Math 283 §2 - Calculus III: Multivariable Calculus

To do your homework you will need to login to Course Compass. Here is a link for student support. If you need technical support, scroll down towards the bottom of the page to find the appropriate link. If all else fail try calling 1-800-677-6337.

If you need help with the mathematics, please do not hesitate to ask me. If you think that the automatic grading system didn't give you fair credit on a HW problem, please come see me during office hours after you have completed the assignment (but no later than a couple of days, please). If I agree with you, I'll adjust your score on the assignment. Any such adjustment must be done after you have completed the assignment but no later than two days after the assignment is due.

You get four "tries" on each HW problem. This means that if the computer marks you wrong (with a red "x"), you can click on the button that says "similar exercise" at the bottom of the screen to get a different version of the problem (and if necessary you can do this up to two more times). On each version of the problem you will normally be given several attempts.

Here is an interesting applet related to vector functions (see section 11.1). Here is another applet related to the circle of curvature discussed in 11.4 (applet 1). Here is another example of such a circle of curvature. Here is another interesting applet for graphing functions of two variables.

Here is are some maple worksheets for 12.1, 12.5 and 12.6.

One can use maple to plot the gradient vector field. See the grad and contour plot for the function f(x, y) = x^2 - y^2.

In 12.8: Lagrange multipliers, a key geometric insight is that critical points for constrained optimization occur when the level curve of the function is tangent to the constraint curve. In the example, f(x, y) = x^2 + xy + y^2 and the constraint is x^2 + y^2 = 2. Here is another example.

Here is another applet for plotting parametric curves in the plane.

Here is a maple worksheet for viewing vector fields as discussed in 14.2.

Here are two applets related to spherical coordinates:
basic (for plotting points),
surfaces (for graphing surfaces).

Here is an applet for tracing curves represented by vector functions.

Here is a link to a planimeter page; this is related to Green's Theorem (14.4).

Grading policy: Your grade will be a function of your scores on tests, homework and the final. There will be three full period tests. Your grade will be computed as follows:

Tests: All tests will be taken in class. All cell phones and wireless devices must be switched off. No laptops will be allowed.

Homework: We will use an online homework system administered by the textbook company. The big advantage of this system is that you can try the problem several times and online help is available (this will count as a "try"). Check your Course Compass account for the current homework assignments and due dates.

Doing mathematics is the best way of learning. Homework will help you understand the key concepts and to master the skills you will need to succeed in this course. You should try to work on the problems assigned for a section as soon as the material is covered (if not earlier).

Some announcements relating to tests etc. may be posted at the top of this page. I also plan to post review sheets and solutions to tests.

Here are some applets that aid in visualization of mathematical objects in three-dimensions. The first one listed, "Parametric Surfaces in Rectangular Coordinates," is especially interesting.

Maple (a mathematical software package) is available for use on the computers in the Math Center, AB 610. Maple is particularly effective in helping the student visualize graphs of functions of two or more variables.

The Department of Mathematics and Statistics supports providing equal access for students with disabilities. I encourage any student needing to request accommodations for a specific disability to please meet with me at your earliest convenience to ensure timely and appropriate accommodations.

Test II: Thursday, 29 Oct.
Here are the solutions: IIA, IIB, IIC.
There will be a review Wednesday. The test will consist of two parts: multiple choice (with no partial credit) and free response (where all work must be shown). The two parts will be worth roughly the same number of points. Here are sample tests with both types of questions:

• multiple choice sample test,
• free response sample test.

Note that make-up exams will not be given without prior notice and approval. Only a medical emergency (or equivalent) will constitute grounds for granting a make-up. If there is a medical emergency, a doctor's note will be required.