Introduction to Complex Analysis and Its Applications

Textbook Media Press presents Introduction to Complex Analysis and Its Applications (2e), written for undergraduate students in science and engineering. Discussions are rigorous, but the approach is intuitive.

This text explores the intimate relationships among the three major topics of complex calculus — differentiation, integration, and infinite series. Properties in any one of these topics are reflected in properties in the other two, so much so that one could commence complex calculus with any one of the three topics.

The preference in this text is to begin with differentiation, it being, perhaps, the easiest of the three topics for most students in real calculus. This is then followed with integration and infinite series. Geometric visualizations are used to introduce and clarify ideas whenever possible.

The study of calculus of complex functions can be a very rewarding experience. Topics unfold naturally, and each new topic intimately relates to everything that has gone before. Proofs of most results, even the very profound, are usually quite straightforward, and the material is rich in applications.

Applications are woven through the book rather than saved for the end: steady-state two-dimensional heat conduction, electrostatics, and fluid flow appear alongside the elementary functions and again under conformal mapping, and the final three chapters develop the Laplace, Fourier, and z-transforms.

Prerequisites. The presentation assumes a working knowledge of single-variable real calculus, including infinite series, and familiarity with partial differentiation and line integrals.

A Student Solution Manual is also available for the text. This manual contains solutions to even-numbered exercises in the text. Solutions are sufficiently detailed that the reader should have no difficulty following the logic.