Math 242, Spring 2019, Assignment 9
From cartan.math.umb.edu
The moving power of mathematical invention is not reasoning but the imagination.
- - Augustus de Morgan
Carefully define the following terms, then give one example and one non-example of each:[edit]
- $\int\int_R f(x,y)\,dA$ (the double integral of $f$ over the rectangle $R$).
- $\int_a^b\int_c^d f(x,y)\,dy\,dx$ (the iterated integral of $f$ with respect to $y$ then $x$).
- $\int_c^d\int_a^b f(x,y)\,dx\,dy$ (the iterated integral of $f$ with respect to $x$ then $y$.
Carefully state the following theorems (you do not need to prove them):[edit]
- Lagrange multiplier equation for multiple constraints.
- Fubini's Theorem.
Solve the following problems:[edit]
- Section 14.8, problems 7, 17, 19, 21, and 23.
- Section 15.1, problems 1, 15, 17, 19, 27, and 33.