Calculus II (Math 105B) Fall 2004

Syllabus

Dr. Katherine F. Stevenson

· Office: FOB 410

• Phone: x6446
• Email: Katherine.Stevenson@csun.edu(kfs4816@csun.edu)
• Webpage: http://www.csun.edu/~kfs4816/
• Office hours: MWF 1-2 (or by appointment)
• Math tutoring lab: SB 300; Hours TBA.

Description: Calculus II covers several topics: Integration, applications, sequences and series.

• The integration section is the most technical. You will have to master various techniques for integrating basic functions like exponential, logarithmic, and rational functions as well as functions made up by composing and multiplying these types of functions. The only way to do well in this section is by doing enough examples so that you become completely comfortable with all the twists and turns. To accomplish this level of comfort, we will spend a lot of time in class on examples (as a class and in small groups). It is essential that you keep up to date on the homework. This does not mean just getting through the assignment, it means understanding the concepts (and that may require that individual students do extra problems).
• The application section is perhaps the most fun part of the course. Here you will see some of the techniques from integration at work. Moreover (and more importantly) you will see the concept of the integral at work. What we do in each application is to break up a problem into “pieces” on which the desired quantity (weight, volume, probability) can be easily approximated. Then we “add up” these local approximations to get a global approximation. Finally by shrinking the “pieces” we get better and better approximations, and in the limit what we have is an integral that computes the quantity exactly. There are two goals for this section: First, breaking up problems into “doable” pieces and second having the discipline to carry the calculations through. Students must become sufficiently comfortable with the first of these goals to able work with completely unfamiliar problem in order to come up with a way to break it up into “doable” pieces.
• The section on sequences, series, and power series has a bad reputation of being very hard. In fact, it need not be. First of all it is important to remember why we do this section. Sequences and series open a door to a more sophisticated way of looking at numbers. It allows us to better understand why we work with the real numbers and not just the rational numbers. Moreover, series give a whole new family of functions to work with, namely power series. The power series look like infinite degree polynomials, and as such they behave very well in terms of calculus. (For example, it is relatively easy to compute their derivatives.) What these power series give us are polynomial functions that approximate more complicated functions locally, and this is very good news. We will spend a lot of class time talking about why! As in the section on integration, students must develop the technical skills to determine whether or not (or where) a sequence or series or power series “converges”. They must also understand why/how the approximation by taylor series (and fourier series) is important.

Text: Hughes-Hallett et. al. Single Variable Calculus

Grading:

• Work during the semester:

· Homework: Due every day in class for approx. 40 grades. The lowest 3 will be dropped and the average of the remaining grades will be your accumulated homework grade.

· 3 Midterms: (Sept. 17, Oct. 15, Nov. 12). No make-ups without a confirmed medical or emergency excuse.

· At the end of the semester, you will have ONE accumulated homework grade and THREE exam grades. The best 3 of these 4 grades will EACH count for 20% of your final grade; the lowest will count for 10% of your final grade.

• Final (Friday, Dec. 10, 9:00-11:00 AM): The final exam will count for 30% of your final grade in the course.

Schedule: There is a schedule for this class posted on the web. It lists an approximation of the order in which we will cover the material. The dates for the midterms and the final exam are fixed.

Homework: Assignments will be posted (MWF) on the course web page (go to my web page an click on Calculus II). I recommend that you work together in groups of about three people who are all of your own level. However, you must hand in your own write up of the assignment. You should spend about 6 hours outside of class working on calculus.

Rules for homework presentation: (Following these rules with be worth 1 out of the 10 points assigned for each homework)

1. The entire homework must be neatly written and clearly presented.
2. The homework should be in the following format:
1. It should be stapled.
2. No spiral notebook paper, please.
3. Your name and the due date must appear clearly in the upper right hand side of the front page.
3. The grader must be able to follow your work and have room to comment on each problem.
1. Rewrite or summarize each problem.
2. Leave space after your solution. Also leave some margin space.

Your homework should be presented at a level geared towards your fellow students. Do not rely on the expertise of the reader (he/she will be instructed to take everything you say literally). When computing, indicate what your calculations are trying to accomplish.

Late assignments: There is a “one class” grace period on all homework. Late homework will not be accepted. Your lowest three homework grades will be dropped. Please save these for emergencies.