George F. Carrier (1918-2002) was one of the world's preeminent applied mathematicians and the T. Jefferson Coolidge Professor of Applied Mathematics at Harvard University. He was honored for his scientific accomplishments by election to the National Academy of Sciences, the National Academy of Engineering, the American Academy of Art and Sciences, and the American Philosophical Society. He was the author of numerous papers and books. Max Krook (1913-1985) was Gordon McKay Professor of Applied Mathematics and Professor of Astrophysics at Harvard University. He was widely recognized for his work on stellar and interstellar atmospheres and for his explanations of unusual phenomena in fluids and plasmas. He also was renowned for the invention of several simple models that have given scientists new insights into kinetic theory and statistical mechanics. Carl E. Pearson has a wide variety of experience in both the academic and the professional worlds. He has taught at Harvard, the Technical University of Denmark, and the University of Washington, and he has spent years in industry as well, including work at Arthur D. Little Inc., Sperry Rand Company, and Boeing Aerospace Company. Dr. Pearson is the author of several books, some of them classics in the field of applied mathematics.

• PrefaceErratumChapter 1: Complex Numbers And Their Elementary PropertiesChapter 2: Analytic FunctionsChapter 3: Contour IntegrationChapter 4: Conformal MappingChapter 5: Special FunctionsChapter 6: Asymptotic MethodsChapter 7: Transform MethodsChapter 8: Special TechniquesIndex.

'[This volume] is a classic textbook and reference on the subject of complex variables. It established a gold standard against which all other texts in applied mathematics should be judged … As the authors intended, the theory part is concise and quickly leads the reader from an introduction to complex numbers to useful and powerful techniques, with applications to integral representation of special functions, transform and asymptotic methods in the complex plane, and integral equations, just to name a few. It is in the application of these techniques where the authors devoted most of the efforts. These were done masterfully. This book remains a relevant and must-read book for applied mathematicians today.' K. K. Tung, Professor and Chair of Applied Mathematics, University of Washington