A Course of Pure Mathematics
by G.H. Hardy
Publisher: Cambridge University Press 1921
Number of pages: 476
This classic book has inspired successive generations of budding mathematicians at the beginning of their undergraduate courses. Hardy combines the enthusiasm of the missionary with the rigor of the purist in his exposition of the fundamental ideas of the differential and integral calculus, of the properties of infinite series and of other topics involving the notion of limit.
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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.
by John Franks - arXiv
My intent is to introduce the Lebesgue integral in a quick, and hopefully painless, way and then go on to investigate the standard convergence theorems and a brief introduction to the Hilbert space of L2 functions on the interval.
by Robert B. Ash - Institute of Electrical & Electronics Engineering
A text for a first course in real variables for students of engineering, physics, and economics, who need to know real analysis in order to cope with the professional literature. The subject matter is fundamental for more advanced mathematical work.