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More copies of this ISBNOther titles in the Mathematics Series series:Applied Complex Variables (Mathematics Series)by John W Dettman
Synopses & ReviewsPublisher Comments:Analytic function theory is a traditional subject going back to Cauchy and Riemann in the 19th century. Once the exclusive province of advanced mathematics students, its applications have proven vital to today's physicists and engineers. In this highly regarded work, Professor John W. Dettman offers a clear, wellorganized overview of the subject and various applications — making the oftenperplexing study of analytic functions of complex variables more accessible to a wider audience. The first half of Applied Complex Variables, designed for sequential study, is a stepbystep treatment of fundamentals, presenting superior coverage of concepts of complex analysis, including the complex number plane; functions and limits; the CauchyRiemann conditions for differentiability; Riemann surfaces; the definite integral; power series; meromorphic functions; and much more. The second half provides lucid exposition of five important applications of analytic function theory, each approachable independently of the others: potential theory; ordinary differential equations; Fourier transforms; Laplace transforms; and asymptotic expansions. Helpful exercises are included at the end of each topic in every chapter. The twopart structure of Applied Complex Variables affords the college instructor maximum classroom flexibility. Once fundamentals are mastered, applications can be studied in any sequence desired. Depending on how many are selected for study, Professor Dettman's impressive text is ideal for either a one or twosemester course. And, of course, the ambitious student possessing a knowledge of basic calculus will find its straightforward approach rewarding to his independent study efforts. Applied Complex Variables is a cogent, wellwritten introduction to an important and exciting branch of advanced mathematics — serving both the theoretical needs of the mathematics specialist and the applied math needs of the physicist and engineer. Students and teachers alike will welcome this timely, moderately priced reissue of a widely respected work. Synopsis:Fundamentals of analytic function theory — plus lucid exposition of 5 important applications: potential theory, ordinary differential equations, Fourier transforms, Laplace transforms, and asymptotic expansions. Includes 66 figures. Synopsis:Fundamentals of analytic function theory — plus lucid exposition of 5 important applications: potential theory, ordinary differential equations, Fourier transforms, Laplace transforms, asymptotic expansions. Includes 66 figures and features exercises at end of each chapter.
Synopsis:First half of this highlyregarded book covers complex number plane; functions and limits; Riemann surfaces, the definite integral; power series; meromorphic functions, and much more. The second half deals with potential theory; ordinary differential equations; Fourier transforms; Laplace transforms and asymptotic expansion. Exercises included. Table of ContentsPart I. Analytic Function Theory
Chapter 1. The Complex Number Plane 1.1 Introduction 1.2 Complex Numbers 1.3 The Complex Plane 1.4 Point Sets in the Plane 1.5 Stereographic Projection. The Extended Complex Plane 1.6 Curves and Regions Chapter 2. Functions of a Complex Variable 2.1 Functions and Limits 2.2 Differentiability and Analyticity 2.3 The CauchyRiemann Conditions 2.4 Linear Fractional Transformations 2.5 Transcendental functions 2.6 Riemann Surfaces Chapter 3. Integration in the Complex Plane 3.1 Line Integrals 3.2 The Definite Integral 3.3 Cauchy's Theorem 3.4 Implications of Cauchy's Theorem 3.5 Functions Defined by Integration 3.6 Cauchy Formulas 3.7 Maximum Modulus Principle Chapter 4. Sequences and Series 4.1 Sequences of Complex Numbers 4.2 Sequences of Complex Functions 4.3 Infinite Series 4.4 Power Series 4.5 Analytic Continuation 4.6 Laurent Series 4.7 Double Series 4.8 Infinite Products 4.9 Improper Integrals 4.10 The Gamma Function Chapter 5. Residue Calculus 5.1 The Residue Theorem 5.2 Evaluation of Real Integrals 5.3 The Principle of the Argument 5.4 Meromorphic Functions 5.5 Entire Functions Part II. Applications of Analytic Function Theory Chapter 6. Potential Theory 6.1 Laplace's Equation in Physics 6.2 The Dirichlet Problem 6.3 Green's Functions 6.4 Conformal Mapping 6.5 The SchwarzChristoffel Transformation 6.6 Flows with Sources and Sinks 6.7 Volume and Surface Distributions 6.8 Singular Integral Equations Chapter 7. Ordinary Differential Equations 7.1 Separation of Variables 7.2 Existence and Uniqueness Theorems 7.3 Solution of a Linear SecondOrder Differential Equation Near an Ordinary Point 7.4 Solution of a Linear SecondOrder Differential Equation Near a Regular Singular Point 7.5 Bessel Functions 7.6 Legendre Functions 7.7 SturmLiouville Problems 7.8 Fredholm Integral Equations Chapter 8. Fourier Transforms 8.1 Fourier Series 8.2 The Fourier Integral Theorem 8.3 The Complex Fourier Transform 8.4 Properties of the Fourier Transform 8.5 The Solution of Ordinary Differential Equations 8.6 The Solution of Partial Differential Equations 8.7 The Solution of Integral Equations Chapter 9. Laplace Transforms 9.1 From Fourier to Laplace Transform 9.2 Properties of the Laplace Transform 9.3 Inversion of Laplace Transforms 9.4 The Solution of Ordinary Differential Equations 9.5 Stability 9.6 The Solution of Partial Differential Equations 9.7 The Solution of Integral Equations Chapter 10. Asymptotic Expansions 10.1 Introduction and Definitions 10.2 Operations on Asymptotic Expansions 10.3 Asymptotic Expansion of Integrals 10.4 Asymptotic Solutions of Ordinary Differential Equations References; Index What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
Other books you might likeRelated SubjectsScience and Mathematics » Mathematics » Advanced Science and Mathematics » Mathematics » Calculus » General Science and Mathematics » Mathematics » Complex Analysis Science and Mathematics » Mathematics » Functional Analysis Science and Mathematics » Mathematics » General 

