morera’s Theorem. --
Integral Functions. --
The Fundamental Theorem of Algebra. --
Chapter VI --
VQVTER. SERIES [98] --
Taylor’s Series. --
Observations and Examples. --
Laurent’s Series. --
Properties of Power Series. --
Uniform Convergence. --
Integration and Differentiation of Power Serie. --
Uniqueness of Representations by Power Senes. --
Multiplication and Division. --
Examples. --
Chapter VII RESIDUES AND POLES [116] --
Residues. --
The Residue Theorem. --
Poles. --
Computation of Residues at Poles. --
Evaluation of Real Infinite Integrals. --
Another Example. --
Infinite Integrals Involving Trigonometric Functions. --
Definite Integrals of Trigonometric Functions. --
Integration around a Branch Point. --
Chapter VIII CQNFQRMAL MAPPING [135] --
Rotation of Tangents. --
Conformal Mapping. --
Examples. --
Conjugate Harmonic Functions. --
Inverse Functions. --
Transformation of Harmonic Functions. --
Transformation of Boundary Conditions. --
Chapter IX --
APPLICATIONS OF CONFORMAL MAPPING [147] --
Steady Temperatures. --
Steady Temperatures in a Wall. --
Temperatures in a Quadrant with Part of One Boundary Insulated. --
Electric Potential. --
Potential in a Cylindrical Space. --
Two-dimensional Fluid Flow. --
The Stream Function. --
Flow around a Corner; Flow around a Cylinder. --
Chapter X --
THE SCHWARZ-CHRISTOFFEL TRANSFORMATION [171] --
The Transformation of the Real Axis into a Polygon. --
The Schwarz-Christof-fel Transformation. --
Triangles and Rectangles. --
Degenerate Polygons. --
The Infinite Strip. --
Fluid Flow in a Channel through a Slit. --
Flow in a Channel with an Offset. --
Electrostatic Potential about an Edge of a Conducting Plate. --
Chapter XI --
ANALYTIC CONTINUATION [188] --
Analytic Continuation. --
Examples. --
Natural Boundaries. --
The Principle of Reflection. --
The Zeros of Analytic Functions. --
Essential Singular --
Points --
Chapter XII --
RIEMANN SURFACES [197] --
A Surface for the Function log z. --
A Surface for the Function z1/2 --
Other Irrational Functions. --
Appendix I --
BIBLIOGRAPHY [203] --
Appendix II --
TABLE OF TRANSFORMATIONS OF REGIONS [.205] --
INDEX [213] --

MR, 10,439f