# Math 131 - Fall 2018

Instructor: Dr. Silas Johnson
Office: Cupples I, room 107A
Email: silas@wustl.edu
Office hours: MWF 3:30-4:30

Lectures (with Dr. Johnson):

• Section 1: 9-10 MWF, Brown 100
• Section 2: 10-11 MWF, Brown 100

Assistants to the Instructor:

AI office hours are shared among all calculus courses in the Calculus Help Room. It is open approximately 12-4pm Monday through Friday; a detailed schedule is available at the Help Room page. Remember, you can go there anytime, not just when your AI is present.

## Course Outline

This is the first course in a three-semester calculus sequence. Major topics include:

• Functions
• Limits
• Derivatives - the definition and what they represent, how to calculate them, and various applications
• Integrals - the definitions, and simple techniques for calculating them
Later courses in the sequence will develop more advanced integration techniques, further applications, other concepts related to limits, and the extension of all of these ideas to functions of more than one variable.

Learning Objectives: By the end of the semester, you should be able to do the following things with a reasonable degree of fluency:

• Use limits to describe and analyze the behavior of functions.
• Calculate limits using appropriate rules.
• Define the derivative in terms of limits, and use this definition to compute derivatives of simple functions.
• Use an array of differentiation rules to calculate derivatives of more complicated functions.
• Use derivatives and related theorems to describe and analyze the behavior of functions, including in application problems.
• Define the definite and indefinite integral, and describe how they relate to each other.
• Compute definite and indefinite integrals of reasonably simple functions.
In addition, you should be building a number of general skills throughout the course, such as:
• Solving problems you have never seen before
• Working with others to solve problems, including communicating your own work to them in a way they can understand
• Comparing and contrasting different problems or topics
• Understanding how different ideas depend on each other
• Using mathematics to model the world

Discussion Sections are held on Thursdays with the AI's, and will focus primarily on small-group problem solving. You will be responsible for turning in answers to a handful of problems at the end of section, which will count as part of your homework grade. Therefore, attendance at discussion sections is required. Your lowest two discussion section grades will be dropped; any absences will count as one of these two dropped grades.

## Teaching and Learning Philosophy

While it is easy in a large lecture class to sit back and watch math happen on the blackboard, remember that the only way to learn math is to do math. It is crucial to your success that you engage with the material both in and outside of class. We will spend as much class time as we can allowing you to learn actively, rather than passively, in a variety of ways. Be open to the fact that class may not always look like what you think a lecture has to look like!

It is also easy to get lost in a crowd in a class like this, but you will have better results if you approach learning as a community activity. (After all, if that weren't important, you could take this class online!) The best resource you have is not the textbook, old exams, homework problems, or office hours, but your classmates. Use them! Work together in and outside of class, form study groups, ask for and give help. Conversely, remember that you are the best resource they have too, and communicating your ideas to others is a great learning technique and a crucially important skill.

Finally, don't be afraid to make mistakes. Despite all our emphasis on grades, failure is a crucial part of the learning process, and you should not expect to get everything right the first time. It is also your responsibility to help create an environment in which your classmates can safely engage in productive failure.

## Textbook and Materials

Textbook: Calculus, Early Transcendentals, 8th edition, by Stewart. You do not need to purchase any access code for online content along with the book. It is fine to get an old edition, and may save you quite a bit of money. If you do, please check regularly with classmates to make sure you are reading the correct sections.

If you are also taking chemistry, you may be able to save money by buying both textbooks in electronic form through Cengage Unlimited. I've never used this before, so I may not be much help getting it to work, but here is a video from the publisher explaining it. If you need a class key, use wustl 8449 0904. Note that none of this is required! You do not need WebAssign access to take this course; see below about WeBWorK, which is free.

Calculators: You may use any calculator for your homework, but calculators will not be allowed on exams. Formula sheets will be provided for some exams, where appropriate, and these formula sheets will be published ahead of time.

Blackboard: Blackboard is our course management system; grades and homework will be posted there, as well as occasional announcements. To access Blackboard, go to wustl.blackboard.com. Note that all content will be posted under the "Calculus I Merge" course; if you can see your individual section, ignore it.

WeBWorK: WeBWorK is our online homework system. It comes at no cost to you. To use it, navigate to this course's Blackboard page, click on "Content" on the left side, and click the WeBWorK link. The first WeBWorK assignment is already available. It covers only review material and items on this syllabus, so you can try it now to make sure everything is working.

## Homework and Exams

Homework will be assigned weekly via WeBWorK. Homework is due Friday at noon; no late submissions are accepted. WeBWorK problem sets will generally be tied to one section of the book, so there will be multiple sets due each week. Make sure you complete all problem sets each week.

I strongly encourage you to collaborate on your WeBWorK assignments, as long as you are able to solve each problem on your own after discussing it with your classmates. See the section "Teaching and Learning Philosophy" above for more thoughts on the role of collaboration in the learning process.

Discussion section problems: Discussion section problems, which you will solve in small groups, will make up 1/3 of your homework grade. You will turn them in at the end of each section; no make-ups or late submissions will be allowed, but your lowest two scores (including absences) will be dropped.

Suggested problems: I intend to periodically post lists of suggested problems from the textbook. These do not need to be turned in, but they will serve as useful practice for exams and for building your skills.

Exams: There will be three exams, plus a final exam. The dates of these exams are:

• Thursday, September 20th, 6:30-8:30pm
• Wednesday, October 10th, 6:30-8:30pm
• Wednesday, November 14th, 6:30-8:30pm
• Thursday, December 13th, 3:30-5:30pm (final exam)
You are responsible for arranging your schedule so that you can take these exams at the assigned time. If an emergency arises that will preclude your attendance, contact Dr. Johnson as soon as possible. Do not book winter break travel that will conflict with the final exam.

