Complex Variables for Scientists and Engineers: An Introduction

ISBN : 9780198509837

Richard Norton; Ernest S. Abers
464 Pages
174 x 246 mm
Pub date
Jul 2010
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Norton's Complex Variables for Scientists and Engineers is a new textbook, originally written for the Complex Analysis term of an undergraduate Mathematical Methods of Physics sequence at UCLA. It does not assume any prior knowledge of complex numbers or functions and is therefore suitable for a first course in the subject for undergraduate students who have had an introductory course in the standard calculus of real variables. The book provides a thorough grounding in the theory of complex functions. The mathematics is careful, yet accessible to any student who knows basic calculus. It covers the subjects essential in any scientific or engineering discipline that uses mathematics beyond the elementary level. The reader will find a clear presentation of complex differentiation and integration, Cauchy's theorem and integral formula, and infinite series and products. There is a long and thorough section on applying the residue theorem to the evaluation of real integrals, and a section on special functions and their integral representations. The book includes the conformal property of analytic functions and its applications to boundary value problems in electrostatics; a topological analysis that leads to the extension of the residue theorem to multiply-connected regions and contours; a section on the method of steepest descent; a section on the Riemann zeta function; and a discussion of the convergence of integral representations, which is rarely presented in detail in introductory texts. Those who want to see the mathematics done carefully, and who are looking for more than a 'cook-book' treatment that presents the basic techniques without exploring all the nooks and crannies of the subject, will find these sections especially satisfying. The preface suggests how to extract a bare-bones course for those in a hurry, without losing sight of the beauty and depth of the subjects.


1. Complex Numbers
2. Complex Functions
3. Differentiation and Analyticity
4. Complex Functions as Mappings
5. Closed Contours and Homology
6. Integration
7. Cauchy's Integral Formula
8. Multiply Connected Domains
9. Power Series
10. Sequences, Series, and Infinite Products
11. Isolated Singularities
12. The Residue Theorem
13. Real Integrals
14. Infinite Sums
15. Factoring Entire and Meromorphic Functions
16. Method of Steepest Descent
17. Integral Representations of the Gamma and Zeta Functions
18. Special Functions and Integral Representations

About the author: 

Richard Norton received his PhD from the University of Pennsylvania in 1958. After a few years as a Research Fellow at CalTech (California Institute of Technology), he joined the faculty of the Physics department at UCLA in 1962, where he remained until he retired in 1971. During that period he spent several sabbatical years at the Ecole Polytechnique in Paris (now at Palaiseau) and one year at the University of Paris at Orsay with a Guggenheim fellowship. His principal research interests were elementary particle theory and quantum field theory. From 1976 to 1885 be worked primarily in the area of relativistic many body systems. He died in 2009.

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