15.1: 2, 5, 8, 9, 11, 12, 13
15.2: 3, 5, 8, 9, 16, 19, 23, 27
15.3: 2, 5, 8, 9, 13, 22, 25, 42, 43, 44, 45, 49, 50*

To hand in Thursday, June 5: 15.3.50. Please present your solution and also address whether it was necessary to reverse the order of integration to obtain the answer.

To prepare for the final. At least one of these problems will appear on the final.

15:5: 3, 10, 12, 18
15.6: 3, 7, 27, 28, 35

Suggested problems for homework:

14.6: 6, 9, 11, 16, 23, 28, 41, 43
14.7: 3, 4, 9, 13, 31, 35, 39
14.8: 6, 7, 19, 21*, 27

To hand in Thursday, May 29: 14.8.21

Suggested Problems for homework

14.1:5, 6, 15, 24, 30, 39, 42, 43, 47*, 55-60
14.3: 4, 10, 15, 16, 21, 22*, 40, 45, 48, 51, 56, 57
14.4: 3, 4, 12, 13, 17, 19, 22, 25, 26, 33, 42 

 To hand in Thursday, May 22: 14.1.47 and 14.3.22.

Suggested Problems for homework

10.2: 33, 36, 42, 43
13.3: 3, 6, 8, 13, 15, 19,22, 30, 31, 33*, 43
13.4: 3, 6, 11, 15, 25, 27, 28, 33, 34

To hand in Thursday, May 15: 13.3.33

Note: Writing assignment II is now assigned. Your group membership and preliminary report are due May 16.

Suggested Problems for Homework

10.1: 12, 15, 16, 25, 28
13.1: 22*, 25, 26, 37, 41, 42*

10.2: 1, 5, 8, 13, 15, 18, 25, 29
13.2: 2, 5, 8, 15, 16, 17, 23, 3, 35

Quiz on Tuesday will be two problems from the assigned problems above. Unlike a homework quiz, I will give you the questions and ask you to solve the problems without your notes. So it it to your advantage to complete all the problems by Tuesday.

To hand in Thursday, May 8: 13.1.22 and 13.1.42

Suggested Problems for Homework

12.5: 1, 5, 9, 10, 12, 25, 27, 5, 39, 43, 51, 55, 67, 69, 71
12.6: 3, 4*, 5, 7, 14, 15, 20, 21-28, 31, 35
10.1: 7, 8, 9, 24
13.1: 2, 5, 11 14, 20, 24

To hand in Thursday: 12.6.4: The directions ask you to describe and sketch the surface. Assume your target audience is either your mother or a younger sibling.

Suggested Problems for homework

12.1: 3, 10af, 11, 14, 17, 21a, 28, 31, 36
12.2: 2, 7, 10, 13, 18, 23, 28, 29, 39
12.3: 1*, 6, 7, 11, 17, 19, 23, 26, 36, 37, 44, 47
12.4: 2, 3,7, 9, 10, 13*, 15, 18, 19, 27, 29, 33, 37, 45, 49

To hand in Thursday: 12.3.1. and 12.4.13. You are asked to explain which expressions are meaningless. Write this up as a clear, self-contained paragraph without stating the question separately. It's trying to help you sort through the notation. What quantities can be added? dotted? scalar multiplied? distributed? crossed? Why might an unthinking student get confused. What are the clues or guideposts to keep you on the right track?

Suggested problems for Taylor Series. You are to hand in your solution to problem 10 on Thursday, April 17.

Solutions are now available.

TN. Find the second Taylor polynomial T2(x) for the  functions f(x) based at b and use the Quadratic Approximation Error Bound to bound the error |f(x) − T2(x)| on the interval I where

1. f(x) = x^5 at b=2 on I=[1.9, 2.1]
2. f(x)=e^{-x} at b=0 on I=[-.1, .1]
3. f(x)=x^{2/3}at b=8 on I=[7.95, 8.05]
4. f(x)=1/x at b=1000 on I=[995,1005]
5. How did the error estimate change from the first time you considered these problems?

Find the nth Taylor polynomial Tn(x) for the functions f(x) based at b given below.

1. sin(x) at b=0
2. e^{-x} at b=0
3. e^{3x} at b=0
4. ln(x) at b=1

To hand-in on Thursday:

Find the 5th Taylor polynomial for f(x) = x^5-3x^4+5x^2+6x-2 based at b=1 two different ways.

1. Use the formula for finding T5(x) discussed in the TN directly.
2. Substitute x=u+1, multiply out the polynomial, collect together powers of u and substitute back u=x-1.

Which method do you prefer? Why is the nth Taylor polynomial equal to f whenever n is greater than or equal to 5? Can you make a similar state for any polynomial?

11.1: 2*, 5, 6, and as many of 17-46 as you can stomach but at a minimum at least 19, 21, 27, 29, 45.

11.2: 1*, 21, 23, 24, 34, 35, 47-51

Please hand in 11.1.2 and 11.2.1 (you might even consider typing your response) by 4 pm, Thursday, April 3.

TN1. Find the first Taylor polynomial T1(x) for the  functions f(x) based at b and use the Tangent Line Error Bound to bound the error |f(x) − T1(x)| on the interval I where

1. f(x) = x^5 at b=2 on I=[1.9, 2.1]
2. f(x)=e^{-x} at b=0 on I=[-.1, .1]
3. f(x)=x^{2/3}at b=8 on I=[7.95, 8.05]
4. f(x)=1/x at b=1000 on I=[995,1005]