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El. knyga: Complex Variables Demystified

3.88/5 (32 ratings by Goodreads)
  • Formatas: 384 pages
  • Serija: Demystified
  • Išleidimo metai: 14-Aug-2008
  • Leidėjas: McGraw-Hill Professional
  • Kalba: eng
  • ISBN-13: 9780071549219
Kitos knygos pagal šią temą:
  • Formatas: 384 pages
  • Serija: Demystified
  • Išleidimo metai: 14-Aug-2008
  • Leidėjas: McGraw-Hill Professional
  • Kalba: eng
  • ISBN-13: 9780071549219
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Take the complication out of COMPLEX VARIABLES

Ready to learn the fundamentals of complex variables but can't seem to get your brain to function on the right level? No problem! Add Complex Variables Demystified to the equation and you'll exponentially increase your chances of understanding this fascinating subject.

Written in an easy-to-follow format, this book begins by covering complex numbers, functions, limits, and continuity, and the Cauchy-Riemann equations. You'll delve into sequences, Laurent series, complex integration, and residue theory. Then it's on to conformal mapping, transformations, and boundary value problems. Hundreds of examples and worked equations make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce learning.

This fast and easy guide offers:





Numerous figures to illustrate key concepts

Sample problems with worked solutions

Coverage of Cauchy-Riemann equations and the Laplace transform

Chapters on the Schwarz-Christoffel transformation and the gamma and zeta functions

A time-saving approach to performing better on an exam or at work

Simple enough for a beginner, but challenging enough for an advanced student, Complex Variables Demystified is your integral tool for understanding this essential mathematics topic.
Preface xi
Complex Numbers
1(20)
The Algebra of Complex Numbers
2(2)
Complex Variables
4(1)
Rules for the Complex Conjugate
5(4)
Pascal's Triangle
9(1)
Axioms Satisfied by th Complex Number System
10(2)
Properties to the Modulus
12(1)
The Polar Representation
12(4)
The nth Roots of Unity
16(3)
Summary
19(1)
Quiz
19(2)
Functions, Limits, and Continuity
21(20)
Complex Functions
21(7)
Plotting Complex Functions
28(5)
Multivalued Functions
33(1)
Limits of Complex Functions
33(5)
Limits Involving Functions
38(1)
Continuity
38(2)
Summary
40(1)
Quiz
40(1)
The Derivative and Analytic Functions
41(24)
The Derivative Defined
42(1)
Leibniz Notation
43(2)
Rules for Differentiation
45(2)
Derivatives the Some Elementary Functions
47(1)
The Product and Quotient Rules
48(3)
The Cauchy-Riemann Equations
51(1)
The Polar Representation
51(8)
Some Consequences of the Cauchy-Riemann Equations
59(2)
Harmonic Functions
61(2)
The Reflection Principle
63(1)
Summary
64(1)
Quiz
64(1)
Elementary Functions
65(26)
Complix Polynomials
65(5)
The Complex Exponential
70(5)
Trigonometric Functions
75(3)
The Hyperbolic Functions
78(6)
Complex Exponents
84(1)
Derivaties of Some Elementary Functions
85(3)
Branches
88(1)
Summary
89(1)
Quiz
89(2)
Sequences and Series
91(26)
Sequences
91(3)
Infinite Series
94(1)
Convergence
94(2)
Convergence Tests
96(1)
Uniformly Converging Series
97(1)
Power Series
97(1)
Taylor and Maclaurin Series
98(1)
Theorems and Power Series
98(2)
Some Common Series
100(9)
Laurent Series
109(2)
Types of Singularities
111(1)
Entire Functions
112(1)
Meromorphic Functions
112(2)
Summary
114(1)
Quiz
114(3)
Complex Integration
117(7)
Complex Functins w(t)
117(2)
Properties of Complex Integrals
119(2)
Contours in the Complex Plane
121(3)
Complex Line Integrals
124(11)
The Cauchy-Goursat Theorem
127(6)
Summary
133(1)
Quiz
134(1)
Residue Theory
135(28)
Theorems Related to Cauchy's Integral Formula
135(8)
The Cauch's Integral Formula as a Sampling Function
143(1)
Some Properties of Analytic Functions
144(4)
The Residue Theorem
148(3)
Evaluation of Real, Definite Integrals
151(4)
Integral of a Rational Function
155(6)
Summary
161(1)
Quiz
161(2)
More Complex Integration and the Laplace Transform
163(20)
Contour Integration Continued
163(4)
The Laplace Transform
167(12)
The Bromvich Inversion Integral
179(2)
Summary
181(1)
Quiz
181(2)
Mapping and Transformations
183(20)
Linear Transformations
184(4)
The Transformation zn
188(2)
Conformal Mapping
190(1)
The Mapping 1/z
190(2)
Mapping of Infinite Strips
192(2)
Rules of Thumb
194(1)
Mobius Transformations
195(6)
Fixed Points
201(1)
Summary
202(1)
Quiz
202(1)
The Schwarz-Christoffel Tranformation
203(6)
The Riemann Mapping Theorem
203(1)
The Schwarz-Christoffel Transformation
204(3)
Summary
207(1)
Quiz
207(2)
The Gamma and Zeta Functions
209(22)
The Gamma Function
209(10)
More Properties of the Gamma Function
219(5)
Contour Integral Representation and Stirling' Formula
224(1)
The Beta Fuction
224(1)
The Riemann Zeta Function
225(5)
Summary
230(1)
Quiz
230(1)
Boundary Valur Problems
231(18)
Laplace's Equations and Harmonic Functions
231(3)
Solving Boundary Valure Problems Using Conformal Mapping
234(10)
Green's Functions
244(3)
Summary
247
Quiz
246(3)
Final Exam 249(6)
Quiz Solutions 255(6)
Final Exam Solutions 261(6)
Bibliography 267(2)
Index 269
David McMahon is a Microsoft Certified Visual Basic developer. He writes object-oriented software and hardware drivers for Windows NT and 95/98 using Visual Basic and Visual C++. He is also a Microsoft Certification instructor for Visual Basic and Microsoft Access.