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Complex Analysis.

By: Contributor(s): Material type: TextTextSeries: Jones & Bartlett Learning series in mathematics., Complex analysisPublication details: New Delhi : Jones & Bartlett India, 2016Edition: 3rd Edition (Indian Edition)Description: 385 pISBN:
  • 9789384323127
DDC classification:
  • 515.9 ZIL
Contents:
Cover; Title Page; Copyright; Dedication; Contents; Preface; Chapter 1. Complex Numbers and the Complex Plane; 1.1 Complex Numbers and Their Properties; 1.2 Complex Plane; 1.3 Polar Form of Complex Numbers; 1.4 Powers and Roots; 1.5 Sets of Points in the Complex Plane; 1.6 Applications; Chapter 1 Review Quiz; Chapter 2. Complex Functions and Mappings; 2.1 Complex Functions; 2.2 Complex Functions as Mappings; 2.3 Linear Mappings; 2.4 Special Power Functions; 2.4.1 The Power Function zn; 2.4.2 The Power Function z1/n; 2.5 Reciprocal Function; 2.6 Applications; Chapter 2 Review Quiz. Chapter 3. Analytic Functions3.1 Limits and Continuity; 3.1.1 Limits; 3.1.2 Continuity; 3.2 Differentiability and Analyticity; 3.3 Cauchy-Riemann Equations; 3.4 Harmonic Functions; 3.5 Applications; Chapter 3 Review Quiz; Chapter 4. Elementary Functions; 4.1 Exponential and Logarithmic Functions; 4.1.1 Complex Exponential Function; 4.1.2 Complex Logarithmic Function; 4.2 Complex Powers; 4.3 Trigonometric and Hyperbolic Functions; 4.3.1 Complex Trigonometric Functions; 4.3.2 Complex Hyperbolic Functions; 4.4 Inverse Trigonometric and Hyperbolic Functions; 4.5 Applications. Chapter 4 Review QuizChapter 5. Integration in the Complex Plane; 5.1 Real Integrals; 5.2 Complex Integrals; 5.3 Cauchy-Goursat Theorem; 5.4 Independence of Path; 5.5 Cauchy's Integral Formulas and Their Consequences; 5.5.1 Cauchy's Two Integral Formulas; 5.5.2 Some Consequences of the Integral Formulas; 5.6 Applications; Chapter 5 Review Quiz; Chapter 6. Series and Residues; 6.1 Sequences and Series; 6.2 Taylor Series; 6.3 Laurent Series; 6.4 Zeros and Poles; 6.5 Residues and Residue Theorem; 6.6 Some Consequences of the Residue Theorem; 6.6.1 Evaluation of Real Trigonometric Integrals. 6.6.2 Evaluation of Real Improper Integrals6.6.3 Integration along a Branch Cut; 6.6.4 The Argument Principle and Rouché's Theorem; 6.6.5 Summing Infinite Series; 6.7 Applications; Chapter 6 Review Quiz; Chapter 7. Conformal Mappings; 7.1 Conformal Mapping; 7.2 Linear Fractional Transformations; 7.3 Schwarz-Christoffel Transformations; 7.4 Poisson Integral Formulas; 7.5 Applications; 7.5.1 Boundary-Value Problems; 7.5.2 Fluid Flow; Chapter 7 Review Quiz; Appendixes; I: Proof of Theorem 3.1.1; II: Proof of the Cauchy-Goursat Theorem; III: Table of Conformal Mappings. Answers to Selected Odd-Numbered ProblemsSymbol Index; Word Index.
Summary: Revision of: A first course in complex analysis with applications. -- 2nd ed. -- 2009.
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Item type Current library Collection Call number Status Date due Barcode Item holds
Lending Books Lending Books Main Library Stacks Reference 515.9 ZIL (Browse shelf(Opens below)) Available 015857
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Index annexed

Cover; Title Page; Copyright; Dedication; Contents; Preface; Chapter 1. Complex Numbers and the Complex Plane; 1.1 Complex Numbers and Their Properties; 1.2 Complex Plane; 1.3 Polar Form of Complex Numbers; 1.4 Powers and Roots; 1.5 Sets of Points in the Complex Plane; 1.6 Applications; Chapter 1 Review Quiz; Chapter 2. Complex Functions and Mappings; 2.1 Complex Functions; 2.2 Complex Functions as Mappings; 2.3 Linear Mappings; 2.4 Special Power Functions; 2.4.1 The Power Function zn; 2.4.2 The Power Function z1/n; 2.5 Reciprocal Function; 2.6 Applications; Chapter 2 Review Quiz. Chapter 3. Analytic Functions3.1 Limits and Continuity; 3.1.1 Limits; 3.1.2 Continuity; 3.2 Differentiability and Analyticity; 3.3 Cauchy-Riemann Equations; 3.4 Harmonic Functions; 3.5 Applications; Chapter 3 Review Quiz; Chapter 4. Elementary Functions; 4.1 Exponential and Logarithmic Functions; 4.1.1 Complex Exponential Function; 4.1.2 Complex Logarithmic Function; 4.2 Complex Powers; 4.3 Trigonometric and Hyperbolic Functions; 4.3.1 Complex Trigonometric Functions; 4.3.2 Complex Hyperbolic Functions; 4.4 Inverse Trigonometric and Hyperbolic Functions; 4.5 Applications. Chapter 4 Review QuizChapter 5. Integration in the Complex Plane; 5.1 Real Integrals; 5.2 Complex Integrals; 5.3 Cauchy-Goursat Theorem; 5.4 Independence of Path; 5.5 Cauchy's Integral Formulas and Their Consequences; 5.5.1 Cauchy's Two Integral Formulas; 5.5.2 Some Consequences of the Integral Formulas; 5.6 Applications; Chapter 5 Review Quiz; Chapter 6. Series and Residues; 6.1 Sequences and Series; 6.2 Taylor Series; 6.3 Laurent Series; 6.4 Zeros and Poles; 6.5 Residues and Residue Theorem; 6.6 Some Consequences of the Residue Theorem; 6.6.1 Evaluation of Real Trigonometric Integrals. 6.6.2 Evaluation of Real Improper Integrals6.6.3 Integration along a Branch Cut; 6.6.4 The Argument Principle and Rouché's Theorem; 6.6.5 Summing Infinite Series; 6.7 Applications; Chapter 6 Review Quiz; Chapter 7. Conformal Mappings; 7.1 Conformal Mapping; 7.2 Linear Fractional Transformations; 7.3 Schwarz-Christoffel Transformations; 7.4 Poisson Integral Formulas; 7.5 Applications; 7.5.1 Boundary-Value Problems; 7.5.2 Fluid Flow; Chapter 7 Review Quiz; Appendixes; I: Proof of Theorem 3.1.1; II: Proof of the Cauchy-Goursat Theorem; III: Table of Conformal Mappings. Answers to Selected Odd-Numbered ProblemsSymbol Index; Word Index.

Revision of: A first course in complex analysis with applications. -- 2nd ed. -- 2009.

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