Complex analysis and applications /
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| Author / Creator: | Pathak, Hemant Kumar, author. |
|---|---|
| Imprint: | Singapore : Springer, 2019. |
| Description: | 1 online resource (xxv, 928 pages) : illustrations |
| Language: | English |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11938918 |
Table of Contents:
- Intro; Preface; Contents; About the Author; Acronyms; Glossary of Symbols; 1 Complex Numbers and Metric Topology of mathbbC; 1.1 Introduction; 1.2 Complex Numbers; 1.2.1 Equality of Complex Numbers; 1.2.2 Fundamental Laws of Addition and Multiplication; 1.2.3 Difference and Division of Two Complex Numbers; 1.3 Modulus and Argument of Complex Numbers; 1.4 Geometrical Representations of Complex Numbers; 1.5 Modulus and Argument of Complex Numbers; 1.5.1 Polar Forms of Complex Numbers; 1.5.2 Conjugates; 1.5.3 Vector Representation of Complex Numbers; 1.5.4 Multiplication of a Complex Number by i
- 1.6 Properties of Moduli1.7 Properties of Arguments; 1.8 Equations of Straight Lines; 1.9 Equations of Circles; 1.9.1 General Equation of a Circle; 1.9.2 Equations of Circles Through Three Points; 1.10 Inverse Points; 1.10.1 Inverse Points with Respect to Lines; 1.10.2 Inverse Points with Respect to Circles; 1.11 Relations Between Inverse Points with Respect To Circles; 1.12 Riemann Spheres and Point at Infinity; 1.12.1 Point at Infinity; 1.12.2 Riemann Spheres; 1.13 Cauchy-Schwarz's Inequality and Lagrange's Identity; 1.14 Metric Spaces and Topology of mathbbC; 1.14.1 Metric Spaces
- 1.14.2 Dense Set1.14.3 Connectedness; 1.14.4 Convergence and Completeness; 1.14.5 Component; 1.14.6 Compactness; 1.14.7 Continuity; 1.14.8 Topological Spaces; 1.14.9 Metrizable Spaces; 1.14.10 Homeomorphism; 2 Analytic Functions, Power Series, and Uniform Convergence; 2.1 Introduction; 2.2 Functions of Complex Variables; 2.2.1 Limits of Functions; 2.2.2 Continuity; 2.3 Uniform Continuity; 2.4 Differentiability; 2.5 Analytic and Regular Functions; 2.6 Cauchy-Riemann Equations; 2.6.1 Conjugate Functions; 2.6.2 Harmonic Functions; 2.6.3 Polar Form of the Cauchy-Riemann Equations
- 2.7 Methods of Constructing Analytic Functions2.7.1 Simple Methods of Constructing Analytic Functions (Without Using Integrals); 2.8 Power Series; 2.8.1 Absolute Convergence of a Power Series; 2.8.2 Some Special Test for Convergence of Series; 2.9 Certain Theorems on Power Series; 2.9.1 Abel's Theorem; 2.9.2 Cauchy-Hadamard's Theorem; 2.9.3 Circle and Radius of Convergence of a Power Series; 2.9.4 Analyticity of the Sum Function of a Power Series; 2.9.5 Abel's Limit Theorem; 2.10 Elementary Functions of a Complex Variable; 2.11 Many-Valued Functions: Branches
- 2.12 The Logarithm and Power Functions2.13 The Riemann Surface for Log z; 2.14 Uniform Convergence of a Sequence; 2.14.1 General Principle of Uniform Convergence of a Sequence; 2.15 Uniform Convergence of a Series; 2.15.1 Principle of Uniform Convergence of a Series; 2.15.2 Sufficient Tests for Uniform Convergence of a Series; 2.15.3 Weierstrass M-Test; 2.16 Hardy's Tests for Uniform Convergence; 2.17 Continuity of the Sum Function of a Series; 3 Complex Integrations; 3.1 Introduction; 3.2 Complex Integrations; 3.2.1 Some Definitions; 3.2.2 Rectifiable Curves; 3.3 Complex Integrals