18.100A: Schedule

18.100A: Schedule

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Tuesday Thursday
Feb 4:
Ch. 1, App. A. Monotone sequences; completeness property
Ch. 2. Estimations and approximations
Read Appendix A
Feb 6:
Ch. 2. Estimations and approximations, cont'd
Ch. 3. Limit of a sequence
Read Chapter 2, do Exercises 2.1(3), 2.3(1).
Also, read about "the harmonic sum" in sec 1.5
Feb 11:
Ch. 4, 5.1. Error term; algebraic limit theorems
Ch. 5. Limit theorem for sequences
Exercises 3.1(1c), 3.2(1), 3.2(5).
Prove Theorem 5.1(infinity) in the text.
Feb 13:
Ch. 5. Limit theorem for sequences, cont'd
Ch. 6.1-2. Nested intervals; cluster points
Exercise 5.2(1)
Feb 18:
MIT Monday = no class
Feb 20:
Ch. 6.3-4. Bolzano-Weierstrass theorem; Cauchy sequences
Ch. 6.5. Completeness property for sets
Exercises 6.2(2), 6.3(1), 6.4(1), 6.5(1), 6.5(4)
Feb 25:
Ch. 7.1-6. Infinite series
Feb 27:
Ch. 7. Infinite series, cont'd, Rearrangement
Exercises 7.2(2), 7.4(1a-d), 7.5(4), 7.6(1a-b)
Mar 4:
Ch 8. Power Series
Ch. 9. Functions
READ: sections 8.3, 8.4.
Exercises 8.1(1a,d,g), 8.4(1)
Mar 6:
Ch. 9. Functions, cont'd
Ch. 10. Local and global principles
Mar 11:
MIDTERM 1
Mar 13:
Ch. 11. Continuity
Read Chapter 11, sections 11.3-11.5.
Do exercises 11.1(2), 11.1(5), 11.2(1)
Mar 18:
Ch. 11 - Continuity, cont'd
Ch. 12. Intermediate value theorem
Do Exercise 11.3(4), 11.4(2), 11.5(1).
Mar 20:
Ch. 12. Intermediate value theorem, cont'd
Do Exercises 12.1(1) and 12.1(5), Problem 12-2.
Mar 25:
SPRING BREAK
Mar 27:
SPRING BREAK
Apr 1:
Ch 13: Continuity and compactness,
uniform continuity
Do exercises 13.1(1), 13.2(1), and 13.3(1a-b).
Apr 3:
Ch 13: uniform continuity, cont'd
Ch. 14. Differentiation - local
Do exercise 13.5(1) and problem 13-4.
Apr 8:
Ch. 15. Differentiation - Global
Ch. 17. Taylor's thm
Do Problems 14-5 and 15-1, and Exercise 15.2(1).
(in Problem 15-1, you may ignore the comment on
induction if you don't know what this is)
Apr 10:
Ch. 17. Taylor's thm, cont'd
Ch. 17: Integrability
Do Exercise 17.4(1a).
Apr 15:
Ch. 18: Integrability
Ch. 19: Riemann Integral
Read section 18.4. Do exercise 18.3(4).
Apr 17:
Ch. 19: Riemann Integral, cont'd,
Ch 20: Fundemental thm of calc
Read: sections 19.4 and 19.5 Do Exercise 19.3(1), problem 19-1(a)
Apr 22:
PATRIOT'S DAY: NO CLASS
Apr 24:
MIDTERM 2 (covers through chapter 19)
Apr 29:
Ch 20, cont'd
Exp and Log - brief remarks in improper integrals
Read chapter 21: improper integrals. Do exercise 20.1(1).
May 1
Chapter 22: uniform convergence
Do exercises 21.2(4), 22.1(1)(a), 22.1(3), 22.2(2)(a) 22.2(2)(d)
May 6:
Chap 22, cont'd: integration, differentiation of seq's
Do Exercises 22.3(2), 22.6(5) (don't turn in)
May 8:
Finish chap 22.
Analytic functions.

May 13:
Lebesgue Integration
May 15: (Last day of class)
Review
FINAL EXAM, Wed, May 21, 1:30-4:30, Johnson Ice rink.