18.100B | Fall 2010 | Undergraduate

Analysis I

Readings & Notes

Readings are assigned in Rudin, W. Principles of Mathematical Analysis. 3rd ed. McGraw-Hill Science/Engineering/Math, New York, NY: McGraw-Hill, 1976. ISBN: 9780070542358.

The supplementary notes are courtesy of Prof. Todd Kemp and are used with permission.

SES # TOPICS READINGS
1 Ordered sets and fields Section 1.1-31
2 Countability, Euclidean spaces Section 1.32-38, and 2.1-17
3 Metric spaces Section 2.15-28
4 Relative topology, compact sets Section 2.29-40
5 Compact sets Section 2.36-44
6 Connected sets, convergence Section 2.45-47, and 3.1-7
7 Sequential compactness Notes (PDF)
8 Completeness Section 3.8-20
9 Construction of the real numbers Notes (PDF)
10 Series Section 3.20-37
11 Series (cont.) Section 3.38-55
12 Continuity Section 4.1-12
13 l^p spaces Notes (PDF)
14 Continuity and compactness, connectedness Section 4.13-24
15 Discontinuities, monotone functions Section 4.25-34
16 Differentiability, mean value theorem Section 5.1-11
17 l’Hospital’s rule, Taylor’s theorem Section 5.12-19
18 Riemann integral Section 6.1-12 with alpha(x)=x
19 Riemann integrability and continuity almost everywhere Notes (PDF)
20 Stieltjes integral, fundamental theorem of calculus Section 6.1-22
21 Sequences and series of functions Section 7.1-17
22 Equicontinuity Section 7.18-25
23 Optional material: Weierstrass function, Devil’s staircase Weierstrass function (PDF), Devil’s staircase (PDF)
24 Review for final exam No readings
25 Review for final exam (cont.) No readings

Course Info

Departments
As Taught In
Fall 2010
Learning Resource Types
Problem Sets with Solutions
Lecture Notes
Exams with Solutions