Introduction to Real Analysis
by William F. Trench
Publisher: Prentice Hall 2003
Number of pages: 583
Using an extremely clear and informal approach, this book introduces readers to a rigorous understanding of mathematical analysis and presents challenging math concepts as clearly as possible. The book is written for those who want to gain an understanding of mathematical analysis and challenging mathematical concepts.
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by Pierre Schapira - Université Paris VI
The notes provide a short presentation of the main concepts of differential calculus. Our point of view is the abstract setting of a real normed space, and when necessary to specialize to the case of a finite dimensional space endowed with a basis.
by Shlomo Sternberg
The topology of metric spaces, Hilbert spaces and compact operators, the Fourier transform, measure theory, the Lebesgue integral, the Daniell integral, Wiener measure, Brownian motion and white noise, Haar measure, Banach algebras, etc.
by Joseph L. Taylor
The goal is to develop in students the mathematical maturity they will need when they move on to senior level mathematics courses, and to present a rigorous development of the calculus, beginning with the properties of the real number system.
by Bruce K. Driver - Springer
These are lecture notes from Real analysis and PDE: Basic Topological, Metric and Banach Space Notions; Riemann Integral and ODE; Lebesbgue Integration; Hilbert Spaces and Spectral Theory of Compact Operators; Complex Variable Theory; etc.