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Other titles in the Dover Books on Mathematics series:
Complex Analysis with Applicationsby Richard A. Silverman
Synopses & ReviewsPublisher Comments:This volume contains the basics of what every scientist and engineer should know about complex analysis. A lively style combined with a simple, direct approach helps readers grasp the fundamentals, from complex numbers, limits in the complex plane, and complex functions to Cauchy's theory, power series, and applications of residues. 1974 edition. Synopsis:The basics of what every scientist and engineer should know, from complex numbers, limits in the complex plane, and complex functions to Cauchy's theory, power series, and applications of residues. 1974 edition. About the AuthorRichard A. Silverman: Dover's Trusted Advisor Richard Silverman was the primary reviewer of our mathematics books for well over 25 years starting in the 1970s. And, as one of the preeminent translators of scientific Russian, his work also appears in our catalog in the form of his translations of essential works by many of the greatest names in Russian mathematics and physics of the twentieth century. These titles include (but are by no means limited to): Special Functions and Their Applications (Lebedev); Methods of Quantum Field Theory in Statistical Physics (Abrikosov, et al); An Introduction to the Theory of Linear Spaces, Linear Algebra, and Elementary Real and Complex Analysis (all three by Shilov); and many more. During the Silverman years, the Dover math program attained and deepened its reach and depth to a level that would not have been possible without his valuable contributions. Table of ContentsPreface
1. Complex Numbers 1.1. Basic Concepts 1.2. The Complex Plane 1.3. The Modulus and Argument 1.4. Inversion Comments Problems 2. Limits in the Complex Plane 2.1. The Principle of Nested Rectangles 2.2. Limit Points 2.3. Convergent Complex Sequences 2.4. The Riemann Sphere and the Extended Complex Plane Comments Problems 3. Complex Functions 3.1. Basic Concepts 3.2. Curves and Domains 3.3. Continuity of a Complex Function 3.4. Uniform Continuity Comments Problems 4. Differentiation in the Complex Plane 4.1. The Derivative of a Complex Function 4.2. The CauchyRiemann Equations 4.3. Conformal Mapping Comments Problems 5. Integration in the Complex Plane 5.1. The Integral of a Complex Function 5.2. Basic Properties of the Integral 5.3. Integrals along Polygonal Curves 5.4. Cauchy's Integral Theorem 5.5. Indefinite Complex Integrals 5.6. Cauchy's Integral Formula 5.7. Infinite Differentiability of Analytic Functions 5.8. Harmonic Functions Comments Problems 6. Complex Series 6.1. Convergence vs. Divergence 6.2. Absolute vs. Conditional Convergence 6.3. Uniform Convergence Comments Problems 7. Power Series 7.1. Basic Theory 7.2. Determination of the Radius of Convergence Comments Problems 8. Some Special Mappings 8.1. The Exponential and Related Functions 8.2. Fractional Linear Transformations Comments Problems 9. MultipleValued Functions 9.1. Domains of Univalence 9.2. Branches and Branch Points 9.3. Riemann Surfaces Comments Problems 10. Taylor Series 10.1. The Taylor Expansion of an Analytic Function 10.2. Uniqueness Theorems 10.3. The Maximum Modulus Principle and Its Implications Comments Problems 11. Laurent Series 11.1. The Laurent Expansion of an Analytic Function 11.2. Isolated Singular Points 11.3. Residues Comments Problems 12. Applications of Residues 12.1. Logarithmic Residues and the Argument Principle 12.2. Rouché's Theorem and Its Implications 12.3. Evaluation of Improper Real Integrals 12.4. Integrals Involving MultipleValued Functions Comments Problems 13. Further Theory 13.1. More on Harmonic Functions 13.2. The Dirichlet Problem 13.3. More Conformal Mapping 13.4. Analytic Continuation 13.5. The Symmetry Principle Comments Problems 14. Mapping of Polygonal Domains 14.1. The SchwarzChristoffel Transformation 14.2. Examples Comments Examples 15. Some Physical Applications 15.1. Fluid Dynamics 15.2. Examples 15.3. Electrostatics Comments Problems Selcted Hints and Answers Bibliography Index What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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