Complex Variables II Essentials
Published on 1. January 2013
196 pages
978-0-7386-7217-5 (ISBN)
Description
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Complex Variables II includes elementary mappings and Mobius transformation, mappings by general functions, conformal mappings and harmonic functions, applying complex functions to applied mathematics, analytic continuation, and analytic function properties.
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A. Solomon
Complex Variables: v. 2
Book
01/1994
Research & Education Association,U.S.
€26.13
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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
