Courses   <-  Sean Forman   <-  You Are Here Calculus III

April 19, 2006

Third Exam Review. The third exam is Wednesday, April 26, 2006.

You will not need a special calculator, one able to do basic arithmetric will be sufficient. Any calculator capable of doing symbolic differentiation will not be allowed (for example the TI-89 and above). You will not have any notes or formulas available to you. Here is a summary of topics covered in the last part of the course. There may be other topics not listed here. You are responsible for all material covered in class and on homework.

The solutions to all assigned homework problems will be available on reserve in the library by Friday afternoon. Go to the front desk and ask for the homework solutions to Dr. Forman's Math 1371 class. The exam will be designed so that you should be able to complete it in 60 minutes.

Do not count on being allowed to do rewrites again.

1. Section 12.7 Converting and using spherical and cylindrical coordinates.

2. Section 14.8 Lagrange multipliers. Setting up and solving constrained max and min problems in two variables. How to set up problems with more than two variables. Any solutions I ask you to find will be solvable in a similar manner to what we've seen in homework or in class.

3. Section 15.1 Double integrals over rectangles. The midpoint rule, and how Riemann integration extends to 2-D.

4. Section 15.2 Iterated Integrals and Fubini's theorem. You should be able to switch the order of integration if asked. And integrate basic functions.

5. Section 15.3 Iterated Integrals over general regions. You should understand how we extend the material in 15.2 to general regions. How to recognize Type I and Type II and how to convert from one to the other if needed.

6. Section 15.4 Integration using polar coordinates. Setting up and solving integrals involving polar coordinates.

7. Section 15.5 Applications of double integrals. I will not ask a probability problem. Mass, centroids, and moments are the application I will test you on.

8. Section 15.6 The formula for surface area of a 3-D surface.

9. Section 15.7 Triple integrals. Using this to find volumes, centroids, etc.

10. Section 15.8 Recognizing and setting up integrals that require cylindrical and spherical coordinates. Being able to integrate them once set up.

There is a lot of integration on this test. Some you may have to do the whole way through. Many you will just have to set up, but not solve. As for integration techniques, I will assume you know and understand substitution and integration by parts.

The exam is not yet completed, but I anticipate the test looking very similar to the homework problems. There may be some true-false questions where I ask you about properties we have covered in class. There may be a couple of extra questions that aren't homework questions, but knowing how to do all of the homework will prepare you very well. Obviously, you should also read through the text and notes as well.