Roger Godement Book order

Focusing on classical Cauchy theory, this volume emphasizes its diverse applications rather than solely the theory of analytic functions. It explores the generalization of Cauchy-type curvilinear integrals to multiple real variables and introduces the fundamentals of manifold theory, equipping readers with essential terminology and key theorems. The concluding chapter demonstrates the practical use of these theorems in constructing the compact Riemann surface of an algebraic function, a topic often overlooked in standard literature yet approachable with basic techniques.

Analysis Volume IV introduces the reader to functional analysis (integration, Hilbert spaces, harmonic analysis in group theory) and to the methods of the theory of modular functions (theta and L series, elliptic functions, use of the Lie algebra of SL2).

Functions in R and C, including the theory of Fourier series, Fourier integrals and part of that of holomorphic functions, form the focal topic of these two volumes.