Lecture Room: B102 VAN VLECK Lecture Time: TuTh 11:00–12:15 Office: 503 Van Vleck Phone: (608)263-4089 Email: Office Hours: 1:00–2:00 Tu, 2:00–3:00 Th, or by appointment.

## Final exam

Here is the practice exam, Sam's solutions, and Yu's solutions.

## Schedule of Topics and Homework

Chapter, section, and page numbers refer to Thomas, 12th ed.

 lecture date sections topic homework 1 09/02 chapt. 1 Functions 1.1: 1–6, 7, 9, 10, 13, 15, 18, 21, 22, 24, 27, 30, 38, 39, 45, 49, 50, 54, 55, 58, 60, 63, 72 2 09/07 2.1–2.2 Average value; limits 2.1: 1, 3, 4, 6; 2.2: 1, 2, 3, 5, 7, 8, 11–22 3 09/09 2.2–2.3 Limits (precise def'n) 2.2: 23, 24, 26, 31, 32, 34, 37–40 (see example 9, p. 52), 43, 44, 48, 52, 55, 56, 63, 64 4 09/14 2.3–2.4 Limits (precise def'n); One-sided limits 2.3 2–5, 8, 9, 11, 16, 17, 18, 20, 21, 22, 23, 25, 31, 32, 35, 38, 42, 43 5 09/16 2.5 Continuity 2.4 1, 2, 4, 5, 8, 13, 14, 16, 18, 21–30; 2.5 1–10, 13–20, 26–30, 32–35, 39–44 6 09/21 2.6 Limits and infinity 2.6: 1, 2, 4–6, 10–12, 16–20, 26–32, 40–44, 50, 51, 55, 56, 65, 66, 82–84, 100–102 7 09/23 3.1–3.2 Differentiation 3.2: 3–6, 10–12, 14, 15, 18, 21, 22, 24, 27–30, 32, 36, 37, 38, 44–46 8 09/28 3.3 Differentiation rules 3.3: 1–7, 15, 16, 17, 19, 22, 23, 27, 31, 33–36, 41, 44. 9 09/30 3.4–3.6 Rate of change; Trig functions; Chain rule 3.4: 2–5, 9, 12, 13, 23, 24, 25, 26; 3.5: 1–3, 7–10, 15, 16, 23, 26, 30, 31, 34, 37, 49, 50, 53, 57. 10 10/05 3.7–3.8 Implicit differentiation; Related rates 3.6: 1–6, 15–18, 27–33, 47–51, 59, 62, 65, 68; 3.7: 1–9, 17, 22–25, 31–33, 41, 42. 11 10/07 — Review and questions 12 10/12 — Midterm 1 13 10/14 3.8–3.9 Related rates; Linearization and differentials 3.8: 1, 2, 11, 13, 14, 15, 18, 19, 29; 3.9: 1–3, 5, 6, 9–11, 14, 15, 17, 20, 25 14 10/19 4.1–4.2 Extreme values; Mean value theorem 4.1: 1–5, 8, 9, 11–14, 23, 25, 26, 28, 30, 31, 32, 35, 36, 38, 39, 41, 46, 47, 49, 52, 55, 60, 61, 65, 68; 4.2: 1, 4, 5, 7, 8, 11, 13. 15 10/21 4.3–4.4 First derivative test; Concavity 4.3: 3–11, 15, 16, 28–31, 36, 37, 43, 44, 49, 51, 55, 60. 16 10/26 4.4–4.5 Applied optimization 4.4: 1–6, 9, 12, 15, 23, 25, 29, 40, 47, 53, 75, 84, 87, 91. 17 10/28 4.7 Antiderivatives 4.5: 1, 3, 8, 10, 14, 22, 27, 47 (d optional). 4.7: 1–5, 10–14, 21–26, 35–42, 49, 50, 57, 58, 62, 68, 69–72, 76–79, 81, 82, 95, 98. 18 11/2 5.1–5.3 Definite integrals — 19 11/4 5.3–5.4 Area; Fundamental theorem 5.3: 9, 10, 12, 14, 15, 20, 29, 31, 32, 36, 40, 43, 46, 47, 50, 51, 54, 56, 61, 72, 73, 75, 82. 20 11/9 5.5–5.6 Substitution 5.4: 1–8, 21–28, 30, 31, 35, 36, 41, 42, 44, 47, 49; 5.5: 1–4, 10, 11, 14, 23–25, 37, 40, 42, 50, 51, 56. 21 11/11 6.1 Area between curves; Volumes 5.6: 1–4, 9–12, 14, 15, 22, 19, 24, 25, 27, 33, 37, 41, 44, 47, 49, 52, 55, 61, 65, 69, 81; 6.1: 1, 2, 5, 7, 11, 14, 15, 17, 21, 25, 33, 34, 38, 43, 45, 51. 22 11/16 — Review and questions 23 11/18 — Midterm 2 24 11/23 6.2–6.3 Volumes by shell method; Arc length 6.2: 1, 4, 5, 9, 12, 14, 17, 21, 24, 28, 29, 34, 41. 6.3: 1, 2, 4, 6, 9, 19, 21. 25 11/30 7.1 Derivative of inverse functions 7.1: 1–6, 8, 11, 12, 14, 18, 19, 22, 29, 31, 33, 35, 38, 42, 43. 27 12/2 7.2 Natural logarithms 7.2: 1, 3, 5, 8–16, 29–34, 39–44, 55–60, 65–68. 28 12/7 7.3–7.4 Exponential functions 7.3: 1, 3, 5, 11, 20, 23, 28, 29, 33, 35, 42, 43, 50, 51, 52, 55, 58, 63–69, 76, 83, 86, 91, 97, 101, 106, 108, 111, 114, 118. 7.4: 23, 25, 27, 30, 33. 29 12/9 7.6 Inverse trig functions 7.6: 4, 5, 9, 12, 21, 26–30, 37–41, 43, 50, 53, 59, 65, 67, 73, 75, 79, 84. 30 12/14 — Review and questions 31 12/16 — Mock final (optional) From 11:00am to 1:00pm in usual classroom (bring paper to write on, since questions will be written on board)

