An introduction to the theory of complex variables
Publisher: Bookboon
Published: 2013
ISBN-13: 9788740301625
Table of contents: title: Part I: An introduction to complex variables; title: Preface; title: Introduction; title: Complex Numbers; title: Elementary properties; title: Inequalities; title: Roots; title: Exercises 1; title: Functions; title: Elementary functions; title: Exercises 2; title: Differentiability; title: Definition; title: The derivative in detail; title: Analyticity; title: Harmonic functions; title: Exercises 3; title: Integration in the complex plane; title: The line integral; title: The fundamental theorem of calculus; title: Closed contours; title: Exercises 4; title: The Integral Theorems; title: Cauchy’s Integral Theorem (1825); title: Cauchy’s Integral Formula (1831); title: An integral inequality; title: An application to the evaluation of real integrals; title: Exercises 5; title: Power Series; title: The Laurent expansion (1843); title: Exercises 6; title: The Residue Theorem; title: The (Cauchy) Residue Theorem (1846); title: Application to real integrals; title: Using a different contour; title: Exercises 7; title: The Fourier Transform; title: FTs of derivatives; title: Exercises 8; title: Answers; title: Part II: The integral theorems of complex analysis with applications to the evaluation of real integrals; title: List of Integrals; title: Preface; title: Introduction; title: Complex integration; title: Exercises 1; title: The integral theorems; title: Green’s theorem; title: Cauchy’s integral theorem; title: Cauchy’s integral formula; title: The (Cauchy) residue theorem; title: Exercises 2; title: Evaluation of simple, improper real integrals; title: Estimating integrals on semi-circular arcs; title: Real integrals of type 1; title: Real integrals of type 2; title: Exercises 3; title: Indented contours, contours with branch cuts and other special contours; title: Cauchy principal value; title: The indented contour; title: Contours with branch cuts; title: Special contours; title: Exercises 4; title: Integration of rational functions of trigonometric functions; title: Exercises 5; title: Answers; title: Biographical Notes; title: Index