Courses:

Analysis I >> Content Detail



Study Materials



Readings

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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 #TOPICSREADINGS
L1Real Numberspp. 1-12
L2Complex Numbers

Euclidean Spaces
pp. 12-17
L3Countable, Uncountable Setspp. 24-30
L4Metric Spacespp. 30-36
L5Compact Setspp. 36-39
L6Heine-Borel Theorem

Connected Sets
pp. 40-43
L7Convergent Sequencespp. 47-52 and 58
L8Cauchy Sequences, Completenesspp. 52-57
L9Seriespp. 59-72
L10Limits of Functions, Continuitypp. 83-88
L11Continuity, Compactness, Connectednesspp. 89-93
L12Discontinuities, Monotonic Functionspp. 94-97
L13Differentiation

Mean Values Theorem
pp. 103-107
L14l'Hopital

Taylor's Theorem
pp. 108-112
L15Riemann-Stieltjes Integralpp. 120-124
L16Riemann-Stieltjes Integral (cont.)pp. 124-127
L17Properties of the Integralpp. 128-133
L18The Fundamental Theorem of Calculuspp. 133-136
L19Sequences of Functions

Uniform Convergence
pp. 143-151
L20Uniform Convergence, Equicontinuitypp. 151-158
L21Stone-Weierstrass Theorempp. 159-165
L22Analytic Functions

Algebraic Completeness
pp. 173-185
L23Fourier Seriespp. 185-192
L24Review

 








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