Applied complex variables for scientists and engineers - Kwok, Yue Kuen (Cambridge University Press, 2002)
This introduction to complex variable methods for scientists and engineers begins by carefully defining complex numbers and analytic functions and then offers accounts of complex integration, Taylor series, singularities, residues, and mappings. Both algebraic and geometric tools are employed to provide the greatest understanding, with many diagrams illustrating the concepts introduced. The book emphasizes the importance of understanding the use of methods, rather than on rigorous proofs. The book's devotion to applications of the material to physical problems will appeal to scientists. Example applications include detailed treatments of potential theory, hydrodynamics, electrostatics, gravitation and the uses of the Laplace transform for partial differential equations. With 300 stimulating exercises and solutions it will be highly suitable for students wishing to learn the elements of complex analysis in an applied context.