
Complex Variables II Essentials
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Content
- Intro
- Title Page
- Copyright Page
- WHAT "THE ESSENTIALS" WILL DO FOR YOU
- Table of Contents
- CHAPTER 7 - ELEMENTARY MAPPINGS AND THE MOBIUS TRANSFORMATION
- 7.1 REVIEW OF BASIC CONCEPTS
- 7.2 EXPANSIONS AND CONTRACTIONS
- 7.3 ROTATIONS
- 7.4 TRANSLATIONS
- 7.5 COMPOUND MAPPINGS
- 7.6 USING LINES, CIRCLES AND RECTANGLES TO UNDERSTAND MAPPINGS
- 7.7 THE LINEAR TRANSFORMATION
- 7.8 REFLECTION WITH RESPECT TO A CIRCLE AND THE REAL AXIS
- 7.9 INVERSION: THE MAPPING w = 1 / z
- 7.10 THE MOBIUS, OR LINEAR FRACTIONAL TRANSFORMATION
- CHAPTER 8 - MAPPINGS BY GENERAL FUNCTIONS
- 8.1 THE MAPPING w = z2
- 8.2 THE MAPPING w = z + 1/z
- 8.3. w = zn FOR n = 3,4,...
- 8.4 W = z1/2
- 8.5 THE MAPPING w = z1/n, n = 3, 4,...
- 8.6 w = ez
- 8.7 THE MAPPING w = log[(z - 1)/(z + 1)]
- 8.8 THE MAPPING w = sin(z)
- 8.9 THE SCHWARZ-CHRISTOFFEL TRANSFORMATION
- CHAPTER 9 - CONFORMAL MAPPINGS AND HARMONIC FUNCTIONS
- 9.1 CONFORMALITY
- 9.2 THE MAGNIFICATION AND SCALE FACTORS FOR AN ANALYTIC FUNCTION
- 9.3 HARMONIC FUNCTIONS
- 9.4 HARMONIC CONJUGATES
- 9.5 FINDING THE HARMONIC CONJUGATE OF A HARMONIC FUNCTION
- 9.6 PRESERVATION OF HARMONICITY UNDER A CONFORMAL MAPPING
- 9.7 THE POISSON AND SCHWARZ INTEGRAL FORMULAS
- CHAPTER 10 - APPLYING COMPLEX FUNCTIONS TO PROBLEMS OF APPLIED MATHEMATICS
- 10.1 BACKGROUND REMARKS ON HEAT TRANSFER
- 10.2 BOUNDARY CONDITIONS FOR THE STEADY STATE HEAT EQUATION
- 10.3 THE STEADY STATE HEAT CONDUCTION PROBLEM
- 10.4 SOLVING BOUNDARY VALUE PROBLEMS VIA CONFORMAL MAPPING
- 10.5 ELECTROSTATIC POTENTIALS AND CAPACITORS
- 10.6 APPLICATIONS TO FLUID DYNAMICS
- CHAPTER 11 - ANALYTIC CONTINUATION AND ADDITIONAL PROPERTIES OF ANALYTIC FUNCTIONS
- 11.1 THE ZEROS OF AN ANALYTIC FUNCTION
- 11.2 THE ANALYTIC CONTINUATION OF A FUNCTION
- 11.3 ANALYTIC CONTINUATION BY REFLECTION
- 11.4 ZEROS AND SINGULAR POINTS OF ANALYTIC FUNCTIONS
- 11.5 THE HADAMARD THREE-CIRCLES THEOREM
- 11.6 THE PHRAGMEN-LINDELOF THEOREM
- 11.7 REMARKS ON INFINITE PRODUCTS
- CHAPTER 12 - ADDITIONAL REMARKS ON CONFORMAL MAPPINGS
- 12.1 THE RIEMANN MAPPING THEOREM
- 12.2 INTRODUCTION TO RIEMANN SURFACES
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