MATH 243 - Calculus III

# FINAL EXAMS ARE DONE, RAW SCORES ARE POSTED HERE.

I am still working on the curve; check back later. The total possible was 220+10 extra credit. Those of you that scored over 200, great job, especially the one who scored over 220!

Office Hours:

• MWF 10:30-11:20
• + by appointment

Tutoring:

Date: Assignment(s): Handouts
January 11 Go over syllabus, etc.

January 13

Start Vectors.

Homework:

Problems: (not to be turned in):
11.1/35, 37, 41, 51
11.2/3-39 odd mult of 3; 31, 41, 49
Will be discussed Friday

Vectors

January 15 Class: Vectors continued. Dot products.

Homework:

Problems:
11.3/3,5, 8, 15,17,19,25b,27
HW will be discussed Next Wednesday

Dot products

Cross products

January 18 No Class (MLK birthday. If you are around, do read the essay posted on my door, written by King when he was still a student.)
January 20

Class: Finish dot products. Start cross products

In-class discussions of problems from 11.3

More 11.3 problems:
11.3/9, 13, 18, 21 (compare to 19!), 27, 28 (these are easier than they look)

January 22 Solution to 11.2#49 (by request) <<=============NEW

Quiz on 11.1-3

#### Solution to Quiz 1

January 25 Cross products (11.4)

11.4/3,5, 7, 11, 23,27,28, 30abc,31,33 (27-31 should go quickly)

(Quiz on the above problems on Friday)

11.4/15, 17, 21,29,35,39, 41

January 27 Finish 11.4

Start 11.5

Lines and Planes
January 29 Finish 11.5(?)

Quiz on 11.4 (first set of problems)

11.5/3,9, 10, 23,25,26,27,31,35,41,45,59,61,65,67

On all of these problems if the answer is a line then give the equation in all three forms: vector, parametric, *and* Cartesian

#### Solution to Quiz 2

February 1 Finish 11.5
February 3 Go over problems from 11.5

Start Ch 12?

February 3

### 4:30-5:30 (or later), Keller 401

February 5 Midterm Exam I

Coverage: Chapters 11.1-5
Approximate breakdown:

25% 11.1,2
25% 11.3
25% 11.4
25% 11.5

Anything covered on the HW or in class is fair game. I cannot advise you too strongly to make sure you (a) understand the difference between a vector and a scalar, and which operations are permissible on which, (b) are quick and accurate at taking norms, dot products, and cross products.

You can bring a crib sheet consisting of one side of one sheet of paper with any notes/formulas/whatever you want on it.

Calculators are NOT allowed.

Quiet food and drinks are OK

Solution to Exam 1. Sorry, I had problems with the audio, so no audio.
February 8 Start Chapter 12

12.1/3, 7,8, 9, 13, 21,23,25,27,28,29b,30

12.2/2, 3, 5,9,17, 18, 27ab,29

Quiz Wednesday, Feb 17 on 12.1, 2

### Here are some solutions to questions asked in class.

Notes on Vector functions 1

Notes on Vector functions 2

February 10 Finish 12.2

Start 12.3

February 12 Finish 12.3

12.3/3,5,7,13; look at 18, 19 (which is easier than it looks, and combines ideas we've been doing), and 20 should be easy for you using the answer to 19!

Discuss HW

February 17 Quiz on 12.1,2 (not trajectories) (Warning: beginning of the period! Don't be late!)

Start 12.4

February 19 Finish 12.4; Start 12.5

12.4/1,5bc,6ab,7ab,9,11, 23,26; look at 17 (for the graphs in 23, 26 feel free to use a computer)

February 22 Finish 12.5

12.5/1,3,5 (see text example 1), 7,11,13,23. (See Figure 12.27 for 7-13; I only care about the normal and osculating planes, not the rectifying plane) Think about 17-19!

Some solutions:
February 24 Discuss HW on 12.3-5

Start Chapter 10(!)

February 26 Quiz on 12.3-5

Continue Ch. 10

10.1/1-21 odd multiples of 3; 23,27,29,33,40,45 (these shouldn't take you more than a few minutes each

### NEW (feb 27)

Lecture notes 1 on Polar Coordinates (includes notes for Feb 26 lecture)

Lecture notes 2 on Polar Coordinates

February 29 10.2/2, 27, , 7, 11, 19,21-24, 25, 32, 34cd

You should be able to do all of these without a computer, but feel free to use a computer to check your answers!

March 4 Discuss 10.1, 10.2 HW

10.3 (cont)

10.3/5,9,11

March 7 Finish 10.3; start 10.4

10.3/17, 23, 29

March 9 Exam Review

HW questions on 10.3 (first part - areas)

Solutions to Quiz 4
March 11 Midterm Exam II

Covers: 11.5, 12.1-12.5,10.1,10.2,10.3 (not arclengths for 10.3)

As usual: no calculators, you may use one side of an 8x11 piece of paper for notes. If any difficult integrals appear on the exam I will provide a table of integrals.

