A Course of Modern Analysis: Third Edition (Dover Books on Mathematics)

Still in print more than a century after its 1902 publication, this historic text by two great mathematicians has inspired generations of students and scholars. The original treatment consists of two parts, The Processes of Analysis and The Transcendental Functions; a final chapter, Ellipsoidal Harmonies and Lamé's Equations, was added in 1920.
The first part covers complex numbers, the theories of convergence and Riemann integration, the expansion of functions in infinite series, Fourier and trigonometrical series, and linear differential and integral equations, among other subjects. Part two explores the gamma function, Legendre and Bessel functions, equations of mathematical physics, Mathieu and theta functions, and other topics. A Course of Modern Analysis is suitable for advanced undergraduates and graduate students of mathematics as well as historians of mathematics.