An Introduction to Complex Analysis and the Laplace Transform (Hardcover, 1)

Preface Introduction1. Complex Numbers and Their Arithmetic Operations with Complex Numbers 2. Functions of a Complex Variable Complex Plane Sequences of Complex Numbers and Their Limits Functions of Complex Variable. Limit and Continuity 3. Differentiation of Functions of a Complex Variable Derivative and Differential The Cauchy-Riemann Equations Analytic Functions Relations between Analytic and Harmonic Functions Geometric Interpretation of a Derivative of a Function of Complex Variable Notion of a Conformal Mapping 4. Conformal Mappings Linear and Linear Fractional Functions Power Function Notion of a Riemann Surface Exponential and Logarithmic Functions General Power Function and Trigonometric Functions Zukowski Function General Properties of Conformal Mappings An Application of Functions of Complex Variable in Hydrodynamics 5. Integration of Functions of a Complex Variable Integral of a Function of Complex Variable Cauchy Theorem Indefinite Integral Fundamental Theorem of Calculus Cauchy’s Integral Formula and Their Applications 6. Series Number Series Functional Series Uniform Convergence Power series Expansion of Functions in Power Series Taylor Series Uniqueness Property Analytic Continuation Complete Analytic Function Loran Series 7. Isolated Singularities and Residues Classification of Isolated Singular Points Residue of a Function in an Isolated Singular Point Evaluation of Integrals by Means of Residues Logarithmic Residue and Argument Principle 8. The Laplace Transform Laplace Transform Basic Properties of the Laplace Transform Application of the Laplace Transform to Solving Ordinary Differential Equations 9. Practicum Solving of Typical Problems Tasks for Self-Study Literature Index