Homework #1

Due by 5 pm Wednesday September 2^nd.

Problems from book

1. 1-3 This is quite straightforward so long as you visualise the geometry correctly.
2. 1-10 Again, simple practice.
3. 1-18 Hint, how are cross-products related to triangle areas?
4. 1-24 I am especially interested in the answer to the question at the end.
5. 1-27 Calculus practice.
6. 1-33 More calculus practice. Remember the fundamental theorem of calculus!
7. 1-36 And still more. Don't forget about the flat surfaces closing the ends of the cylinder.
8. 1-38 This is clearly a case for Stoke's law. I will offer the direct evaluation, not using Stoke's law, as an challenge for extra credit.
9. (Taken from Fowle's book) A fly moves in a spiral path according to the formula (in Cartesians)
   r(t) = (b sin(ωt), b cos(ωt), c t²)
   Show that the magnitude of the fly's acceleration is constant (assuming that b, c, and ω are constant).
10. A little chain rule practice taken from a problem that we will encounter in chapter 6.
    If we have a function f(r(θ),r'(θ))=√(r(θ)² + r(θ)'²) then evaluate and simplify
    d   ∂f - ∂f.
    dθ ∂r'  ∂r