Math 2673, Spring Semester, 2009

Class Time Tues and Thurs. 1:00 -2:50

I HOPE ALL OF YOU PASS THIS COURSE, BUT, FOR MOST STUDENTS,
INFORMATION FROM THIS WEB SITE WILL NOT SUBSTITUTE
FOR COMING TO CLASS AND DOING HOMEWORK.

Course Outline for Math 2673

• Upon completing this course the successful Calculus III student will accomplished the following:

1. Graph and find the equation of a line and plane in space.
2. Graph and find the equations of surfaces in space such as cylinders and quadric surfaces.
3. Convert between rectangular, cylindrical and spherical coordinates.
4. Differentiate and integrate vector-valued functions.
5. Find the unit tangent vector and principal unit normal vector of a smooth curve and use to find the arc length .
6. Find the tangential and normal components of acceleration for a smooth curve.
7. Describe graphs, level curves and level surfaces of functions of several variables and evaluate limits of functions of several variables.
8. Discuss the continuity and differentiability of a function of several variables.
9. Find partial derivatives, directional derivatives, gradients and differentials of functions of several variables and use them to solve applied problems.
10. Find equations of tangent planes and normal lines to surfaces.
11. Use the chain rule for functions of several variables (including implicit differentiation).
12. Find extrema of functions of several variables using the second partials test and Lagrange multipliers and solve applied problems.
13. Evaluate iterated integrals and use them to find the area of plane regions.
14. Evaluate multiple integrals in rectangular, polar, cylindrical and spherical coordinates and use them to solve applications involving volume.
15. Use a Jacobian to change variables in multiple integrals.
16. Identify conservative fields.
17. Find the curl and divergence of a vector field and the flux of a field through a surface and solve applied problems.
18. Evaluate line integrals and solve applied problems.
19. Identify when a line integral is independent of path and use the Fundamental Theorem of Line Integrals.
Use Green's Theorem.

Spartan King Leonidas "Before this battle is over, the world will know that few stood against many."

Assignments for the course, to be updated daily.

Week 1, 1/13/09

Tues Ex. 13.1 p. 805 5,11,13,21,23,27,31,35,39,40;

Ex. 13.2 p813,1,3,5,11,17,23,25,35,37,39,41,45

13.3 p. 820 Ex. 15 - 23 odds

Thurs

13.3 Ex. P.821 all the odds

13.4 P.828- 829 EX 3, 5, 7 8

Week 2, 1/20

Tues 13.4 P.828- 829 Every 4th one from 11 - 35 , and 37

&13.5 p.838 1,3,9,13,21,23.29.33.39,45,53,59;

Two cylinders maple and pdf

Bring the next pdf file to class

Some Maple code for the text examples maple and pdf

Some Maple code for the text examples in Section 13.6 in maple and pdf

Thurs 13.6 p.847 EX.11- 19(odds),21-28,41,43,45,4725,35,43,55,57 (DO FOR NEXT TUESDAY)

Week 3 1/27

Tues assigned workp. 865 ex odds 3 thru 25, odss 33- 41 and 49

Thurs Assigned materia; p.847 21 thru 28 maple code or pdf format

P.872 ex 1,3,5, arc length vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv

• MAPLE HOMEWORK #1 You are to do 4 problems using maple and the using a hand drawing. Select one problem from each group.
• The hand drawing should sketch the graph in each of the Planes (Z=0,X=0,Y=0)
• DUE Thursday 2/12/2007
• Problem #1 do one of the folowing: p 847 ex 37 or 39
• Problem #2 do one of the folowing: p 847 ex 38 or 40
• Problem #3 do one of the folowing: p 850 ex33 or 35
• Problem #4 do one of the folowing: p 850 ex 34 or 36
• The following maple sheets for ----------------may be helpful. To download a maple program, you must have Maple.

Week 4, 2/3/2097

Handout maple code and pdf

Tues
Sec 14.3 p 872- 873 EX 1 - 5 odds, 17 - 23 odds

%14.4 ex. 3 thru 15 odds

also some review. SAMPLE EXAM I

some solutions to sample exam maple code or in pdf format

• Week 5 2/10

• The following Sample Exam includes many of the previous questions and is updated withh current page numbers.
• It will be covered in Tuesday's class

Exam1 is posted here

and the maple solutions in pdf are here

( please feel free to use my solutions in your second project).