Exams will generally consist of about 15 multiple-choice problems and about 2 free-response (hand-graded) problems. Past exams can be found on the math department website, and I highly recommend taking at least one past exam under timed conditions prior to the first real exam.

Students requiring accommodations for a disability during exams or otherwise should register with Disability Resources as soon as possible. Send your VISA (which you will receive from Disability Resources) to Dr. Johnson at least two weeks in advance of the first exam so your accommodations can be arranged.

grade = (exam1 + exam2 + exam3 + 2*final - min(exam1,exam2,exam3,final) + 2/3*WeBWorK + 1/3*groupwork)/5
where each item is your score expressed as a percentage.
Put another way, each exam is worth 20% of your grade, and your final exam can (if it is to your advantage) replace your lowest other exam score. WeBWorK and groupwork combined are the remaining 20%.

Curve Policy: If the average score on an exam is below 75%, a constant will be added to each student's score for that exam only to bring the average to 75%. This adjustment will take place before scores are plugged into the formula above for total course grade.

Grades will never be adjusted down if the average is over 75%. No adjustment will take place for homework scores or the overall course grade.

• A+: Only given at instructor's discretion
• A: 90 and up
• A-: 85-90
• B+: 80-85
• B: 75-80
• B-: 70-75
• C+: 65-70
• C: 60-65
• C-: 55-60
• D: 50-55 (D+ and D- ranges determined later)
• F: below 50
Note that scores will not be rounded; a total grade of 84.99 is still a B+, not an A-.

If you take the class on a credit/no credit (pass/fail) basis, you must earn at least a C- to pass.

## Useful Resources

Campus Resources

External Math Resources

• Wolfram Alpha is a great way to check your work. Do not use it, however, to do homework problems for you.
• Sage is a Python-based system intended as an open-source alternative to Wolfram Alpha, Mathematica, and similar systems.
• GNU Octave is an open-source alternative to Matlab.
• Khan Academy has been immensely popular with many of my students as a supplemental resource.
• This free textbook from the University of Wisconsin has problems that are more difficult and "thinky" than most of those in Stewart. (Apologies if this link stops working.)

• Do as many problems as you can. Do every problem in the textbook, even, if that's consistent with your mental health and success in other courses.
• Do homework sets as soon as we've covered the relevant material, not right before they're due.
• Read a section or two ahead before class, and attempt a few problems. This shouldn't make class boring; rather, it makes class an opportunity to clarify your thoughts and get a different perspective.
• Come prepared to discussion section so you can make the most of it. You should already have worked on the homework assignment at that point.

## Approximate Schedule

This schedule is only an estimate! If you miss class, please confirm with another student so you can make sure you catch up on the correct material.

Suggested problems are not required, and you do not need to turn them in, but they are a good starting point for your practice. You may find that you need to do more, or fewer, problems to master the material.

Week Dates Sections and Suggested Problems Notes
1 8/27-8/31 Diagnostic Test D: 1-9
1.1: 1-4, 7-10, 16-17, 38-41, 49, 71-72
1.2: 1-4, 8, 11, 17-18, 29-30
1.3: 1-5, 8-14, 29, 33-35, 43-45, 61-62
1.4: 1-4, 11-13, 18-19, 24
1.5: 1-2, 5-15, 18, 21-23, 35-39, 45, 51-52, 63-64, 69-71
2 9/4-9/7 1.5: See last week
2.1: 1-9 (pick any)
2.2: 1-2, 4-6, 9-11, 15-16, 21, 31-33, 45, 52, 54
2.6: 4-8
No class Monday
3 9/10-9/14 2.3: 1, 10-14, 20-25, 29-31, 59-63
2.5: 5-8, 11-12, 19-24, 35-36, 43-48, 53-54, 69
2.6: 17-22, 28-29, 47-49, 55, 63-65
Chapter 1-2 T/F quizzes (for exam review)
Just for fun: 2.5 #67, 68
4 9/17-9/21 2.7: 1, 5-8, 11-13, 23-25, 31-36
2.8: 1-13, 21-31, 41-44, 47-51, 57
3.1: 3-36, 50, 55-56, 65, 68
EXAM 1; Thursday 6:30-8:30pm
5 9/24-9/28 3.2: 3-23, 51-53
3.3: 1-19, 31
3.4: any of 1-54, 77-78, 84-85
6 10/1-10/5 3.5: 5-32, 49-57
3.6: 2-19, 23-26, 31-34
3.8: 1-6
7 10/8-10/12 3.7: 1-10, 15-16, 23-26, 38-39
3.8: 7-17
3.9: 1-6, 13-20, 29-38, 44-50
EXAM 2; Wednesday 6:30-8:30pm
Last day to change to pass/fail Friday 9pm
8 10/17-10/19 3.10: 1-10, 23-28, 32-38
4.1: 3-14, 29-44
No class Monday-Tuesday
9 10/22-10/26 4.1: 47-62
4.7: 2-10, 13-46, and as many more as you want
4.2: 5-14, 17-18, 24-27, 36-38
10 10/29-11/2 4.3: 1-2, 5-6, 8-21, 24-31, 33-48, 66-68, 72
4.4: 1-4, 8-68
4.5: 1-54, 56, 71-72
11 11/5-11/9 4.3-4.5: Continue from last week
4.7: 47-82, as many as you can stand
12 11/12-11/16 4.9: 1-22, 25-48, 51-54 EXAM 3; Wednesday 6:30-8:30pm