## Fundamentals of complex analysis with applications to engineering and scienceThis book provides a comprehensive introduction to complex variable theory and its applications to current engineering problems and is designed to make the fundamentals of the subject more easily accessible to readers who have little inclination to wade through the rigors of the axiomatic approach. Modeled after standard calculus books--both in level of exposition and layout--it incorporates physical applications throughout, so that the mathematical methodology appears less sterile to engineers. It makes frequent use of analogies from elementary calculus or algebra to introduce complex concepts, includes fully worked examples, and provides a dual heuristic/analytic discussion of all topics. A downloadable MATLAB toolbox--a state-of-the-art computer aid--is available. Complex Numbers. Analytic Functions. Elementary Functions. Complex Integration. Series Representations for Analytic Functions. Residue Theory. Conformal Mapping. The Transforms of Applied Mathematics. MATLAB ToolBox for Visualization of Conformal Maps. Numerical Construction of Conformal Maps. Table of Conformal Mappings. Features coverage of Julia Sets; modern exposition of the use of complex numbers in linear analysis (e.g., AC circuits, kinematics, signal processing); applications of complex algebra in celestial mechanics and gear kinematics; and an introduction to Cauchy integrals and the Sokhotskyi-Plemeij formulas. For mathematicians and engineers interested in Complex Analysis and Mathematical Physics. |

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### Contents

Analytic Functions | 53 |

Elementary Functions | 99 |

Complex Integration | 149 |

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analytic continuation analytic function analytic inside angle antiderivative boundary values Cauchy Cauchy-Riemann equations Cauchy's coefficients complex numbers complex plane compute conformal map constant Contour for Example defined Definition deformed depicted in Fig derivative differentiable essential singularity evaluate Exercises Figure Find function f(z given harmonic function Hence Hilbert transform HINT integral formula integrand interior inverse Laplace's equation Laurent series Lemma limit line segment loop Mobius transformation multiplication neighborhood nonzero one-to-one pole of order polygon polynomial positively oriented power series problem proof properties Prove rational function real and imaginary real axis real number removable singularity residue Riemann sphere satisfies Schwarz-Christoffel sequence Show simple closed contour simple pole simply connected simply connected domain sinusoid Solution solve Taylor series Theorem traversed once unit circle unit disk upper half-plane vector verify z-plane z-transform zero