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Calculus: A Complete Course - Finney, Demana, Waits, Kennedy

Course Description:

This is Calculus II. We will start with a quick review of the ideas of derivatives and integrals. This will include an introduction to the computer program Maple and its applications to calculus. We will then go on to cover more in depth applications of derivatives and integrals, and further topics including Differential equations, parametric equations, and power series. (This will take us up to about chapter 10).

Homework:

It is hard to learn math just by watching a professor talk about it for three hours a week. Much of your learning will have to take place outside of class through doing the homework problems and projects. Also, class time will often be spent doing group activities.

I will assign homework approximately once a week. Each assignment will have two parts. Part I will consist of more routine problems that are meant to help you become comfortable with the concepts. They will not be graded carefully, but make sure to look at them, they will give you practice with the basic skills that you need to do more complicated problems.

Part II of the homework will consist of more involved problems, giving you chances to look more deeply into the concepts and to get practice expressing mathematical thoughts clearly. You will be expected to write up the required problems carefully; presentation will count.

There will also be two projects. These will be very involved problems and will have very high standards for presentation. You will do them in groups.

Computers and Calculators:

Computers are becoming an important part of Mathematics and science, and so one of the goals of this course will be to gain some familiarity and comfort with computational software. In particular, we will spend some time learning Maple: a powerful mathematical software package.

Class will meet in a computer lab on some days (maybe once every two weeks). And some of the part II homework problems will be done on the computer and turned in electronically.

No particular calculator will be required. In general you will be free to use any calculator that you want to, but be aware that you will always have to show your work clearly (writing down "I used my calculator" doesn't count), and give exact answers where possible.

Tests:

There will be three "midterms" on the following dates: Feb 9, March 16 and April 13. There will be cumulative final exam at the end of the semester. It will be at the officially scheduled final time.

You can make up a test ONLY if you have a compelling and well documented reason for missing it.

Your Final Grade:

The above factors will count towards your final grade as follows:

Final:	100 points
Midterms:	50 points each
Projects:	50 points each
Homework and Participation:	150 total points

When ever I return an assignment or test I will announce the cut offs for A-, B-, and C- for that piece of work. The overall cut offs for your final grade will be the sum of the cut offs for each assignment or test. The cut offs will always be at least 90%=A-, 80%=B-, and 70%=C-, but they will often be lower than that.

Homework Assignments:

Due Monday 1/22:

• Part I: Chapter 3 Review 1-15, 45 (a), 46(a), 60, 61
• Part II: Intro to Maple Worksheet (more on this later), Chapter 3 Review 71, 75

Due Monday 1/29:

• Part I: Section 4.3 1-6, 33 Section 4.5 11-16, 52 a,b
• Part II:
  1. Section 4.3 34, 36 Section 4.5 51
  2. Use Newton's method to find an approximate solution to 1-x² = sin(x), make your approximation accurate to 6 decimal places.
  3. Use Maple to draw a sequence of pictures that illustrate how Newton's method worked in the previous problem. (That is: draw the graph of the function you did Newton's method on, and the tangent lines that were used in the process.)

Due Monday 2/4:

• Part I: Section 6.1 7-25 odd, 31-35 odd, 53 Section 6.2 9-21 odd
• Part II: Section 6.1 26, 54 Section 6.2 48
• Do Section 6.1 28 in Maple.

Due Monday 2/19:

• Part I: Section 6.2 39, 41 Section 6.3 1-15 odd Section 6.4 10-17
• Part II: Section 6.3 26 (a)-(d) Section 6.4 22,35

Due Monday 2/26:

• Part I: Section 5.1 5-8, Section 5.5 1-4, Section 6.6 1-4, 9,10,19,20
• Part II:
  1. Consider the integral from 0 to 3 of e^-x2 (Sorry, I can't figure out an easy way to get a nice looking integral on this web page). Approximate it using:
     1. 6 rectangles
     2. Simpson's rule with n=6
     3. Euler's method with step size 0.5. (Here think of the integral in terms of an anti-derivative: let f(x) be a solution to f'(x)=e^-x2 with f(0)=0, the number you are looking for is f(3).
  2. Look at problem 31 in section 6.5 do part (a), then sketch a slope field for the differential equation, and carefully explain what it tells you about the population.

Due Monday 3/5:

• Part I: Section 5.5 7, 19, 21 Section 7.1 1-8, 12-16
• Part II: Section 5.5 8, Section 7.1 10,25
  Do 20 from section 5.5 in Maple.

Due Monday 4/2:

• Part I: Section 7.5 1, 3, 11, 13, 17, 23, 31
• Part II: Section 7.5 8, 14, 20, 26

Due Monday 4/9:

• Part I: Section 1.4 1-5 Section 7.4 7-13 odd Section 10.1 7-13 odd
• Part II: Section 7.4 4 (add part (d): use geometry to find the exact answer) Section 10.1 16, 27, 36