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Complex variable theory constitutes a very elegant and extremely useful branch of mathematics. The range of applications of complex variables in the sciences, engineering, and mathematics is broad and far-reaching. The use of complex variable theory in studying functions arising from physical problems often leads to a deeper insight into the general properties of these functions.
The material in this book is organized and presented in a manner designed to provide a comprehensive first look at complex variable theory. Most of the sources for this book are
given in the references at the end of the book.
Complex Numbers and the Complex Plane,
Complex Functions.
Complex Differentiation.
Elementary Complex Functions.
Complex Integration.
Cauchy’s Integral Formula.
Complex Sequences.
Complex Series.
Singularities and Zeros.
Residues.
Conformal Mapping.
Infinite Products.
Appendix A The Greek Alphabet.
Appendix B Complex Exponential Function.
Appendix C Differentiation of the Cauchy Integral Formula.
Appendix D Summary of Propositions.
Appendix E Identities of Elementary Complex Functions.
References