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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.
Course readings.
| 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 |
|