A Course in Mathematical Analysis

by R. R. Goldberg • 2012

This revised edition provides an excellent introduction to topics in Real Analysis through an elaborate exposition of all fundamental concepts and results. The treatment is rigorous and exhaustive—both classical and modern topics are presented in a lucid manner in order to make this text appealing to students. Clear explanations, many detailed worked examples and several challenging ones included in the exercises, enable students to develop problem-solving skills and foster critical thinking. The coverage of the book is incredibly comprehensive, with due emphasis on Lebesgue theory, metric spaces, uniform convergence, Riemann–Stieltjes integral, multi-variable theory, Fourier series, improper integration, and parametric integration. The book is suitable for a complete course in real analysis at the advanced undergraduate or postgraduate level.