Calculus with Complex Numbers

Przednia okładka
CRC Press, 13 mar 2003 - 112
This practical treatment explains the applications complex calculus without requiring the rigor of a real analysis background. The author explores algebraic and geometric aspects of complex numbers, differentiation, contour integration, finite and infinite real integrals, summation of series, and the fundamental theorem of algebra. The Residue Theorem for evaluating complex integrals is presented in a straightforward way, laying the groundwork for further study. A working knowledge of real calculus and familiarity with complex numbers is assumed. This book is useful for graduate students in calculus and undergraduate students of applied mathematics, physical science, and engineering.
 

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Spis treści

Complex numbers
1
Complex functions
14
Derivatives
24
Integrals
36
Evaluation of finite real integrals
49
Evaluation of infinite real integrals
53
Summation of series
65
Fundamental theorem of algebra
75
Solutions to examples
82
Cauchys theorem
93
Half residue theorem
95
Bibliography
97
Index of symbols and abbreviations
98
General index
99
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Informacje o autorze (2003)

John B. Reade is a lecturer in mathematics at Manchester University, UK.

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