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Complex Variables 2ND Editionby Stephen Fisher
Synopses & ReviewsPlease note that used books may not include additional media (study guides, CDs, DVDs, solutions manuals, etc.) as described in the publisher comments.
Publisher Comments:Hundreds of solved examples, exercises, and applications help students gain a firm understanding of the most important topics in the theory and applications of complex variables. Topics include the complex plane, basic properties of analytic functions, analytic functions as mappings, analytic and harmonic functions in applications, and transform methods. Perfect for undergrads/grad students in science, mathematics, engineering. A threesemester course in calculus is sole prerequisite. 1990 edition. Appendices. Book News Annotation:Fisher (Northwestern U.) introduces students with a calculus background to the theory and applications of complex variables. Appends exercise solutions and mapping and transform tables. This is a slightly corrected replication of the 1990 edition, differing mainly in its treatment of Cauchy's Theorem. Lacks references.
Annotation c. Book News, Inc., Portland, OR (booknews.com) Synopsis:Topics include the complex plane, basic properties of analytic functions, analytic functions as mappings, analytic and harmonic functions in applications, transform methods. Hundreds of solved examples, exercises, applications. 1990 edition. Appendices. Synopsis:Topics include the complex plane, basic properties of analytic functions, analytic functions as mappings, analytic and harmonic functions in applications, transform methods. Hundreds of solved examples, exercises, applications. 1990 edition. Appendices. Synopsis:Topics include the complex plane, basic properties of analytic functions, analytic functions as mappings, analytic and harmonic functions in applications, transform methods. Hundreds of solved examples, exercises, applications. 1990 edition. Appendices.
Table of Contents1. The complex plane
1.1 The complex numbers and the complex plane 1.1.1 A formal view of the complex numbers 1.2 Some geometry 1.3 Subsets of the plane 1.4 Functions and limits 1.5 The exponential, logarithm, and trigonometric functions 1.6 Line integrals and Green's theorem 2. Basic properties of analytic functions 2.1 Analytic and harmonic functions; the CauchyRiemann equations 2.1.1 Flows, fields, and analytic functions 2.2 Power series 2.3 Cauchy's theorem and Cauchy's formula 2.3.1 The CauchyGoursat theorem 2.4 Consequences of Cauchy's formula 2.5 Isolated singularities 2.6 The residue theorem and its application to the evaluation of definite integrals 3. Analytic functions as mappings 3.1 The zeros of an analytic function 3.1.1 The stability of solutions of a system of linear differential equations 3.2 Maximum modulus and mean value 3.3 Linear fractional transformations 3.4 Conformal mapping 3.4.1 Conformal mapping and flows 3.5 The Riemann mapping theorem and SchwarzChristoffel transformations 4. Analytic and harmonic functions in applications 4.1 Harmonic functions 4.2 Harmonic functions as solutions to physical problems 4.3 Integral representations of harmonic functions 4.4 Boundaryvalue problems 4.5 Impulse functions and the Green's function of a domain 5. Transform methods 5.1 The Fourier transform: basic properties 5.2 Formulas Relating u and û 5.3 The Laplace transform 5.4 Applications of the Laplace transform to differential equations 5.5 The ZTransform 5.5.1 The stability of a discrete linear system Appendix 1. The stability of a discrete linear system Appendix 2. A Table of Conformal Mappings Appendix 3. A Table of Laplace Transforms Solutions to OddNumbered Exercises Index What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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