Advanced Calculus and Analysis
by Ian Craw
Publisher: University of Aberdeen 2000
Number of pages: 110
An introductory Calculus course, with some leanings to analysis, at one time given in second year. It covers sequences, monotone convergence, limits and continuity, differentiability, infinite series, power series, differentiation of functions of several variables, and multiple integrals.
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by J. Ponstein
This book is concerned with an attempt to introduce the infinitesimals and the other 'nonstandard' numbers in a naive, simpleminded way. Nevertheless, the resulting theory is hoped to be mathematically sound, and to be complete within obvious limits.
by Irena Swanson - Reed College
Students learn to write proofs while at the same time learning about binary operations, orders, fields, ordered fields, complete fields, complex numbers, sequences, and series. We also review limits, continuity, differentiation, and integration.
by Stanislaw Saks - Polish Mathematical Society
Covering all the standard topics, the author begins with a discussion of the integral in an abstract space, additive classes of sets, measurable functions, and integration of sequences of functions. Succeeding chapters cover Caratheodory measure.
by Gerald Teschl - American Mathematical Society
Introduction and a reference to spectral and inverse spectral theory of Jacobi operators and applications of these theories to the Toda and Kac-van Moerbeke hierarchy. It covers second order difference equations, self-adjoint operators, etc.