Do check the homework page periodically for new homework or changed homework. Hitting the "Reload" or "Refresh" button on your browser with Ctrl or Shift pressed down (depends on the browser) usually makes absolutely sure that you have the newest version.

3.5: 3.5.2, 3.5.7

3.6: 3.6.7, 3.6.8

4.4: 4.4.1, 4.4.4

Honors/Graduate also hand in:

3.6: 3.6.9

4.4: 4.4.6

Sorry but I just noticed that there is no class on monday (duh!) So I moved the 5.4 down to homework 2, and added a couple more problems to homework 1.

5.4: 5.4.1, 5.4.5, 5.4.6

7.1: 7.1.1, 7.1.5, 7.1.6

Honors/Graduate also hand in:

5.4: 5.4.4 The first formula has a typo it should be
$\frac{1}{1+t}-\frac{(-1)^{n+1}}{1+t} t^{n+1}$, the $t^{n+1}$ is missing

7.1: 7.1.7

7.2: 7.2.1, 7.2.2, 7.2.7

7.3: 7.3.1, 7.3.2, 7.3.6

Honors/Graduate also hand in:

7.2: 7.2.11, 7.2.12

7.3: 7.3.9

7.4: 7.4.3, 7.4.4, 7.4.10

7.5: 7.5.1, 7.5.5, 7.5.8

Honors/Graduate also hand in:

7.4: 7.4.9 (Hint: the metric does not need to be at all related to the standard metric)

7.5: 7.5.9

8.1: 8.1.3, 8.1.5, 8.1.7, 8.1.8, 8.1.9, 8.1.12

8.2: 8.2.1, 8.2.3

Honors/Graduate also hand in:

7.6: 7.6.6

8.1: 8.1.14

8.2: 8.2.5

8.2: 8.2.2, 8.2.6, 8.2.7, 8.2.8

8.3: 8.3.2, 8.3.3, 8.3.7

E1) Also compute the derivative of $f(x,y) = (1,x^2+y^2)$ at the point $(1,2)$.

Honors/Graduate also hand in:

8.2: 8.2.12, 8.2.11

8.4: 8.4.1, 8.4.2, 8.4.3 (assume $f$ is differentiable, also on part b, it is same as part a, show it for all $(x,y) \in C(0,1)$)

8.5: 8.5.1, 8.5.2, 8.5.3 (here the function should be $f \colon {\mathbb{R}}^2 \to {\mathbb{R}}^2 \setminus \{ 0 \}$, similarly in part c, $(a,b)$ should not be $(0,0)$),
8.5.5 (there is a missing hypothesis, and another typo, let me just rewrite the problem here:

8.5.5: Consider $z^2 + xz + y =0$ in ${\mathbb{R}}^3$. Find an equation $D(x,y)=0$, such that if $D(x_0,y_0) \not= 0$ and $z^2+x_0z+y_0 = 0$ for some $z \in {\mathbb{R}}$, then for points near $(x_0,y_0)$ there exist exactly two distinct continuously differentiable functions $r_1(x,y)$ and $r_2(x,y)$ such that $z=r_1(x,y)$ and $z=r_2(x,y)$ solve $z^2 + xz + y =0$. Do you recognize the expression $D$ from algebra?

Honors/Graduate also hand in:

8.4: 8.4.5

8.5: 8.5.4, 8.5.7

Make sure to use the new version of the notes (version 2 of chapter 8)

8.6: 8.6.2, 8.6.3

9.1: 9.1.2, 9.1.3, 9.1.4

9.2: 9.2.1, 9.2.3

Honors/Graduate also hand in:

8.6: 8.6.4

9.2: 9.2.6

Make sure to use the new version of the notes (namely version 3 of chapter 9).

9.2: 9.2.10, 9.2.11, 9.2.14 (you don't have to do part e)

9.3: 9.3.3, 9.3.4, 9.3.5

Honors/Graduate also hand in:

9.2: 9.2.12

9.3: 9.3.6

10.1: 10.1.2, 10.1.5, 10.1.6, 10.1.8, 10.1.9

10.2: 10.2.7

Honors/Graduate also hand in:

10.1: 10.1.7

10.2: 10.2.5