## Math 151, Sections 1-3 and 74 Fall 2004

### Schedule

Please also consult the Math 151 syllabus.

Week Date of Monday Topic/Section of book Suggested Homework Workshop Comment
1 Aug. 30 Overview of calculus. Rapid review of pre-calculus. Chapter 1. p. 78 (Exercises): 1-3, 5-8, 10-16, 17, 20, 22, 24, 25, 29 None Rutgers classes start on Sept. 1.
2 Sept. 6 Geometric definition of derivative. Limits. Sections 2.1-2 p. 91: 3, 4, 5, 9; p. 102: 5, 6, 8, 9, 13, 17, 19, 27, 28, 31, 38 1 No classes Monday - Labor Day.
3 Sept. 13 Precise definition of limits. Continuity. Sections 2.3-5 p. 111: 1-4, 19-24, 47, 57; p. 122: 3, 6, 20, 42; p. 133: 4, 15, 20, 25, 27, 51, 52, 61 2
4 Sept. 20 Limits at infinity. Precise definition of the derivative. Sections 2.6-9 p. 146: 4, 5, 11, 12, 16-19, 23-26, 39, 40; p. 156: 5, 8, 11, 12, 15; p. 163: 3, 4, 11, 15, 16 (Hint: cross-multiply, do not use the quotient rule); p. 173: 4, 6, 8, 10, 12, 22, 24, 26, 33, 34, 37, 47; 3
5 Sept. 27 Formulas for the derivative. Related rates. Sections 3.1-4 p. 191: 3-24 (sic), 33, 40, 46, 51, 53, 57; p. 197: 3-12, 19-22, 27, 41, 42; p. 208: 8, 18, 25; p. 216: 1-16, 29, 33, 35, 36, 39; 4 This weeks homework is unusually long. You should be able to take derivatives in your sleep when you are done.
6 Oct. 4 Chain rule. Derivatives of inverses. Implicit differentiation. Sections 3.5-6, 3.8 p. 224: 1-24, 46, 54, 66; p. 233: 3, 9, 16, 29, 41-48; p. 249: 3, 4, 7, 8, 13, 15, 24, 25, 26, 32, 35, 38, 41; 5 Midterm next week
7 Oct. 11 Higher derivatives. Related rates. Sections 3.7-8, 3.10 p. 240: 1, 5, 8, 11, 19, 20, 39, 48, 51, 57; p. 249: 28, 31, 49, 50; p. 260: 1, 6, 14, 23, 24, 31; 6 Midterm on the 11th. Version 1, 2, 3.
8 Oct. 18 Finding roots. l'Hospital's rule. Sections 3.11, 4.9, 4.4 p. 267: 5-8, 10, 13, 32, 36; p. 351: 5-8, 14, 29, 30, 31; p. 313: 1, 2, 3, 7, 10, 15, 21, 22, 29, 36, 37, 38, 47, 53, 54, 68; 7
9 Oct. 25 Minima and maxima. Mean Value Theorem. Sections 4.1-3 p. 285: 1, 3, 11, 22, 27, 29, 34, 39, 46, 55, 61, 62, 65, 68, 78; p. 295: 5, 10, 11, 14, 17, 22, 23, 24, 27, 36; p. 304: 1, 5, 7, 11, 21, 22, 33, 36, 37, 45, 47, 64; 8
10 Nov. 1 More curve sketching. Optimization problems. Sections 4.5-7 p. 323: 1-18, 30, 35, 45, 48, 60; p. 330: 7, 14, 15, 26, 27, 29; p. 336: 2, 3, 9, 17, 22, 27, 33, 40, 56; 8 again
11 Nov. 8 Antiderivatives. Section 4.10 p. 358: 3, 10, 12, 15, 25, 28, 35, 40, 48, 53, 55, 60, 63; 9 Second midterm on the 11th.
12 Nov. 15 Integrals. Sections 5.1-2, Appendix E. p. A38: 1, 6, 12, 14, 25, 30, 44; p. 378: 4, 11, 18, 21; p. 390: 3, 5, 12, 23, 33, 34, 37, 38, 48, 49, 53, 54; 10
13 Nov. 22 Fundamental Theorem of Calculus. Section 5.3. p. 402: 2, 8, 11, 17, 18, 25, 30, 31, 35, 37, 62, 68; 11 No classes WTh - Thanksgiving!
14 Nov. 29 Net change and substitution. Sections 5.4-5. p. 411: 1, 2, 5, 7, 8, 10, 11, 18, 19, 22, 29, 30, 38, 47, 54, 55; p. 420: 1-6, 10, 12, 19, 20, 21, 25, 32, 44, 51, 53, 58, 63, 66, 68; 12
15 Dec. 6 Definition of the logarithm, Areas. Sections 5.6, 6.1. p. 429: 1, 3, 4, 5; p. 442: 1, 2, 3, 4, 9, 14, 17, 18, 43, 44, 45; Review The review problems are quite similar to the final exam. Please email me with any typos you find in this version.
16 Dec. 13 All questions answered. No homework. I will answer any question, excluding those on religion, politics, or the final exam. No workshop. Monday is last day of class.