Math 221 - First Semester Calculus

Topics and approximate lecture schedule

1. Numbers and Functions.
2. The derivative — introduction.
3. Limits. ε and δ.
4. Other kinds of limits. Limit properties.
5. How to show a limit doesn't exist. The sandwich theorem.
6. Continuous Functions. Two trigonometric limits.
7. Derivatives.
8. The differentiation rules.
9. Derivative of powers of functions, Higher derivatives.
10. Derivatives of Sine&co. The Chain Rule.
11. Implicit derivatives and Related Rates.
12. Graph sketching: Tangents, Normals and The Intermediate Value Theorem.
13. Increasing/Decreasing functions, the Mean Value Theorem. Maxima and Minima.
14. Maxima and Minima (continued). Convexity and Concavity.
15. Optimization problems.
16. Exponential functions and their derivatives: the number e.
17. The Natural Logarithm and its Derivative. Limits involving exponents and logarithms. Exponential growth and decay.
18. Area under a graph of a function, Riemann sums, and the integral.
19. The fundamental theorem of calculus.
20. Properties of the integral, The integral as a function of its integration bounds.
21. The method of substitution for finding antiderivatives.
22. Applications of the integral: area between graphs. Cavalieri's principle and Volumes by the method of slicing.
23. Solids of revolution — “washers”.
24. Solids of revolution — “shells”.
25. Recovering position from velocity, and velocity from acceleration. Parametric Curves.
26. Length of a curve.
27. Work is an integral.

Midterms and Finals:

First midterm - Thursday October 10 at 7:15pm, place to be announced.

Second midterm - Thursday November 21 at 7:15pm, place to be announced.

Final - Wesnesday, December 18 at 2:45-4:45pm, place to be announced.

Makeups will be very rarely given. If you have a conflict, please let us know as soon as possible. Only in some serious cases we will give make-ups and the sooner you tell us about it, the easier will be for us to find a solution to the conflict.

Distribution of grades:

Each midterm will be worth 85 points (17% each);
homework 100 points (50 group work, 25 on-line homework, 25 standard) (20%);
discussion quizzes 75 points (15%);
and the final 155 points (31%), for a total of 500 points.
The class will not be graded on a curve, the standard final curve is A 90%, AB 87%, B 76%, BC 74%, C 62%, D 50%. This will be changed if the circumstances require it (the exam was unexpectedly difficult, etc), but it will only be changed downwards.

Homework:

Students are responsible for all problems in the book. Each individual TA will choose which homework to collect, or what material will be included in quizzes. Students will have individual homework, group homework and pre-Lecture readying.

Calculators and computers:

You can use calculators and/or computer while working in the homework (to double check answers, investigate further, etc). But you will NOT be allowed to have any calculator or computer in the exam, so you might want to minimize its use. All exams are written so that you show your work and your understanding of the material, the use of calculators is not needed.

Notes:

This course does not use a comercial textbook, we use an e-book especially written for the course. You DO NOT need to buy any textbook, if you need more practice problems, the math library has standard textbooks in reserve that you can consult.

Classroom etiquette:

While in the classroom students will be asked to turn off their cell phones/tablets/pads, etc, and to refrain from texting, connecting to the internet or readying e-mail. We will ask students to put away any computer and/or tablet. Students should be listening and participating in the discussion, and distractions are not welcome.

Communication between students and Professor:

The best way to communicate with me is coming to my office hours. If you cannot make it to these, try your TA office hours. If you rather talk to me and can't make it to my office hours, please let me know after the lecture and I will try to set an appointment.

Using e-mail is not advisible in general and I discourage it. E-mail leads to many misunderstandings and in large lectures it can be very overwhelming for the Professor. I might not be able to answer them if the numbers are too large. The only way I will be able to answer e-mail is if everyone uses them only for emergencies, that is, when you REALLY need to reach me and can't do it by phone or in person. Use your common sense here.

Further help: There are several ways students can get further help.

The math department has a drop-in tutorial service, the Math lab . It runs afternoon/evening, Monday through Thursday, sometimes on Sunday. It will help with small questions in your homework, etc, but it will not tutor entensively.

The Math Tutorial service does more extensive tutoring, but you need to commit several hours a week. If you do not attend, they will stop your tutoring. You need a referral from your TA to enter the Tutorial service.

Finally, if you feel you are in real trouble in the class early in the semester, you can ask your TA to refer you to the Early Alert System during the third week of classes. The system will have an adviser review your background and issue recommendations on what else you can do to improve your situation.

All services are free of charge.