This comprehensive, well-planned text offers broad coverage and a wide range of examples and problems to meet the various needs of undergraduate engineering mathematics and applied mathematics courses as they evolve in line with changes of emphasis and application. Essential results and methods are summarized where appropriate to make the material easily accessible. The book includes not only the standard problems students might expect, but also those that will occur in actual practice when slightly different formulations are involved. The main structure of the text follows the generally established pattern of chapter headings for a book on complex analysis, but the order in which the topics are presented is unique. The approach adopted with this book distinguishes it from other texts in part because of the care that has been taken in how old and new topics are discussed, as well as in the interconnections that are established between the chapters, including their order of presentation. Students will be able to apply their mathematical knowledge more effectively if they understand the interconnections between different branches of mathematics such as engineering mathematics and applied mathematics.

Contenuti

ANALYTIC FUNCTIONS. Review of Complex Numbers. Arcs, Curves, Domains and Regions. Analytic Functions. Cauchy-Riemann Equations. Laplace's Equation and Harmonic Functions. Elementary Functions. CONFORMAL MAPPING. Geometrical Aspects of Analytic Functions. Mapping. Conformal Mapping. Laplace's Equation and Conformal Mapping-Boundary Value Problems. Linear Fractional Transformation. Mappings Provided by Elementary Functions. Schwarz-Christoffel Transformation. BOUNDARY VALUE PROBLEMS, POTENTIAL THEORY AND CONFORMAL MAPPING. Two-Dimensional Boundary Value Problems and Potential Theory. Standard Solutions of Laplace's Equation. Steady-State Temperature Distribution. Steady Two-Dimensional Fluid Flow. Two-Dimensional Electrostatics. COMPLEX INTEGRATION. Contours and Complex Integrals. The Cauchy-Goursat Theorem. Antiderivatives and Definite Integrals. The Cauchy Integral Formula. The Cauchy Integral Formula for Derivatives. Some Useful Theorems Deducible from the Cauchy Integral Formulas. Evaluation of Improper Definite Integrals by Contour Integration. Fourier and Laplace Transforms and Inversion Integrals. The Hilbert Transform. TAYLOR AND LAURENT SERIES, RESIDUE THEOREM AND APPLICATIONS. Sequences, Series and Convergence. Uniform Convergence. Power Series. Taylor Series. Laurent Series. Classification of Singularities and Zeros. Residues and the Residue Theorem. Applications of the Residue Theorem. ANSWERS TO ODD-NUMBERED PROBLEMS. SUGGESTED READING AND REFERENCE LIST. INDEX.

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