"This self-contained text, suitable for advanced undergraduates, provides an extensive introduction to mathematical analysis, from the fundamentals to more advanced material. A large number of examples and nearly 500 exercises allow the reader to test understanding and practice mathematical exposition, and they provide a window into further topics."--BOOK JACKET.
Introduction -- The real and complex numbers -- Real and complex sequences -- Series -- Power series -- Metric spaces -- Continuous functions -- Calculus -- Some special functions -- Lebesgue measure on the Line -- Lebesgue integration on the line -- Function spaces -- Fourier series -- Applications of Fourier Series -- Ordinary differential equations -- Appendix: The Banach-Tarski paradox.