Mathematical Analysis Daily Schedule Term 5

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See also Daily Schedule Term 6

Note: All page numbers, equations, and problem numbers refer to the 3rd Edition of Calculus by Michael Spivak.

Week 1 — Chapter 1 — Basic Properties of Numbers

• Monday, March 15 — Reading: Chapter 1, pp. 3-9, postulates (P1)-(P9) for the real numbers (properties of addition and multiplication) — In-Class: Chapter 1, Problems 1, 2, and 3
• Thursday, March 18 — Reading: Finish Spivak, Chapter 1, pp. 9-13, postulates (P10)-(P12) for the real numbers (properties of inequalities) — In-Class: Chapter 1, Problem 6 (a)-(c) — Problem Set 1: Chapter 1, Problem 5 — PS1 Solution

Week 2 — Chapter 2 — Numbers of Various Sorts

• Monday, March 22 — Reading: Spivak, Chapter 2, pp. 21-22 (the natural numbers, N, and induction) — Problem Set 2: Chapter 1, Problem 19 (a)-(c), Chapter 2, Problems 1 and 2
• Thursday, March 25 — Reading: Spivak, Chapter 2, pp. 23-25 (factorials, summations, the integers, Z) — Problem Set 3: Chapter 2, Problem 3 — Aubryn’s Better Proof of the Pascal’s Triangle Induction

Week 3 — Chapter 3 — Functions

• Monday, March 29 — Reading: Spivak, Finish Chapter 2, (the rationals, Q, and the real numbers, R) and Spivak Chapter 3, pp. 39-46 (to middle of 46) (the provisional — but inadequate and about to be refined — definition of a function as a rule or association) — In-Class: Chapter 3, Problem 1.
• Thursday, April 1 — Finish Chapter 3 (defining functions as collections of ordered pairs) and the first two paragraphs of the Chapter 3 Appendix (towards a definition of ordered pairs) — Problem Set 4: Chapter 3, Problems 6 and 8 — Lagrange Interpolation Example with n=4

Week 4 — Chapter 4 — Graphs

• Monday, April 5 — Reading: Spivak Chapter 4, pp. 56-62 — In-Class: Chapter 4, Problems 2, 3, and 4
• Thursday, April 8 — Reading: Finish Chapter 4 and Appendix 1 to Chapter 4 (Vectors) — Problem Set 5: Chapter 4, Problem 14(ii) and (iv) and plot examples with f(x)=x²-4 and a couple of interesting values for c, Problem 17, Problem 20, Problem 21(a)

Week 5 — Chapters 4 and 5 — Graphs and Limits

• Monday, April 12 — Reading: pp. 90-95 of Chapter 5 (Limits) — Problem Set 6: Problems on Vectors
• Thursday, April 15 — Reading: pp. 96-103 of Chapter 5 (Definition of Continuity and Two Theorems about Limits) — In-Class: Chapter 5, Problems 1, 2, and 3

Week 6 — Chapter 5 — Limits

• Monday, April 19 — Reading: Finish Chapter 5 — Problem Set 7: Chapter 5, Problems 3(iii) and (iv), 6(i)-(iii), and 7
• Thursday, April 22 — Midterm

Week 7 — Chapter 6 — Continuous Functions

• Monday, April 26 — Return and go over Midterm — Reading: Chapter 6 through Theorem 1 (top of p. 115) — In-Class: Prove parts (2) and (3) of Theorem 1
• Thursday, April 29 — Class canceled due to Shakespeare week