Lecture Room: INGRAHAM B10 Lecture Time: MWF 1:20-2:10 Lecturer: Jean-Luc Thiffeault Office: 503 Van Vleck Phone: (608)263-4089 Email: Office Hours: 2:30–3:30 MW, or by appointment.

 grade # of students A 27 AB 20 B 36 BC 15 C 27 D 10 F 17

Class average: 2.55 (roughly BC)

## Schedule of Topics

Key: C = Thomas's Calculus, P = Precalculus

 lecture date sections topic homework 1 01/21 C3 Review of derivatives C p. 235: 1, 4, 5, 6, 10, 11, 13, 14, 25, 26, 36, 37, 40, 42, 46, 47, 63, 64, 65, 70, 73, 77, 108, 110 2 01/23 C4.1 Extreme values C p. 252: 17–21, 28, 29, 35, 39, 40, 45, 48, 53 3 01/26 C4.2 Optimization; Mean value theorem C p. 253: 55, 57, 60, 63, 66, 67; p. 260: 2–7, 23, 24, 26, 27, 31, 33, 34 4 01/28 C4.3 Monotonicity; First derivative test C p. 266: 9–12, 10, 20, 24, 28, 30, 31 5 01/30 C4.4 Concavity; Second derivative test; Curve sketching C p. 275: 9–13, 20, 23, 34, 35, 37, 39 6 02/02 C4.4–4.5 Curve sketching; More optimization C p. 285: 2, 3, 4, 7, 14, 19 7 02/04 C4.6 L'Hopital's rule C p. 298: 7, 8, 12, 15, 19, 23, 25, 28, 29 8 02/06 C4.8;C5.1;C5.2 Antiderivatives; Sigma notation C p. 314: 1–6, 13–15, 17–22, 29–34, 49–52, 68, 69, 77, 78, 81, 94 9 02/09 C5.2;C5.3 Estimating area with finite sums; Definite integral C p. 342: 1, 2, 5, 6, 7, 10, 17, 18; p. 352: 9, 10, 12, 14 10 02/11 C5.3 Area under a curve C p. 353: 15, 19, 20, 27, 29, 30, 32, 37, 49, 50, 55, 56 11 02/13 CA.1 Mathematical induction C p. AP-3: 2, 5, 9, 10 (in Appendix) 12 02/16 C5.4 The fundamental theorem of calculus C p. 365: 2, 3, 5, 6, 9, 14, 17, 19, 25, 28, 29, 30, 32, 33, 35 13 02/18 C5.4;C5.5 Area revisited; Substitution rule C p. 365: 37, 38, 40, 41, 44, 47, 48, 51; p. 374: 1, 2, 4, 7, 11, 12, 14, 17, 24, 29, 41, 43, 44, 46, 48, 50, 54, 55, 56 14 02/20 C5.6 Substitution in definite integrals C p. 383: 1, 3, 6, 8, 13, 14, 22, 26, 28, 32, 34, 39, 46, 50, 55, 56, 60 15 02/23 C5.6; C6.1 Area between curves; Volumes by slicing C p. 405: 1, 3, 6, 9, 12, 15, 16, 25, 29. (see lecture 14 homework as well) 16 02/25 – Midterm 1 17 02/27 C6.1; C6.2 Washer method; Volume by shells C p. 407: 31, 32, 36, 41, 44. p. 414: 2, 3, 8, 14, 22 18 03/02 C6.1; C6.2 More volume examples 19 03/04 C6.4 Moments and centers of mass C p. 434: 3, 6, 8, 10, 12 (35, 36 removed) 20 03/06 P3-6; C7.1 Inverse functions and their derivatives C p. 473: 14, 16, 18, 19, 20, 21, 23, 27, 28, 30, 31, 33, 36 21 03/09 C7.2 Natural logarithms C p. 484: 2, 3, 4, 5, 6, 10, 17, 18, 21, 24, 26, 28, 35 22 03/11 C7.2 Natural logarithms (cont'd); Logarithmic differentiation C p. 484: 37, 38, 44, 49, 52, 54, 55, 60, 64, 68 23 03/13 – Exam tips; Example problems 24 03/23 C7.3; C7.4 Exponential function; General exponential and logarithm C p. 493: 1, 2, 4, 7, 10, 15, 16, 20, 21, 23, 26, 35, 41, 48, 49, 54, 56, 63, 64 25 03/25 C7.4; C7.5 General exp. and