## Teaching Assistants

 Name Office Phone E-Mail Sam Eckels 718 Van Vleck 2-0079 eckels @ math.wisc.edu Ed Dewey 420 Van Vleck 2-3853 dewey @ math.wisc.edu Ting-ting Nan 416 Van Vleck 3-6258 nan @ math.wisc.edu Huanyu Wen 620 Van Vleck 2-3600 wen @ math.wisc.edu Yu Zeng 620 Van Vleck 2-3600 zeng @ math.wisc.edu

## Discussion Sections

 Number Time Days Room TA 340 7:45 MW B337 VAN VLECK Ting-ting Nan 342 8:50 MW B333 VAN VLECK Huanyu Wen 343 9:55 MWF 277 BASCOM Sam Eckels 344 9:55 MW B333 VAN VLECK Ting-ting Nan 346 11:00 MW B333 VAN VLECK Ed Dewey 348 12:05 MW B317 VAN VLECK Ed Dewey 349 13:20 MW B329 VAN VLECK Yu Zeng 350 11:00 MW B123 VAN VLECK Huanyu Wen 351 14:25 MW B203 VAN VLECK Yu Zeng

## Syllabus

See the official list of topics from the textbook.

## Textbook

The textbook for the class is Thomas' Calculus, 12th edition (with 2nd-order differential equations; ISBN 9780321726414). Be careful about the version you buy: the university bookstore has the right one, but Amazon doesn't seem to carry this specific edition. We will cover chapters 1 to 7, inclusive.

If you want additional viewpoints, have a look at the excellent notes by Prof. J. W. Robbin and the equally-excellent notes by Prof. S. B. Angenent.

## Prerequisites

The official prerequisite is one of

• satisfactory placement scores, OR
• Math 112 and Math 113, OR
• Math 114.

You should be comfortable with basic algebra and trigonometry. If you want to do some revision beforehand, work through Chapter 1 of Thomas and of the lecture notes mentioned above.

If you want to check your basic algebra skills, you can take Prof. Robbin's pre-test, with answers.

Attend the Review Workshops (What are you expected to know in your math class?) if you are not sure you know enough precalculus.

## Homework and Quizzes

Each week I will assign homework from the textbooks and post it here (above). Each following Wednesday (starting Sept. 8), 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.

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% (Tuesday October 12, 2010) Midterm Exam II 20% (Thursday November 18, 2010) Final Exam 40% (Wednesday December 22, 2010 at 7:45 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

Read Christelle Vincent's math study guide.

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 nonzero scores 192 (excluding WES) mean score 74 standard deviation 16 median score 77.5

Midterm 1 solutions.

## Midterm 2 Results

 # of nonzero scores 184 (excluding WES) mean score 54% standard deviation 13 median score 54

 grade cut-off score (%) A ≥ 70 AB ≥ 64 B ≥ 56 BC ≥ 50 C ≥ 44 D ≥ 39 F < 39

Class grade average: 2.41 (roughly BC)

Midterm 2 solutions.