MA2321 - Analysis in Several Real Variables
Dr. David R. Wilkins

MA2321     Michaelmas Term 2015: Resources

Lecture Courses available as Textbooks

Basic Analysis: Introduction to Real Analysis (Jiří Lebl)
This free online textbook is based on lecture notes for lecture courses taught by Jiří Lebl at the University of Illinois at Urbana Champaign and at the University of Wisconsin-Madison. It is also possible to buy paperback copies fo the book.
Advanced Analysis (Yan Min, Hong Kong University of Science and Technology).

Lecture Courses available as Online Notes

Metric and Topological Spaces (P.M.H. Wilson, Cambridge University
These lecture notes relate more directly to MA2223 than to MA2321. Nevertheless there are close correspondences between the subject matter of modules MA2223 and MA2321, and accordingly the notes of the Metric and Topological Paces lecture course within the Cambridge Tripos, as taught by Prof. P.M.H. Wilson, have relevance for both modules MA2223 and MA2321.
Honors Analysis (MATH 55b) (Curtis McMullen, Harvard University).
Analysis II (MATH 114) (Curtis McMullen, Harvard University).

Lecture Courses available as Videos

Real Analysis (YouTube videos)
A lecture course on Real Analysis delived in Spring 2010 at Harvey Mudd College by Professor Francis Su

Websites for computer algebra, 3D plotting etc.

Wolfram Alpha
3D Function Grapher at http://www.math.uri.edu/~bkaskosz/flashmo/graph3d/

Resources related to Specific Topics

The Real Number System

Essays on the Theory of Numbers, by Richard Dedekind, translated by Wooster Woodruff Beman
This book, available online from the Internet Archive, contains two essays. The first of these essays, entitled Continuity and Irrational Numbers develops a rigorous theory of real numbers, where such numbers are constructed via Dedekind Sections. A Dedekind section is a partition of the set of all rational numbers into two subsets A1 and A2, where every rational number belongs to exactly one of the sets A1 and A2, and where every rational number belonging to A1 is less than every rational number belonging to A2. Dedekind's original work, published in German, was translated into English by Wooster Woodruff Beman (1850—1922) (see the webapge at the Bentley Historical Library, University of Michigan).

Fubini's Theorem

Back to D.R. Wilkins: Lecture Notes

Dr. David R. Wilkins: Module MA2321, Dr. David R. Wilkins: Courses, Dr. David R. Wilkins, School of Mathematics, Trinity College Dublin.