Complex Variables I Essentials
Published on 1. January 2013
170 pages
978-0-7386-7243-4 (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 I includes functions of a complex variable, elementary complex functions, integrals of complex functions in the complex plane, sequences and series, and poles and residues.
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A. Solomon
Complex Variables: v.1
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 1 - BASIC DEFINITIONS
- 1.1 COMPLEX NUMBERS
- 1.2 ARITHMETIC OF THE COMPLEX NUMBERS
- 1.3 COMMUTATIVITY, ASSOCIATIVITY, AND DISTRIBUTIVITY
- 1.4 THE COMPLEX PLANE
- 1.5 THE MODULUS OF z
- 1.6 THE ARGUMENT AND THE POLAR FORM
- 1.7 EULER'S FORMULA
- 1.8 THE CIRCLE
- 1.9 n-TH POWERS AND n-TH ROOTS
- 1.10 SETS IN THE COMPLEX PLANE
- 1.11 OPEN, CLOSED, BOUNDED AND CONNECTED SETS
- 1.12 THE STEREOGRAPHIC PROJECTION
- CHAPTER 2 - FUNCTIONS OF A COMPLEX VARIABLE
- 2.1 BASIC CONCEPTS
- 2.2 SOME TYPES OF FUNCTIONS
- 2.3 THE GEOMETRY OF FUNCTIONS
- 2.4 LIMITS OF FUNCTIONS
- 2.5 PROPERTIES OF LIMITS
- 2.6 CONTINUITY
- 2.7 PROPERTIES OF CONTINUITY
- 2.8 DERIVATIVES OF COMPLEX FUNCTIONS
- 2.9 PROPERTIES OF THE DERIVATIVE
- 2.10 DIFFERENTIABILITY AND THE CAUCHY-RIEMANN EQUATIONS
- 2.11 ANALYTICITY
- 2.12 HARMONIC FUNCTIONS
- CHAPTER 3 - THE ELEMENTARY COMPLEX FUNCTIONS
- 3.1 REMARKS ON THE REAL FUNCTION y = tan-1 (x)
- 3.2 PRELIMINARIES
- 3.3 w = ez AND ITS KEY PROPERTIES
- 3.4 w= log(z) AND ITS KEY PROPERTIES
- 3.5 TRIGONOMETRIC FUNCTIONS
- 3.6 ADDITIONAL TRIGONOMETRIC FUNCTIONS
- 3.7 HYPERBOLIC FUNCTIONS AND THEIR PROPERTIES
- 3.8 INVERSE TRIGONOMETRIC AND HYPERBOLIC FUNCTIONS
- 3.9 DERIVATION OF THE RELATION FOR tan-1(z)
- CHAPTER 4 - INTEGRALS OF COMPLEX FUNCTIONS IN THE COMPLEX PLANE
- 4.1 CURVES IN THE COMPLEX PLANE
- 4.2 THE LINE INTEGRAL OF A CONTINUOUS FUNCTION
- 4.3 THE CAUCHY INTEGRAL THEOREM ON SIMPLY AND MULTIPLY CONNECTED DOMAINS
- 4.4 ANTIDERIVATIVES
- 4.5 THE CAUCHY INTEGRAL FORMULA
- 4.6 SOME THEOREMS ON BOUNDS
- 4.7 A PROOF OF THE FUNDAMENTAL THEOREM OF ALGEBRA
- CHAPTER 5 - SEQUENCES AND SERIES
- 5.1 SEQUENCES
- 5.2 SERIES
- 5.3 SEQUENCES AND SERIES OF FUNCTIONS
- 5.4 POWER SERIES
- 5.5 THE TAYLOR SERIES
- 5.6 THE LAURENT EXPANSION
- CHAPTER 6 - POLES AND RESIDUES
- 6.1 SINGULAR POINTS AND ZEROS
- 6.2 TYPES OF SINGULARITIES
- 6.3 IMPROPER INTEGRALS AND RESIDUES
