This is an archived course. A more recent version may be available at ocw.mit.edu.

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Readings

The text for this course is:

Amazon logo Rudin, Walter. Principles of Mathematical Analysis. 3rd ed. New York, NY: McGraw-Hill, Inc., 1976. ISBN: 007054235X.

All page numbers refer to this book.

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