Math 242, Spring 2019, Assignment 11

I have found a very great number of exceedingly beautiful theorems."

- Pierre de Fermat

Read:

1. Section 15.3.
2. (Optional) Section 15.4.
3. Section 15.6.
4. Section 15.7.

Carefully define the following terms, then give one example and one non-example of each:

1. Polar coordinates (of a point in the plane).
2. Triple integral (of a function $f$ over a rectangle $R$).
3. Triple integral (of a function $f$ over a general bounded domain $D$).
4. Cylindrical coordinates (of a point in space).

Carefully state the following theorems (you do not need to prove them):

1. Formula for the reduction of double integrals to iterated integrals in polar coordinates (i.e. $dA=\dots$).
2. Formula for the reduction of triple integrals to iterated integrals in cylindrical coordinates (i.e. $dV=\dots$).

Solve the following problems:

1. Section 15.3, problems 1, 3, 7, 9, 13, 29, 31, and 35.
2. Section 15.6, problems 3, 5, 9, 11, 13, 29, and 31.
3. Section 15.7, problems 1, 3, 5, 7, 9, 17, and 19.

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