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A First Course in Complex Analysis with Applications, 2/e

A First Course in Complex Analysis with Applications, 2/e

          
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About the Book

The new Second Edition of A First Course in Complex Analysis with Applications is a truly accessible introduction to the fundamental principles and applications of complex analysis. Designed for the undergraduate student with a calculus background but no prior experience with complex variables, this text discusses theory of the most relevant mathematical topics in a student-friendly manner. With Zill’s clear and straightforward writing style, concepts are introduced through numerous examples and clear illustrations. Students are guided and supported through numerous proofs providing them with a higher level of mathematical insight and maturity. Each chapter contains a separate section on the applications of complex variables, providing students with the opportunity to develop a practical and clear understanding of complex analysis.

About the Author

Dennis G. Zill - Loyola Marymount University Dennis G. Zill, Loyola Marymount University. He received a PhD in applied mathematics from Iowa State University and is currently professor of mathematics and former chair of the mathematics department at Loyola Marymount University in Los Angeles. Zill’s research interests include Applied Mathematics, Special Functions, and Integral Transforms. Patrick Shanahan - Loyola Marymount University Patrick Shanahan, Loyola Marymount University Shanahan received his Ph.D. from the University of California, Santa Barbara, 1996; his M.A. from the University of California, Santa Barbara, 1992; and his B.A. from California State University, Long Beach, 1990. Currently Patrick’s research interests include Geometric topology, knot theory, hyperbolic geometry, and representation theory.



Table of Contents:
Chapter 1: Complex Numbers and the Complex Plane • Complex numbers and their properties • Complex plane • Polar form of complex numbers • Power and roots • Sets of points in the complex plane • Applications • Chapter 1 Review quiz Chapter 2: Complex Functions and Mappings • Complex functions • Complex functions as mappings • Linear mappings • Special power functions • Reciprocal function • Limits and continuity • Applications • Chapter 2: Review quiz Chapter 3: Analytic Functions • Differentiability and analyticity • Cauchy- Reimann equations • Harmonic functions • Applications • Chapter 3 Review quiz Chapter 4: Elementary Functions • Exponential and logarithmic functions • Complex powers • Trigonometric and hyperbolic functions • Inverse trigonometric and hyperbolic functions • Applications • Chapter 4 Review Quiz Chapter 5: Integration in the Complex Plane • Real integrals • Complex integrals • Cauchy-Goursat Theorem • Independence of Path • Cauchy’s Integral formulas and their consequences • Applications • Chapter 5 Review quiz Chapter 6: Series and Residues • Sequences and series • Taylor series • Laurent series • Zeros and poles • Residue and residue theorem • Some consequences of the residue theorem • Applications • Chapter 6 Review quiz Chapter 7: Conformal Mappings • Conformal mapping • Linear fractional transformations • Schwartz- Christoffel Transformations • Poisson integral formulas • Applications 1 Chapter 7 Review quiz Appendices • Proof of Theorem 2.6.1 APP-1 • Proof of the Cauchy- Goursat Theorem • Table of conformal mappings


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Product Details
  • ISBN-13: 9789380108193
  • Publisher: Jones & Bartlett India Private Limited
  • Binding: Paperback
  • Height: 279 mm
  • No of Pages: 458
  • ISBN-10: 9380108192
  • Publisher Date: 2013
  • Edition: 2
  • Language: English
  • Width: 216 mm

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