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+--------- Thread: Complex Variables and Analytic Functions [ornberg] (/showthread.php?tid=2128)
Complex Variables and Analytic Functions [ornberg] - mklabgr - 09-23-2026
Complex Variables and Analytic Functions: An Illustrated Introduction by Bengt Fornberg and Cécile Piret is an undergraduate-oriented introduction to complex analysis that emphasizes visual understanding alongside the mathematics. It begins with complex numbers and functions of a complex variable, explaining how real and imaginary parts, magnitudes, and arguments can be visualized geometrically. It then develops analytic continuation, complex integration, contour integrals, and residue calculus, showing how these ideas can be used not only theoretically but also to evaluate definite integrals and infinite sums.
The later chapters broaden the subject toward important applications and more advanced topics, including the Gamma and Riemann zeta functions, elliptic functions, conformal mappings, integral transforms, Wiener–Hopf and Riemann–Hilbert methods, special functions defined by differential equations, and the method of steepest descent for approximating integrals. A distinctive feature of the book is its extensive use of graphics to make complex functions and mappings easier to understand.
Overall, it connects classical complex analysis with computational and applied mathematics, making it useful not only for mathematics students but also for physicists, engineers, and researchers who use analytic functions in applications.
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