| Tuesday | Thursday |
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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 |
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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) |
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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) |
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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) |
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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 |
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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) |
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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. |
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Mar 25: SPRING BREAK |
Mar 27: SPRING BREAK |
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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. |
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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). |
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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) |
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Apr 22: PATRIOT'S DAY: NO CLASS |
Apr 24: MIDTERM 2 (covers through chapter 19) |
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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) |
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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. |
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May 13: Lebesgue Integration |
May 15: (Last day of class) Review |
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FINAL EXAM, Wed, May 21, 1:30-4:30, Johnson Ice rink. |