18.100B | Fall 2010 | Undergraduate
Analysis I

Syllabus

Course Meeting Times

Lectures: 2 sessions / week, 1.5 hour / session

Prerequisites

18.02 Multivariable Calculus; 18.03 Differential Equations or 18.034 Honors Differential Equations

Text

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

Assignments

Weekly homework is due on the second day of class each week. There are 10 homework assignments; the lowest two scores will be dropped.

Exams

There are four in-class 30-minute quizzes, and one 3-hour final exam. The worst quiz score is dropped.

Grading

ACTIVITIES PERCENTAGES
Problem sets 20%
In-class quizzes 25%
Final exam 45%
Discussion 10%

Calendar

SES # TOPICS KEY DATES
1 Ordered sets and fields  
2 Metric spaces  
3 Relative topology, compact sets  
4 Compact sets (cont.)  
5 Connected sets, convergence  
6 Sequential compactness Quiz 1
7 Completeness  
8 Construction of the real numbers  
9 Series  
10 Series (cont.)  
11 Continuity  
12 l^p spaces Quiz 2
13 Continuity and compactness, connectedness  
14 Discontinuities, monotone functions  
15 Differentiability, mean value theorem  
16 l’Hospital’s rule, Taylor’s theorem  
17 Riemann integral  
18 Riemann integrability and continuity almost everywhere Quiz 3
19 Stieltjes integral, fundamental theorem of calculus  
20 Sequences and series of functions  
21 Equicontinuity  
22 Optional material: Weierstrass function, Devil’s Staircase Quiz 4
23 Review for final exam  
24 Review for final exam (cont.)  
25  Final exam

Course Info
Departments
As Taught In
Fall 2010
Learning Resource Types
assignment_turned_in Problem Sets with Solutions
notes Lecture Notes
grading Exams with Solutions