From the text:
Section 11.3 page 333 (second edition), #5,7,13.
Section 7.4 page 217 (second edition), #8; (= #8 section
4.7 page 204 in first edition).
Also, from the notes of Friday July 7:
HW1: Prove that if f:R^n --> R^m is
differentiable at a, then f is continuous at a.
HW2: Prove that if f is continuous at a, then
there exists positive r and finite M so that ||f(x)|| is less than
or equal to M for all x in the ball of radius r centered at a.
HW3: Consider the polar coordinate map
(x,y)=f(r,theta)=(rcos(theta), rsin(theta)), and its inverse map
(r, theta)=g(x,y)=(sqrt(x^2 + y^2), arctan(y/x)), (on suitable subdomains
of R^2).
(a) Show that the partial derivative of r with respect to
x does not equal the reciprocal of the partial derivative of x with
respect to r.
(b) Find an actual formula for partial r with respect to x
in terms of the four partial derivatives of x and y with respect to r and
theta. (In this case you may end up with a formula which wouldn't work
for the general case of an arbitrary invertible map from R^2 to
R^2, but see if you can derive such a general formula using
the adjoint formula for the inverse of a matrix.)
Also, from class on Monday July 10:
HW4: Use Taylor's Theorem to find an approximate value
for the following quantities, with and error less than 10^(-6).
(a) sqrt(4.1)
(b) the natural logarithm of 1.2
HW5: This is the problem from 7.4 listed above.