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# Schaum's Outlines: Complex variables by Murray Spiegel, Seymour Lipschutz, John Schiller, Dennis Spellman

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Schaum's Outlines: Complex variables written by Murray Spiegel, Seymour Lipschutz, John Schiller, Dennis Spellman .
The theory of functions of a complex variable, also called for brevity complex variables or complex analysis, is one of the beautiful as well as useful branches of mathematics. Although originating in an atmosphere of mystery, suspicion and distrust, as evidenced by the terms imaginary and complex present in the literature, it was finally placed on a sound foundation in the 19th century through the efforts of Cauchy, Riemann, Weierstrass, Gauss, and other great mathematicians.”
This book is designed for use as a supplement to all current standards texts or as a textbook for a formal course in complex variable theory and applications. It should also be of considerable value to those taking courses in mathematics, physics, aerodynamics, elasticity, and many other fields of science and engineering.”
Each chapter begins with a clear statement of pertinent definitions, principles and theorems together with illustrative and other descriptive material. This is followed by graded sets of solved and supplementary problems. . . . Numerous proofs of theorems and derivations of formulas are included among the solved problems. The large number of supplementary problems with answers serve as complete review of the material of each chapter.”
Topics covered include the algebra and geometry of complex numbers, complex differential and integral calculus, infinite series including Taylor and Laurent series, the theory of residues with applications to the evaluation of integrals and series, and conformal mapping with applications drawn from various fields.”
(Murray Spiegel)

Book Detail :-
Title: Schaum's Outlines: Complex variables
Edition:
Author(s): Murray Spiegel, Seymour Lipschutz, John Schiller, Dennis Spellman
Publisher: McGraw-Hill
Series: Schaum's Outline Series
Year: 2009
Pages: 385
Type: PDF
Language: English
ISBN: 0071615695,9780071615693
Country: US

Author Murray R. Spiegel Murray Ralph Spiegel was an author of technical books on applied mathematics, including a popular collection of Schaum's Outlines.
Spiegel was a native of Brooklyn and a graduate of New Utrecht High School. He received his bachelor's degree in mathematics and physics from Brooklyn College in 1943. He earned a master's degree in 1947 and doctorate in 1949, both in mathematics and both at Cornell University. He was a teaching fellow at Harvard University in 1943–1945, a consultant with Monsanto Chemical Company in the summer of 1946, and a teaching fellow at Cornell University from 1946 to 1949. He was a consultant in geophysics for Beers & Heroy in 1950, and a consultant in aerodynamics for Wright Air Development Center from 1950 to 1954. Spiegel joined the faculty of Rensselaer Polytechnic Institute in 1949 as an assistant professor. He became an associate professor in 1954 and a full professor in 1957. He was assigned to the faculty Rensselaer Polytechnic Institute of Hartford, CT, when that branch was organized in 1955, where he served as chair of the mathematics department. His PhD dissertation, supervised by Marc Kac, was titled On the Random Vibrations of Harmonically Bound Particles in a Viscous Medium.

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Schaum's Outlines: Complex variables written by Murray Spiegel, Seymour Lipschutz, John Schiller, Dennis Spellman cover the following topics.
1. COMPLEX NUMBERS
2. FUNCTIONS, LIMITS, AND CONTINUITY
3. COMPLEX DIFFERENTIATION AND THE CAUCHY–RIEMANN EQUATIONS
4. COMPLEX INTEGRATION AND CAUCHY’S THEOREM
5. CAUCHY’S INTEGRAL FORMULAS AND RELATED THEOREMS
6. INFINITE SERIES TAYLOR’S AND LAURENT’S SERIES
7. THE RESIDUE THEOREM EVALUATION OF INTEGRALS AND SERIES
8. CONFORMAL MAPPING
9. PHYSICAL APPLICATIONS OF CONFORMAL MAPPING
10. SPECIAL TOPICS
Index

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