Elementary Real Analysis
by B. S. Thomson, J. B. Bruckner, A. M. Bruckner
Publisher: Prentice Hall 2001
Number of pages: 735
Elementary Real Analysis is written in a rigorous, yet reader friendly style with motivational and historical material that emphasizes the "big picture" and makes proofs seem natural rather than mysterious. Introduces key concepts such as point set theory, uniform continuity of functions and uniform convergence of sequences of functions. Covers metric spaces. Ideal for readers interested in mathematics, particularly in advanced calculus and real analysis.
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by Gerald Teschl - Universitaet Wien
This manuscript provides a brief introduction to Real and (linear and nonlinear) Functional Analysis. It covers basic Hilbert and Banach space theory as well as basic measure theory including Lebesgue spaces and the Fourier transform.
by G.H. Hardy - Cambridge University Press
This classic book has inspired successive generations of budding mathematicians at the beginning of their undergraduate courses. Hardy explains the fundamental ideas of the differential and integral calculus, and the properties of infinite series.
by Shanti Narayan - S.Chand And Company
Contents: Dedekind's theory of Real Numbers; Bounds and Limiting Points; Sequences; Real Valued Functions of a Real Variable; The derivative; Riemann Theory of Integration; Uniform Convergence; Improper Integrals; Fourier Series; and more.
by W W L Chen - Macquarie University
An introduction to some of the basic ideas in Lebesgue integration with the minimal use of measure theory. Contents: the real numbers and countability, the Riemann integral, point sets, the Lebesgue integral, monotone convergence theorem, etc.