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 William F. Trench - Prentice Hall
This book introduces readers to a rigorous understanding of mathematical analysis and presents challenging concepts as clearly as possible. Written for those who want to gain an understanding of mathematical analysis and challenging concepts.
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 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 Charles Walmsley - Cambridge University Press
Originally published in 1926, this text was aimed at first-year undergraduates studying physics and chemistry, to help them become acquainted with the concepts and processes of differentiation and integration. A prominence is given to inequalities.