Fundamentals of Complex Analysis with Applications to Engineering and Science

E.B. Saff, A.D. Snider

574 pages, parution le 11/02/2003 (3^eme édition)

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Résumé

The raison d'existence for Fundamentals of Complex Analysis with Applications to Engineering and Science, 3/e is our conviction that engineering, science, and mathematics undergraduates who have completed the calculus sequence are capable of understanding the basics of complex analysis and applying its methods to solve engineering problems. Accordingly, we address ourselves to this audience in our attempt to make the fundamentals of the subject more easily accessible to readers who have little inclination to wade through the rigors of the axiomatic approach. To accomplish this goal we have modeled the text after standard calculus books, both in level of exposition and layout, and have incorporated engineering applications throughout the text so that the mathematical methodology will appear less sterile to the reader.

To be more specific about our mode of exposition, we begin by addressing the question most instructors ask first: To what extent is the book self contained, i.e., which results are proved and which are merely stated? Let us say that we have elected to include all the proofs that reflect the spirit of analytic function theory and to omit most of those that involve deeper results from real analysis (such as the convergence of Riemann sums for complex integrals, the Cauchy criterion for convergence, Goursat's generalization of Cauchy's theorem, or the Riemann mapping theorem). Moreover, in keeping with our philosophy of avoiding pedantics, we have shunned the ordered pairs interpretation of complex numbers and retained the more intuitive approach (grounded in algebraic field extensions).

Contents

Complex Numbers
Analytic Functions
Elementary Functions
Complex Integration
Series Representations for Analytic Functions
Residue Theory
Conformal Mapping
The Transforms of Applied Mathematics
Appendix A. Numerical Construction of Conformal Maps
Appendix B. Table of Conformal Mappings
Answers to Odd-Numbered Problems

Caractéristiques techniques

	PAPIER
Éditeur(s)	Prentice Hall
Auteur(s)	E.B. Saff, A.D. Snider
Parution	11/02/2003
Édition	3^eme édition
Nb. de pages	574
Format	18 x 24
Couverture	Relié
Poids	1016g
Intérieur	Noir et Blanc
EAN13	9780139078743
ISBN13	978-0-13-907874-3