Math 221 - First Semester Calculus

Topics and approximate lecture schedule

1. Sets 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.
14. Maxima and Minima.
15. Convexity and Concavity.
16. Optimization problems.
17. Exponential functions and their derivatives: the number e.
18. The Natural Logarithm and its Derivative. Limits involving exponents and logarithms. Exponential growth and decay.
19. Area under a graph of a function, Riemann sums, and the integral.
20. The fundamental theorem of calculus.
21. Properties of the integral, The integral as a function of its integration bounds.
22. The method of substitution for finding antiderivatives.
23. Applications of the integral: area between graphs. Cavalieri's principle and Volumes by the method of slicing.
24. Solids of revolution — “washers”.
25. Solids of revolution — “shells”.
26. Recovering position from velocity, and velocity from acceleration. Parametric Curves.
27. Length of a curve.
28. Work is an integral.

Midterms and Finals:

First midterm - Tuesday October 6 at 7:15pm, place to be announced.

Second midterm - Tuesday November 17 at 7:15pm, place to be announced.

Final - Thursday December 17 at 7:25-9:25pm, 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 100 points (21% each), the homework 120 points (20 pre-Lecture quiz, 40 group work, 60 standard) (25%) and the Final 160 points (33%), for a total of 480 points. The class will not be graded on a curve, the standard final curve is A 86%, AB 85%, B 75%, BC 74%, C 60%, D 50%. This will be changed only if the circumstances require it (the exam was unexpectedly difficult, etc).

Homework:

students are responsible for all problems in the Notes. 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 followed by a pre-Lecture quiz (see "What is the difference between our lecture and other lectures?").

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 textbook, we use notes especially written for the course (see "what is the difference between our lecture and other lectures?"). It is an essential part of the course, and we hope that by the end you will be able to independently read them and understand them. The notes can be obtained from Bob's Copy Shop. If you find any typos/mistakes/misprints in the notes, please report them to me directly, using e-mail if you wish. I will be sure they are corrected and announce it in class if necessary. You DO NOT need to buy any textbook, if you need more practice problems, the math library has standard textbooks in reserve, most students do not need them.

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, 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 me. 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, 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 a recommendations on what else you can do to improve your situation.

All services are free of charge