# Math 251, Fall 2004

## Course Materials

Schedule and Homework (Updated Daily)

******NOTE: THE FINAL WILL BE Wednesday, December 22nd, 2004 1-3 pm in MP 104*****

## Brushing Up on Single Variable Calculus

If you need to brush up on your single variable calculus, here are the sections of Stewart's "Calculus" that we rely on in Math 251. Starred sections are especially important.

2.1, 2.6, 3.2, 3.3, 3.5, 3.6**, 3.8, 4.1, 4.3, 4.7, 4.10, 5.1-4, 5.5**, Chapter 6, 7.2-5, 8.1

The material from Chapter 5,6,8 is used in Math 251 Chapters 16, 17.

## Past Exams

Here are the exams I gave in Math 251H, Fall 2003.

Midterm One (pdf)
Midterm Two (pdf)
Midterm Three (pdf)
Final (pdf)

Here are the exams I gave in Math 251, Spring 2004.

Midterm One (pdf)
Midterm Two (pdf)
Midterm Three (pdf)
Final (pdf)

Here are the solutions to the exams I gave in Math 251, Spring 2004.

Exam One Solutions (pdf)
Exam Two Solutions (pdf)
Exam Three Solutions (pdf)

## Midterm Exam One

Exam 1 will be held Fri Oct 1st.
It will cover Chapter 13, and 14.1-14.3.
We will have a review in class on Wed Sept 29th.
Here are some Review Problems
All required and recommended hwk problems
Page 880: 2-16,18-20
Page 881 True/False: 1-14
Page 881-2 Exercies: 1-6,9-21,24,26-35,37-48
Page 917: 1-3,5,6ab,8a
Page 918 True/False: 1-4,6,7,10
Page 918 Exercises: 1-3, 4a, 6,8,9,10,11ac,12,16

## Instructions for redoing Exam One

All students should redo Exam One as a homework exercise. It will count towards your hwk grade for this week. All questions on the exam will be graded. So you can use books/notes if you wish. The point is to help you master the important material in Chapters 13,14. Please do the version of the exam that you did NOT take on Friday. Exam One (b) below is the version that had a little * in the top left corner of the box where I asked you to write your name. The figures for question 4 can be found on page 891 I-VI of the textbook.

Exam One (a) [pdf]
Exam One (b) [pdf]
Solutions to Exam 1 [pdf]

## Midterm Exam Two

Exam 2 will be held Wed Oct 27th.
It will cover 14.4, 15.1-15.5 and 17.6.
Here are some Review Problems
All required and recommended hwk problems
Page 917: 8, Page 918 Exercises: 1,17,18,19,21
Page 1010: 1-11, Page 1011 T/F: 1-3,5,6,8
Page 1011 Exercies: 1-22,25-29,31-38,40
Page 1171 Concept Check: 11, Page 1172: 26a

Solutions to Exam 2 [pdf]

## Midterm Exam Three

Exam 3 will be held Mon 29th Nov.
It will cover 15.6-15.8, 16.1-16.4, 17.1-17.4.
Here are some Review Problems
All required and recommended hwk problems
Page 1010 13-19
Page 1011 T/F 7,9-12; Ex 43-49,51-56,59-62,64
Page 1085 CC 1-3; T/F 1-4
Page 1086 1-6,9-11,13-22,20,30,32,41
Page 1171 CC 1-8; T/F 4-6
Page 1172 1-17

## More Midterm Exams Stuff (Dec 1st)

Exam Two (a) [pdf]
Exam Two (b) [pdf]
Exam Three (a) [pdf]
Exam Three (b) [pdf]
Solutions to Exam 3 [pdf]

## Solutions to last years final (Dec 7th)

Final Exam Solns S04[pdf]

## Final Info (Dec 13th)

The final will cover all material covered on previous exams as well as 16.6-16.9, 17.5-17.9. Since we only covered them very briefly I would only ask easy problems on the material in 16.7,16.8 and 17.9.

Here are some Review Problems from 16.6-16.9, 17.5-17.9

All required and recommended hwk problems
Page 1085 CC 6,9,10; T/F 7
Page 1086 23-28
Page 1171 CC 11-16
Page 1172 18,25-37

## Potential Theory Questions for Final (Dec 13th)

You should be able to state and use/apply all the definitions and theorems we discussed in the lectures. In addition, I may ask theory questions on the following topics. Usually I would ask for a couple of sentences explanation together with a picture. All of these topics were discussed in class. Some are more important than others.

(1) Geometric explanation of definitions of scalar and vector projections
(2) Geometric meaning of dot and cross products
(3) Proof of formula for volume of parallelipied in terms of scalar-triple product
(4) Geometric explanation of parametrization of a line (p858)
(5) Geometric explnation for why Eq. 5 on page 858 is equation of a plane
(6) Geometric explantion for the formula for a parametrization of a plane
(7) Explanation for why the derivative of a parametrization of a curve is a tangent vector to the curve (p893)
(8) Geometric meaning of partial derivative (p 948-9)
(9) Geometric meaning of partial derivative
(10) Proof of theorem relating directional derivative to gradient
(11) Proof of Theorem about maximization of directional derivative (Thm 15 page 982)
(12) Significance of gradient (p985)
(13) Statements and pictures to explain 5 versions of Fundamental Theorem of Calculus (see page 1170 for a brief summary).
(14) Proof of FTC for line integrals (p 1111, top)
(15) Proof that the curl of the gradient of a funciton is 0
(16) Explanation for physical meaning of surface integral of a vector field in terms of flux
(17) Explanation of geometric/physical meaning of the curl of a vector field in terms of circulation (p1160)
(18) Explanation of geometric/physical meaning of the divergence of a vector field in terms of flux per unit volume (p1167)
(19) Explanation of why we need the Jacobean determinant factor (stretching factor) in Change of Variables Theorem and definition of surface intergals.

Last modified Sept 23, 2004