| ses # | TOPICS | READINGS |
|---|---|---|
| L1 | Real Numbers | pp. 1-12 |
| L2 | Complex Numbers Euclidean Spaces | pp. 12-17 |
| L3 | Countable, Uncountable Sets | pp. 24-30 |
| L4 | Metric Spaces | pp. 30-36 |
| L5 | Compact Sets | pp. 36-39 |
| L6 | Heine-Borel Theorem Connected Sets | pp. 40-43 |
| L7 | Convergent Sequences | pp. 47-52 and 58 |
| L8 | Cauchy Sequences, Completeness | pp. 52-57 |
| L9 | Series | pp. 59-72 |
| L10 | Limits of Functions, Continuity | pp. 83-88 |
| L11 | Continuity, Compactness, Connectedness | pp. 89-93 |
| L12 | Discontinuities, Monotonic Functions | pp. 94-97 |
| L13 | Differentiation Mean Values Theorem | pp. 103-107 |
| L14 | l'Hopital Taylor's Theorem | pp. 108-112 |
| L15 | Riemann-Stieltjes Integral | pp. 120-124 |
| L16 | Riemann-Stieltjes Integral (cont.) | pp. 124-127 |
| L17 | Properties of the Integral | pp. 128-133 |
| L18 | The Fundamental Theorem of Calculus | pp. 133-136 |
| L19 | Sequences of Functions Uniform Convergence | pp. 143-151 |
| L20 | Uniform Convergence, Equicontinuity | pp. 151-158 |
| L21 | Stone-Weierstrass Theorem | pp. 159-165 |
| L22 | Analytic Functions Algebraic Completeness | pp. 173-185 |
| L23 | Fourier Series | pp. 185-192 |
| L24 | Review |
Table of Contents
Study Materials
Readings
 When you click the Amazon logo to the left of any citation and purchase the book (or other media) from Amazon.com, MIT OpenCourseWare will receive up to 10% of this purchase and any other purchases you make during that visit. This will not increase the cost of your purchase. Links provided are to the US Amazon site, but you can also support OCW through Amazon sites in other regions. Learn more. |
The text for this course is:
Rudin, Walter. Principles of Mathematical Analysis. 3rd ed. New York, NY: McGraw-Hill, Inc., 1976. ISBN: 007054235X.
All page numbers refer to this book.