Complex Functions Examples c7
Applications of the Calculus of Residues
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About the book
Description
This is the seventh textbook you can download 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.
This book requires knowledge of Calculus 1 and Calculus 2.
Preface
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
Content
 Some practical formulæ in the applications of the calculation of residues
 Trigonometric integrals
 Improper integrals in general
 Improper integrals, where the integrand is a rational function
 Improper integrals, where the integrand is a rational function time a trigonometric function
 Cauchy’s principal value
 Sum of some series
 Trigonometric integrals
 Improper integrals in general
 Improper integral, where the integrand is a rational function
 Improper integrals, where the integrand is a rational function times a trigonometric function
 Improper integrals, where the integrand is a rational function times an exponential function
 Cauchy’s principal value
 Sum of special types of series
About the Author
Leif Mejlbro was educated as a mathematician at the University of Copenhagen, where he wrote his thesis on Linear Partial Differential Operators and Distributions. Shortly after he obtained a position at the Technical University of Denmark, where he remained until his retirement in 2003. He has twice been on leave, first time one year at the Swedish Academy, Stockholm, and second time at the Copenhagen Telephone Company, now part of the Danish Telecommunication Company, in both places doing research.
At the Technical University of Denmark he has during more than three decades given lectures in such various mathematical subjects as Elementary Calculus, Complex Functions Theory, Functional Analysis, Laplace Transform, Special Functions, Probability Theory and Distribution Theory, as well as some courses where Calculus and various Engineering Sciences were merged into a bigger course, where the lecturers had to cooperate in spite of their different background. He has written textbooks to many of the above courses.
His research in Measure Theory and Complex Functions Theory is too advanced to be of interest for more than just a few specialist, so it is not mentioned here. It must, however, be admitted that the philosophy of Measure Theory has deeply in uenced his thinking also in all the other mathematical topics mentioned above.
After he retired he has been working as a consultant for engineering companies { at the latest for the Femern Belt Consortium, setting up some models for chloride penetration into concrete and giving some easy solution procedures for these models which can be applied straightforward without being an expert in Mathematics. Also, he has written a series of books on some of the topics mentioned above for the publisher Ventus/Bookboon.