Practice quiz on 10.1-10.2

Practice Exam

The following "practice exercises" from the text might also be helpful:

p650-1/43,45,49,51,52,55,59

p690-1/3,5,6,8,17,21,23. For 23, also find the equation of the osculating plane

by request: 2 solutions from the practice exam (<<<==NEW)
March 14 Finish Polar Coordinates

10.5/5, 9, 13, 29, 37, 39

10.5/45-52, 57-64, 77-78 are all good practice in polar<->Cartesian conversion, but are not really about conic sections. These might be good practice for the Final Exam.

March 16 Start Functions of several variables (Ch. 13)
Mrch 18 Continue Ch 13

Return Midterm Exam II.

Extra Credit Diagnostic Quiz: I'm curious how much you remember from Calc I and II, so I want to gove you a Quiz On Things You Should Already Know. Just taking the quiz and getting your name right will be worth 100%, you will not be graded on how well you actually do on it.

Midterm 2 SOLUTIONS

March 21-25 Spring Break

#### Turn in the completed sheet (hardcopy please!) by the last day of the semester

Solution to Extra Credit Quiz 6
March 28 Graphing surfaces in R^3

You should be able to graph cylinders quickly using the fact that they are cylinders (even non-round ones)

As for Quadric surfaces, I don't expect you to be able to name them, but you should hone your graphing skills to the point where you can graph relatively easy ones and can match equations to their graphs. You should also be able to recognize when an equation is the equation of such a surface.

11.6/ 1-12; 15, 19, 23, 35

More general graphing:

13.1/13-18,21,27,39 (I might add more to these!)

Quiz on this Monday, April 4

March 30

Limits and continuity for functions of n variables

13.2/9,13,17,23,29,35,41,45,51,53

Quiz on this Monday, April 4

Start Derivatives in R^n

13.3/9,15,17,21,27,37,49,51,52,57,69,71,77

Lecture notes on derivatives
April 1 Discuss HW for 11.6, 13.1, 13.2

Continue 13.3

April 4 Continue 13.3 Solutions to Quiz 7

(on 11.6, 13.1, 13.2)

April 6 Finish 13.3

13.3/9,15,17,21,27,37,49,51,52,57,69,71,77
13.5/7, 13, 19, 21, 25, 29, 35

Start 13.5
April 8 Finish 13.5
Start 13.4

13.4/3,9-23 odd,27, 29, 30, 41, 45, 47

April 11 Short quiz on 13.3

Finish 13.4
Start 13.6(?)

April 13
April 14 Review Session (optional)

3:00 Kuy 310

April 15 Midterm 3 (Not April 16, oops)

Covers: 10.4, 11.6, 13.1-3, 13.5

Practice Problems for Exam 3

Probable curve:

A92
B85
C65
D42

EXAM SOLUTION

April 18 Finish 13.4,6

13.4/3,9-23 odd,27, 29, 30, 41, 45, 47
13.6/3,5,9,15,17; optional 21,41

Quiz Friday on these

Some 13.6 solutions by request
April 20 Start 13.7
April 22 Continue 13.7

Quiz on 13.4,6

Quiz 9 solution
April 25
April 27

13.7/3,7,17,27, 29; 31, 35, 37, 39, 41, 45, 47,51, 55
This is a lot of problems; get started soon!

Note: there are no word problems here! I am going to try to find some decent word problems...

Finish 13.7

Start 13.8

13.8/5,9,13,19,23,29 <= 1-constraint LaGrange problems
13.8/31,37 <= 2-constraint LaGrange problems
13.8/43 <= just an interesting problem; try it!

(Sorry, I accidentally had the 13.8 problems posted above the 13.7 problems)

Min-Max Examples

More Min-Max examples

April 29 Finish 13.8 Lecture notes on La Grange Multipliers
May 4 Some answers to homework problems from 13.8 as requested
May 6 Review Session (Optional)

Keller 301

2:30-3:30

May 9 (Monday) Final Exam, 12-2

Usual conditions (no calculator, you will be allowed one side BOTH SIDES of one 8x11 sheet of paper for notes, etc)

Some practice final exams:

Practice Final Exam 1

Practice Final Exam 2

Practice Final Exam 3

COVERAGE:

Chapter 10, 11, 12: approx 60%

• 10.1-3
• 11.1-6
• 12.1-12.5

Chapter 13: approx 40% (yes, I know this is disproportionate!)

• 13.1-13.8

### Announcement on the Extra Credit on Kepler's Laws:

I've had several students ask if they can hand that extra credit in Mondy, at the exam. The answer is yes, I'm happy to extend the deadline until then, but: it is not a huge amount of extra credit, your time might be better spent on studying!