THE HOMEWORKER™
© Lourdes Juan, All rights reserved.

Welcome to THE HOMEWORKER, designed to help you do your homework in an efficient way.

Has it ever been the case that you studied VERY hard for that Math test, thought you were ready and suddenly, a slightly different version of a problem confused you all over again? Or maybe that same problem that was in the practice didn’t quite look the same on the test? You are in front of the test getting harpooned by vectors coming from all directions and you don’t know how to react: should you confine the vectors in a plane equation, what does equation mean? Oh, it’s terrible.

My diagnosis for your predicament: you are not studying Math the right way.

My solution for you: THE HOMEWORKER.

Learning Math is different from learning other subjects. Many subjects that you learn during your career only require memorizing a bulk of information. Math is different, and if you try to memorize everything you will be lost. In some sense learning Math is like learning how to drive: you don’t memorize every street in the city and which intersection has a left or right arrow, a stop or yield sign or a traffic light. All you learn is a collection of rules that you apply in every situation you may encounter while driving: if the traffic light is yellow I must slow down and stop. In Math you need to learn definitions and properties satisfied by the objects defined (often called theorems).

For example, the definition of right triangle is a triangle one of whose angles is a right angle. A property that right triangles satisfy is the Pythagorean Theorem: the sum of the squares of the lengths of the sides of a right triangle equals the square of the length of the hypotenuse. You often use this property (theorem) when doing computations involving right triangles.

Now that you are preparing to do your homework on the section of cylindrical and spherical coordinates follow THE HOMEWORKER suggestions:

1. Write down the conversion formulas for both cylindrical and spherical coordinates.

2. Take a minute to think about the coordinates, why they are defined in that way and try to make sense of figures 12.59 and 12.65 in your textbook.

3. Then think of the main purpose for you to learn these types of coordinates at this moment: to simplify integrals. So there comes the question of how to use these coordinates in an integral.

4. Write the form of a triple integral in both types of coordinates and pay attention to the particular expression for dV on each of them.

5. Now look at the examples worked in class and try to do them by yourself, without looking at the solutions. Then compare your solutions with the ones worked in class and see what you may have missed.

6. At this point you should be ready to do your homework on this section. Try it! Keep in mind that you don’t have to memorize the problem but be familiar with the method used to solve it.