Complex Functions Examples c-7 Applications of the Calculus of Residues Download free books at... Leif MejlbroComplex Functions Examples c-7 Applications of the Calculus of Residues Down
Trang 1Complex Functions Examples c-7
Applications of the Calculus of Residues
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Trang 2Leif Mejlbro
Complex Functions Examples c-7
Applications of the Calculus of Residues
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Trang 3Complex Functions Examples c-7 – Applications of the Calculus of Residues
© 2008 Leif Mejlbro & Ventus Publishing ApS
ISBN 978-87-7681-390-1
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Contents
Contents
Introduction
1.1 Trigonometric integrals
1.2 Improper integrals in general
1.3 Improper integrals, where the integrand is a rational function
1.4 Improper integrals, where the integrand is a rational function time a
trigonometric function
1.5 Cauchy’s principal value
1.6 Sum of some series
6
7
7 8 8 8
10 12
13 25 44 72
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function times an exponential function
98
114 130
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Introduction
Introduction
This is the seventh book containing examples from the Theory of Complex Functions In this volume
we shall apply the calculations or residues in computing special types of trigonometric integrals, some
types of improper integrals, including the computation of Cauchy’s principal value of an integral, and
the sum of some types of series We shall of course assume some knowledge of the previous books and
the corresponding theory
Even if I have tried to be careful about this text, it is impossible to avoid errors, in particular in the
first edition It is my hope that the reader will show some understanding of my situation
Leif Mejlbro 19th June 2008
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