Russell Howell and John Mathews

• Supports a one-semester undergraduate complex analysis course
• Suitable for use with mathematics, engineering, and physics students
• 11 chapters, 461 pages
• Originally published by Jones and Bartlett Learning through 6 editions
• Low-cost print version forthcoming
• Numerous exercises at the end of each section
• For more information and to download a PDF or to access HTML

After publishing six editions with Jones and Bartlett, the authors have made this textbook available with an open license. Written to support a traditional complex analysis course for math, physics, and engineering students, the first half of the book lays the foundation for the study of analytic and harmonic functions and contour integration. The second half presents a choice of topics such as residue calculus, conformal mappings, Fourier and Laplace transforms, and a range of applications.

The complex numbers are introduced with a motivating historical treatment. Throughout the text, the writing is clear, and the exposition includes both ample motivation and careful explanations. A later chapter includes a range of applications of harmonic functions to physical situations such as steady-state temperatures, electrostatics, and two-dimensional fluid flow.

Contents:

1. Complex Numbers
2. Complex Functions
3. Analytic and Harmonic Functions
4. Sequences, Series, and Fractals
5. Elementary Functions
6. Complex Integration
7. Taylor and Laurent Series
8. Residue Theory
9. Conformal Mapping
10. Applications of Harmonic Functions
11. Fourier Series and the Laplace Transform