log. (cont'd); Exponential growth C p. 500: 1, 3, 4, 6, 10, 14, 15, 16, 30, 32, 39, 46, 50, 54, 60, 65, 69; C p. 508: 1, 3, 8, 12 (except d), 19 26 03/27 C7.7 Inverse trig functions 27 03/30 C7.7 Derivatives of inverse trig functions C p. 530: 2, 6, 7, 8, 13, 14, 17, 23, 27, 29, 33, 45, 41, 46, 49, 50, 58, 62, 72, 75, 84, 88, 98, 99, 100, 104, 106, 109, 110, 111, 116 28 04/01 – Midterm 2 29 04/03 C7.8 Hyperbolic functions C p. 542: 5, 6, 10, 11, 14, 15, 16, 18, 19, 22, 23,24 30 04/06 P8.1–8.2 Law of sines and law of cosines P p. 686: 1, 2, 6, 10, 13, 16, 18, 19, 23, 26, 29, 38. P p. 695: 1, 2, 6, 10, 12, 13, 14, 20, 22, 26, 27, 28, 30, 34, 37, 42 31 04/08 C7.8 Hyperbolic functions (cont'd) C p. 543: 25, 26, 30, 33, 37, 41, 43, 46, 49, 51, 54, 57, 59. Also: find the error in the formula for inverse cosh in the table at the bottom of page 543. 32 04/10 C7.8 The catenary; Special relativity 33 04/13 P8.3 Vectors P p. 710: 1, 2, 4, 9, 12, 14, 15, 16, 18, 19, 22, 26, 29, 32, 33, 35, 38, 40, 41, 43, 46, 48, 49–56, 65, 71 34 04/15 P1.4 Complex numbers: introduction P p. 126: 1–8, 13, 14, 15, 20, 24, 25, 27, 33, 35, 38, 39, 43, 46, 52, 53, 60, 63, 67, 76, 80, 81, 82 35 04/17 P4.3 Complex numbers: polynomials P p. 410: 1, 3, 5, 6, 10, 11, 13, 16, 23, 25, 26, 27, 30, 32 36 04/20 P8.5 The complex plane P p. 740: 3, 6, 7, 8, 9, 11, 12, 15, 17, 18, 19, 20, 22 37 04/22 P8.5 De Moivre's theorem P p. 741: 23, 25, 26, 27, 30, 31, 34, 35, 37, 38, 40, 41, 42, 45, 46, 48, 50, 52 38 04/24 P8.5 Complex definition of sine and cosine P p. 741: 63, 64, 67, 71, 72 39 04/27 C8.3 Partial fractions decomposition C p. 579: 1, 2, 4, 6, 7, 10, 12, 13, 16, 18, 19, 20 40 04/28 C8.3 Partial fractions decomposition (cont'd) C p. 579: 21, 23, 24, 25, 28, 29, 32, 35, 38 41 05/01 C8.2 Integration by parts C p. 568: 1, 3, 6, 9, 12, 17, 20, 21, 23 (see example from class on 5/04 for the last two) 42 05/04 Review C p. 318: 2, 3, 7, 12, 53, 54, 58, 61, 65, 69, 72, 91, 92; p. 389: 39, 40, 45, 47, 48, 56, 71, 72; p. 461: 2, 3, 7, 8, 9, 12, 13, 15; p. 510: 19, 20, 26; p. 547: 1, 4, 7, 12, 14, 16, 19, 24, 25, 27, 28, 30, 31, 37, 40, 43, 52, 53, 59, 66, 70, 71, 74, 77, 78, 79, 81, 84, 85, 92, 93, 94, 96. 43 05/06 Review C p. AP-21: 2, 11, 12, 13, 14 (Argand diagram means the same as complex plane), 19, 20; P p. 740: 16, 18, 23, 26, 27, 28, 46, 50 (note: no review exercises on partial fractions/integration by parts will be assigned, since this was the last thing covered. However, they are included in the final.) 44 05/08 Review See exercices from 05/04 and 05/06. Note that the exercises are not exhaustive: they might not cover absolutely everything that could be on the final. Review the homeworks as well. Updated: curve sketching exercises: C p. 320: 23, 23, 26, 31, 34, 45, 49

## Prerequisites

The official prerequisite is Math 171.

