Courses:

Analysis I >> Content Detail



Study Materials



Readings

Amazon logo 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:

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

 








© 2009-2020 HigherEdSpace.com, All Rights Reserved.
Higher Ed Space ® is a registered trademark of AmeriCareers LLC.