Cohen G.L. A Course in Modern Analysis and its Applications

Cambridge University Press, 2003. - 348 pages.Designed for one-semester courses at the senior undergraduate level, this book is written for mathematics students and teachers, as well as others needing to learn mathematical analysis for engineering, physics, biology or finance. Nominal divisions between pure and applied mathematics have been merged to provide easier access. Applications are included from differential and integral equations, systems of linear algebraic equations, approximation theory, numerical analysis and quantum mechanics.Preface, Prelude to Modern Analysis, Metric Spaces, The Fixed Point Theorem and its Applications, Compactness, Topological Spaces, Normed Vector Spaces, Mappings on Normed Spaces, Inner Product Spaces, Hilbert Space, Bibliography, Selected Solutions, Index.