9780073051949

Complex Variables and Applications

Brown, Ruel Churchill

8th Edition

This text serves as an introductory course in the theory and application of functions of a complex variable. The text is designed to develop the theory that is prominent in applications of the subject. Readers will find a special emphasis given to the application of residues and conformal mappings.

12

Functions of a Complex Variable

Exercises

p.37

14

Mappings by the Exponential Function

Exercises

p.44

18

Continuity

Exercises

p.55

20

Differentiation Formulas

Exercises

p.62

23

Polar Coordinates

Exercises

p.71

25

Examples

Exercises

p.77

26

Harmonic Functions

Exercises

p.81

28

Reflection Principle

Exercises

p.87

29

The Exponential Function

Exercises

p.92

31

Branches and Derivatives of Logarithms

Exercises

p.97

32

Some Identities Involving Logarithms

Exercises

p.100

33

Complex Exponents

Exercises

p.104

34

Trigonometric Functions

Exercises

p.108

35

Hyperbolic Functions

Exercises

p.111

36

Inverse Trigonometric and Hyperbolic Functions

Exercises

p.114

38

Definite Integrals of Functions w(t)

Exercises

p.121

39

Contours

Exercises

p.125

42

Examples with Branch Cuts

Exercises

p.135

43

Upper Bounds for Moduli of Contour Integrals

Exercises

p.140

45

Proof of the Theorem

Exercises

p.149

49

Multiply Connected Domains

Exercises

p.160

52

Some Consequences of the Extension

Exercises

p.170

54

Maximum Modulus Principle

Exercises

p.178

90

Linear Transformations

Exercises

p.313

92

Mappings by w = 1/z

Exercises

p.317

94

An Implicit Form

Exercises

p.324

95

Mappings of the Upper Half Plane

Exercises

p.329

96

The Transformation w = sin z

Exercises

p.334

97

Mappings by Z2 and Branches of Z1/2

Exercises

p.340

98

Square Roots of Polynomials

Exercises

p.346

99

Riemann Surfaces

Exercises

p.350

100

Surfaces for Related Functions

Exercises

p.353