Applied complex variables for scientists and engineers (Q2778512)

In eight chapters, the book gives a thorough introduction to the analytic and geometric aspects of complex variable theory. Chapters 1 to 3 present complex numbers, analytic functions and basic special functions including Joukowski's mapping. Complex integration including Cauchy's theorem (via Green's theorem) is in Chapter 4, while Taylor and Laurent series are in Chapter 5. Isolated singularities and the calculus of residues are studied in Chapter 6, including a short treatment of Fourier transforms. Chapter 7 treats boundary value problems and initial boundary value problems, while the last chapter comes back to more geometric subjects like bilinear mappings and the Schwarz-Christoffel transformation. -- A special feature of the book is the inclusion of several topics from the physical sciences, for example potential theory, hydrodynamics, electrostatics and gravitation, in which methods from the theory of complex variables are applied. Moreover, each chapter is supplemented by a rich collection of problems illustrating the theory. -- On the other hand, some finer points of the theory are treated somewhat less careful: Uniform convergence, the identity theorem, and Weierstrass' M-test is not proved. Unusual is also that a set \(S\) may be simply connected but not connected.