Transcription of Complex Variables with Applications - GBV
1 Complex Variableswith ApplicationsThird EditionA. David WunschUniversity of Massachusetts LowellPEARSONA ddisonWesleyBoston San Francisco New YorkLondon Toronto Sydney Tokyo Singapore MadridMexico City Munich Paris Cape Town Hong Kong MontrealContentsIntroduction xiComplex Introduction More Properties of Complex Numbers Complex Numbers and the Argand Plane Integer and Fractional Powers of Complex Numbers Points, Sets, Loci.
2 And Regions in the Complex Plane 39 The Complex Function and Its Derivative Introduction Limits and Continuity The Complex Derivative The Derivative and Analyticity Harmonic Functions Some Physical Applications of Harmonic Functions 87 Vllviii ContentsThe Basic Transcendental Functions The Exponential Function Trigonometric Functions Hyperbolic Functions The Logarithmic Function Analytifity of the Logarithmic Function Complex Exponentials Inverse Trigonometric and Hyperbolic Functions More on Branch Cuts and Branch Points 138 Appendix.
3 PhasorsIntegration in the Complex Plane Introduction to Line Integration Complex Line Integration Contour Integration and Green's Theorem Path Independence, Indefinite Integrals, Fundamental Theoremof Calculus in the Complex Plane The Cauchy Integral Formula and Its Extension Some Applications of the Cauchy Integral Formula Introduction to Dirichlet Problems The Poisson Integral Formulafor the Circle and Half Plane 214 Appendix.
4 Green's Theorem in the PlaneInfinite Series Involving a Complex variable Introduction and Review of Real Series Complex Sequences and Convergence of Complex Series Uniform Convergence of Series Power Series and Taylor Series Techniques for Obtaining Taylor Series Expansions Laurent Series 279 Contents Properties of Analytic Functions Related to Taylor Series: Isolationof Zeros, Analytic Continuation, Zeta Function, Reflection The z Transformation 307 Appendix.
5 Fractals and the Mandelbrot SetResidues and Their Use in Integration Introduction and Definition of the Residue Isolated Singularities Finding the Residue Evaluation of Real Integrals with Residue Calculus, I Evaluation of Integrals, II Evaluation of Integrals, III Integrals Involving Indented Contours Contour Integrations Involving Branch Points and Branch Cuts Residue Calculus Applied to Fourier Transforms The Hilbert Transform Uniform Convergence of Integrals and the Gamma Function Principle of the Argument 442 Laplace Transforms and Stability of Systems Laplace Transforms and Their Inversion Stability An Introduction The Nyquist Stability Criterion
6 Generalized Functions, Laplace Transforms, and Stability 4988 Conformal Mapping and Some of Its Applications Introduction The Conformal Property One-to-One Mappings and Mappings of Regions The Bilinear Transformation Conformal Mapping and Boundary Value Problems More on Boundary Value Problems Streamlines as Boundaries Boundary Value Problems with Sources The Schwarz-Christoffel Transformation 605 Appendix.
7 The Stream Function and CapacitanceAdvanced Topics in Infinite Series and Products The Us6 of Residues to Sum Certain Numerical Series Partial Fraction Expansions of Functions with an InfiniteNumber of Poles Introduction to Infinite Products Expanding Functions in Infinite Products 650 Solutions to Odd-Numbered Exercises 659 Index 669
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