Undergraduate Analysis Tools
by Bruce K. Driver
Publisher: University of California, San Diego 2013
Number of pages: 186
Contents: Natural, integer, and rational Numbers; Fields; Real Numbers; Complex Numbers; Set Operations, Functions, and Counting; Metric Spaces; Series and Sums in Banach Spaces; More Sums and Sequences; Topological Considerations; Differential Calculus in One Real Variable; Simple Integration Theory; Extending the Integral by Uniform Limits.
Home page url
Download or read it online for free here:
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 L. C. Young - Cambridge University Press
On the one hand, practically no knowledge is assumed; on the other hand, the ideas of Cauchy, Riemann, Darboux, Weierstrass, familiar to the reader who is acquainted with the elementary theory, are used as much as possible ...
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.
by Larry Clifton - arXiv
This is a detailed introduction to the real number system from a categorical perspective. We begin with the categorical definition of the natural numbers, review the Eudoxus theory of ratios, and then define the positive real numbers categorically.