# Homework

You should make every effort to complete the homework assignments and seek help with problems you have not been able to solve. Be sure to write your name, PID, and section clearly on the front page of your completed assignment. Write clearly and legibly, and make it clear if you are doing the problems out of order.

- Your homework score will be based on your best 4 of 5 homework scores.
- Late homework
**will not be accepted for any reason**. - Any question about HW regrades should be directed to your TA.
- It is strongly suggested that you do extra problems from the book in preparation for the exams.
- Solutions will be posted after the homework is due. If you suspect any typos, please email me about them as soon as possible.

### Homework Assignments

### Homework 1

`Due Friday, August 5 at 5pm`

- 1.1 #4, 10, 11, 16, 18, 20, 24, 26, 28
- 1.2 #6, 12, 15, 18, 20, 23, 30
- 1.3 #4, 5, 6, 8, 10, 15, 16, 18, 20, 26, 31
- Solutions to Homework 1

### Homework 2

`Due Thursday, August 11 at 5pm`

**Section 2.1:**4a, 5, 15, 18 (don't sketch f for 15 and 18), 22, 25, 26**Section 2.2:**3, 4, 6, 9, 10, 14, 24**Section 2.3:**3, 5, 6, 10 (just a and b), 11, 12, 14, 16, 26**Section 2.4:**2, 5, 6, 8, 12, 16, 18, 20, 24- Solutions to Homework 2

### Homework 3

`Due Thursday, August 18 at 5pm`

- Section 2.5: 3, 7, 10, 13, 15, 33, 34, 35
- Section 2.6: 3, 4, 5, 6, 8a, 24, 26, 30
- Section 3.1: 2, 6, 9, 10, 20, 25
- Section 3.3: 4, 6, 10, 22, 26, 30, 40
- 3.3 #42 and 44 were originally assigned, but since we won't cover how to solve these problems until Wednesday they'll be moved to HW 4.
- Note: 3.3 #26 contains a typo. The function should be f(x,y) = ax
^{2}+ by^{2}. - In addition, answer the following questions:
- How many third order partial derivatives does a function of two variables of class C
^{3}have? How many of these are distinct? - How many n
^{th}order partial derivatives does a function of two variables class C^{n}have? How many of these are distinct? - Find all critical points of f(x,y) = x
^{4}+ y^{4}and classify them.

- How many third order partial derivatives does a function of two variables of class C
- Solutions to Homework 3

### Homework 4

`Due Thursday, August 25 at 5pm`

- Section 3.3: 42, 44
- Section 3.4: 2, 3, 4, 15, 19, 20, 38
- Section 4.1: 6, 10, 12, 14, 18, 19, 23
- Section 4.2: 2, 6, 9, 10, 12
- A few notes on this homework:
- In 3.4 #19, you need to assume the three numbers are positive for these problems to make sense.
- In 4.1 #10, you only need to show the rule for paths mapping R to R
^{3}. - In 4.1 #14, find the intersection with the xz plane, NOT the yz plane.

It might be fun for you to think about why there isn't any intersection with the yz plane!

- Solutions to Homework 4

### Homework 5

`Due Thursday, September 1 at 5pm`

- Section 5.1: 2ab, 3ab, 6, 8, 12
- Section 5.2: 2ab, 8, 9, 12, 14
- Section 5.3: 1, 4bcd, 9, 11, 13, 14, 16
- Section 5.4: 4c, 5, 6, 10
- Section 5.5: 1, 2, 11, 12, 26
- Solutions to Homework 5.