18.100A (Introduction to Analysis)

Syllabus and Schedule

1. W   Feb. 4   Ch. 1, App. A. Monotone sequences; completeness property
2. F Feb. 6 Ch. 2. Estimations and approximations
3. M Feb. 9 Ch. 3. Limit of a sequence
4. W Feb. 11 Ch. 4, 5.1. Error term; algebraic limit theorems
5. F Feb. 13 Ch. 5. Limit theorem for sequences
  M Feb. 16    President's day (holiday)
6. T Feb. 17 Ch. 6.1-2. Nested intervals; cluster points
7. W Feb. 18 Ch. 6.3-4. Bolzano-Weierstrass theorem; Cauchy sequences
8. F Feb. 20 Ch. 6.5. Completeness property for sets
9. M Feb. 23 Ch. 7.1-5. Infinite series
10.   W Feb. 25      Ch. 7.6-7. Infinite series, cont'd
11. F Feb. 27 Ch. 8. Power series
12. M Mar. 1 Ch. 9, 10. Functions; local and global properties
  W Mar. 3 Midterm 1
13. F Mar. 5 Ch. 11.1-3. Continuity
14. M Mar. 8 Ch. 11.4-5. Continuity, cont'd
15. W Mar. 10 Ch. 12. Intermediate value theorem
16. F Mar. 12 Ch. 13.1-3. Continuity theorems
17. M Mar. 15 Ch. 13.4-5. Uniform continuity
18. W Feb. 17 Ch. 14. Differentiation: local properties
19. F Mar. 19 Ch. 15. Differentiation: global properties
         Spring break
20. M Mar. 29 Ch. 16, 17. Convexity; Taylor's theorem (skip proofs)
21. W Mar. 31 Ch. 18. Integrability
22. F Apr. 2 Ch. 19. Riemann integral
23. M Apr. 5 Ch. 20.1-4. Fundamental theorem of calculus
24. W Apr. 7 Ch. 20.5-6, 21.1-2. Stirling's formula; improper integrals
  F Apr. 9 Midterm 2
25. M Apr. 12 Ch. 21.3-4. Gamma function; convergence
26. W Apr. 14 Ch. 22.1-2. Uniform convergence
27. F Apr. 16 Ch. 22.3-4. Integration term-by-term
M Apr. 19     Patriot's day (vacation)
28 W Apr. 21 Ch. 22.5-6. Differentiation term-by-term; analyticity
29. F Apr. 23 Ch. 24. Continuous functions on the plane
30. M Apr. 26 Ch. 24. Continuous functions on the plane, cont'd
31. W Apr. 28 App. B. Quantifiers and negation
32. F Apr. 30 Ch. 25. Point-set topology on the plane
33. M May 3 Ch. 26. Differentiating finite integrals
34. W May 5 Ch. 27. Differentiating improper integrals
35. F May 7 Ch. 27. Differentiating improper integrals, cont'd
36. M May 10 App. E. Existence of solutions to ODE's
W May 12 Review

Back to course home page