Math 222 - Second Semester Calculus

Topics and approximate lecture schedule

1. Review. Integration by parts; examples
   §1-7.
2. Reduction formulas; examples
   §8.
3. Brief review of the inverse trigonometric functions. (We won't do this in lecture as this was already done in 221, but if you feel uncomfortable with the ArcSine or ArcTangent you should do these problems.)
   
4. Partial fraction expansion; examples
   §9.
5. Taylor Polynomials: definition, motivation and examples
   §11,12,13.
6. Lagrange's remainder term and “little oh”
   §14,15,16.
7. Computations with Taylor polynomials, using “little oh”
   §16.
8. Sequences and their limits
   §17.
9. Convergence of Taylor series
   §17.
10. Leibniz’ series for π/4 and ln 2
    §18.
11. Complex numbers: definitions, absolute value, argument, argument of product
    §21-24.
12. DeMoivre's formula and the complex exponential function
    §24-26.
13. Applications of the complex exponential
    §27,28.
14. Differential Equations: First order separable; examples
    §30-31.
15. Linear 1st order diffeqs; two methods, examples
    §32,33.
16. Higher order equations: differential operators, linearity, the superposition principle
    §34,35.
17. Characteristic roots, special case of second order equations in detail
    §35.
18. The inhomogeneous equation (undetermined coefficients)
    §36,37.
19. Applications
    §38.
20. Vectors: addition & scalar multiplication; Parametric equations for lines and planes
    §40-42.
21. The dot product, orthogonality; Orthogonal decomposition; defining equation for lines & planes
    §43.
22. Cross product: definition and properties; The triple product and determinants; applications of the cross product
    §44,45.
23. Vector functions, a.k.a. “parametrized curves”: circle, cycloid, helix; Derivative of a vector function; velocity vector; product rules; Tangents, unit tangent vector; Sketching a parametric curve
    §48-55.
24. Length of a curve, arclength function.
    §56,57.
25. Graphs in Cartesian and Polar coordinates
    §58.

Midterms:

First midterm - Tuesday February 24, 7:15-8:45pm, place to be announced.

Second midterm - Tuesday April 14, at 7:15-8:45pm, place to be announced.

Distribution of grades:

Each midterm will be worth 100 points, the homework 75 points and the Final 175 points, for a total of 450 points. The standard final curve is A 86%, AB 85%, B 76%, BC 75%, C 60%, D 50%.

Homework:

Homework will be assigned after each lecture and discussed and evaluated by the TAs. The TAs might choose to give quizzes or collect assignment. We will occasionally have webbased homework.

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. 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 the Printex copy shop on State Street (they are $12). 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.

The notes come without the answers to the problems. We try to provide enough answers to make you comfortable with your performance, but we will NOT provide complete answers to all problems. In Math 222 we expect you to become progressively independent from continuously checking the accuracy of your answers. If you are unsure about whether or not you are doing the problems correctly, please ask the TA. WE STRONGLY ENCOURAGE YOU TO WORK IN GROUPS. That way you can compare answers, and it is a lot more fun! If you are having trouble finding a group, tell the TA or myself and we will ask around to see if there are groups that you can join.

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. 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