Mathematical Analysis
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Daily Schedule Term 5
See also Daily Schedule Term 4
Week 8 — Properties of Continuous Functions — Start Least Upper Bounds
- Monday, March 17 — Reading: Study the first eight theorems in Chapter 7 (note that the proofs of the first three theorems are deferred until Chapter 8) — Problem Set 11: Chapter 7, Problems 1-3
- Thursday, March 20 — Reading: Finish studying Chapter 7 and read Chapter 8 through the proof of Theorem 1 — Problem Set 12: Chapter 7, Problems 10-12, and Chapter 8, Problems 1 and 3
Week 9 — Finish Least Upper Bounds — Uniform Continuity — Start Derivatives
- Monday, March 24 — Reading: Finish Chapter 8 and study the Appendix to Chapter 8 — Presentations: Rania and Will, Problem 1, p. 144; Brian and Hexi, Problem 2, p. 144; Brendan and Jeremy, Problem 10, p. 139 — Surprise: Continuity Implies Uniform Continuity (only on a closed interval)
- Thursday, March 27 — Start Chapter 9, derivatives (which are not on Exam 2!) through to the middle of p. 154 — Problem Set 13: Chapter 9, Problems 1-6 — Brian and Brendan: Newton and Liebniz
Week 10 — Exam 2 — Finish Derivatives
- Monday, March 31 — Exam 2 on Spivak Chapters 5 to 8, including the Appendix to Chapter 8
- Thursday, April 3 — Reading: Finish Chapter 9, derivatives — Problem Set 14: Chapter 9: Problems 7-11 — Two groups presented Problems 12 and 14? — I presented a better solution to the last part of Exam 2 Problem 7
Week 11 — Differentiation (Widely Used Properties of Derivatives) — Start Applications of Derivatives
- Monday, April 7 — Reading: Study Chapter 10 to the bottom of p. 173 — Problem Set 15: Problems 1 to 7, but for Problems 1, 2, 4, 5, and 6, just do the first half of the many parts (e.g., if there 18 parts, only do the first 9)
- Thursday, April 10 — Reading: Finish studying Chapter 10 and continue studying in Chapter 11 to p. 192 — Chain Rule (Derivation and Application) — Problem Set 16: Chapter 10, Problem 17, and Chapter 11, Problems 1-3 — Presentations: Rania presented Chapter 10, Problem 22; Hexi and Jeremy presented applications of the Mean Value Theorem
Week 12 — Finish the Significance of the Derivative — Inverse Functions
- Monday, April 14 — Reading: Finish Chapter 11 (skip the Chapter 11 Appendix) — Problem Set 17: Chapter 11, Problems 6 to 12 (these are typical applications to real-world problems of the extrema-finding techniques in Chapter 11, albeit somewhat contrived)
- Thursday, April 17 — Reading: Only one class devoted to Chapter 12 — Problem Set 18: Chapter 12, Problems 4 to 7 — Discuss the very useful results arising from combining the inverse function idea with the chain rule theorem (Theorem 5, pp. 234-235) — Begin discussing partitions and integrability
Week 13 — Integrals
- Monday, April 21 — Reading: Start Chapter 13 through p. 260 — Problem Set 19: Chapter 13, Problems 1, 2, and 7(i)-7(iv) — You should be able to check (by counting squares on the graph paper) that your analytical results are consistent with the graphs
- Thursday, April 24 — Reading: Finish Chapter 13 — Problem Set 20: Chapter 13, Problems 8, 12, and 15 — Also, problems 18 and 19 are at our current ability level and instructive — — After we are satisfied with Chapter 13, and especially Theorems 3 and 8 which prepare us for the Appendix, we will preview the two versions of “The Fundamental Theorem of Calculus”
Week 14 — The Fundamental Theorem of Calculus — Exam 3
- Monday, April 28 — Reading: Finish Chapter 14 — Problem Set 21: Problems 1 (parts (i)-(iv) only), 4 (take derivatives to show x-independence), and 7 (could be tricky!)
- Thursday, May 1 — Exam 3 on Spivak Chapters 9 to 14