## Syllabus

See the official syllabus.

## Textbooks

The textbooks for the class are

• Precalculus, 6th edition, by Barnett, Ziegler, and Byleen, chapters 3 to 10.
• Thomas' Calculus, 11th edition, chapters 3 to 7.

## Homework and Quizzes

Each week I will assign homework from the textbooks and post it here (above). Each following Tuesday (starting in the second week of class), your TA will give a 20 min quiz during your discussion section, consisting of a few questions from or related to the previous few homeworks. This will make up part of your grade, as described below. The TA for your section might decide to collect some homework or have some additional methods of assessment, at their discretion.

Notes, textbooks, or calculators will not be allowed in the quizzes. At least one of your lowest quiz scores will be discarded, and there will be no make-up quizzes.

Even if it is not collected, you should do all of the homework if you want a chance to do well in the class.

## Teaching Assistants

 Name Office Phone E-Mail Jie Ling 718 Van Vleck 2-0079 ling @ math.wisc.edu Sarah Matz 418 Van Vleck 2-0011 matz @ math.wisc.edu Dan Rosendorf 422 Van Vleck 3-2410 rosendor @ math.wisc.edu Michael Woodbury 422 Van Vleck 3-2410 woodbury @ math.wisc.edu

## Discussion Sections

 Number Time Days Room TA 322 8:50 TR B321 VAN VLECK Woodbury 323 8:50 TR 215 INGRAHAM Ling 325 11:00 TR B235 VAN VLECK Woodbury 328 13:20 TR B135 VAN VLECK Matz 329 14:25 TR B203 VAN VLECK Matz 334 9:55 TR 215 INGRAHAM Ling 335 11:00 TR B131 VAN VLECK Rosendorf 337 12:05 TR 123 INGRAHAM Rosendorf

There will be two midterm exams. Each of the two midterm exams is worth 20 percent, for a total of 40 percent of the final grade. The final exam will count for 40 percent. The remaining 20 percent is a Discussion Section grade allocated by your TA who will base it on homework, quizzes, participation, attendance, and effort. (The Discussion Section grade will be adjusted to account for variations among the TAs.)

 Midterm Exam I 20% (Wednesday Feb 25, 2009, in class) Midterm Exam II 20% (Wednesday Apr 1, 2009, in class) Final Exam 40% (Monday May 11, 2009 at 10:05 A.M.) Discussion section grade 20%

Calculators, notes, and textbooks are not allowed in exams or quizzes. The intelligent use of calculators outside of exam rooms is however encouraged.

## How to do Well in this Course

There are many ways to get help with math. In addition, following these guidelines is a recipe for (but not a guarantee of) success:

### During lectures

• Taking notes (students who are talking, reading newspapers or magazines, or playing with cellphones, laptops, ipods, etc... will be asked to leave the classroom);
• Asking questions if something the instructor says or writes is unclear.

### Outside lectures

• Working out homework problems as well as additional problems;
• Doing problems without looking at the answers or solutions as you go;
• Practicing doing problems under timed, exam-like conditions; you can use past exams to help with this;
• Coming to office hours if necessary (TA first, then instructor);
• The Math Library is located in B224 Van Vleck. This is a nice quiet place to study and has additional sources you may wish to consult if you need a different viewpoint from the textbooks'.

## Midterm 1 Results

 # of scores 155 mean score 61.46 standard deviation 19.2 median score 61

Midterm 1 solutions (courtesy of Sarah)

## Midterm 2 Results

 # of scores 153 mean score 75.08 standard deviation 18.46 median score 80

Midterm 2 solutions (courtesy of Jie)