Math 242, Spring 2019, Assignment 5

I tell them that if they will occupy themselves with the study of mathematics, they will find in it the best remedy against the lusts of the flesh.

- Thomas Mann, The Magic Mountain

Read:

1. Section 14.1.

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

1. $\vec{N}(t)$ (the unit normal to a space curve).
2. $\vec{B}(t)$ (the unit binormal to a space curve).
3. Graph (of a function of two variables).
4. Level curve (of a function of two variables).
5. Contour map (of a function of two variables).

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

1. Formulas for $\vec{T}, \vec{N}, \vec{B},$ and $\kappa$ (in a box at the bottom of page 867).

Solve the following problems:

1. Section 13.3, problems 17, 19, 21, 23, and 47.
2. Section 14.1, problems 7, 9, 13, 15, 19, 33, 36, 38, 45, 47, and 49.

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