Week 6 2/17

Tuesday p 926 - 927 EX 1 - 87 odds

Thurs p.944 Ex 21 -26

Assignment to be handed in and graded in teams of at most 2

p. 945 EX 53 on Thursday 2/27.

i

,

Week 7 2/24

LAB II ( exam 1 redone)due Tuesday 2/24

Tues p.956 - 957 Ex 21 - 33 odds and 39 - 44 odds

%15.7 pp. 966 - 968 ex. 1,5,9, ...49

Announced EXAM II for Thursday March 19 Sample Exam II some solutions in maple or pdf

Thurs sin(x+y) in Maple and pdf

tangent plane example in maple,

• Week 8, 3/3
• Tues p961example 4 in Maple and
• exer 31 p 967 in Maple

Team project assignments: All teams are at most 2 students except where noted below. Before signing up for a project, create a team code name. Only code names will be posted beside the project. Only one project per team and one team per project. Once you have bid on a project, please see me for instructions. Some of the projects below require no research investigation at all, while others may require some outside class work as to literature search etc.

• ALL PROJECTS are due/project interview will take place on the last day of class Thursday 4/30/2009. Please make arrangements to saty late if neccessary. A sign up sheet will be available during the last week of class. Projects/interviews may be handed in before that date.

• Design a dumpster, text p. 969. claimed by team excellent

Quadratic approximation and critical points., text p969. claimed by team engineer

• Rocket science , text p 978. (team of 3)

• Design a cost effective torus ( skimpy donut). claimed by team smart bass
• Develope the 3-d Laplace equation in spherical coordinates. claimed by team LaPlace

• Do the Rodabaugh problem i.e find the volume of a cube, sphere and cylinder are found via triple integration using all 3 coordinate systems( 9 problems).

• Intersect three cylinders text page 1041. claimed by Team MAC

• The roller Derby problem text p. 1048.(team of 3)

• Volume of a hypersphere i.e in 4-dimensions (only) of radius R. See text p. 1036 claimed by team hyperspace

• Volume between a surface and its tangent plane. claimed by team SigTau

• Use Lagrange Multipliera to locate a place to live which minimizes your distance commute to work (W), mall(M) and school(S).
where \$S=(-3,5), W= (1,-4)\$ and \$ M=(6,-2)\$.

• Do five problems from the following: (there 3 possible projects here, your choices are 5 odd problems, 5 even problems and ... .) claimed by team vball

3/19 Thursday EXAM II

• BREAK 3/9- 3/13 ( be safe)

Week 9 3/17 st patty's day

tues review for exam 2

Thurs EXAM 2 and

LABIII REDO EXAM 2 in maple Due 3/31 Tues extra credit redo of the exam

You should be able to do this lab by importying my code for the solutions to the sample exam and my answers to your questions.

Week 10, 3/24 Double e intgration

Tuesday

text % 16.3 p 1008 - 09 ex 19 - 27 odds 39 -49 odds

thursday 3/26 CLASS CANCELLED DUE TO SICKNESS

region problem in pdf and in maple

• text
• % 16.3 p 1008 ex 7 - 51 every fourth and every red

Week 11, 3/31 % 16.4 Polars again

Thurs 4/2 % 16.6 EX 9 - 35 odds a triple integral volume done in maple and in pdf

%16.7 , p. 1040 ex 9 - 27 odds

Week 12 4/7 p 1046 ex 9 -29 pdds, 30

P 1045 in maple and in pdf

thurs triple int in maple and in pdf

two cylinders int in maple and in pdf

silo problems in maple and pdf

EXAM III on 4/16 to study for this exam. please look at the problems on page 1046 as covered in class and the old exam III which appears below.

Old sample exam 3 Solutions in pdf and in maple

Spherical Coordinates can be found at
sphereical coordinates

• LAB IV .: redo exam 3 in maple for Tuesday 4/28/2009

Week 13, 4/14

Tues % 17.1, 17.2 p. 1079 -1081 ex 1 - 25 odds, 33,39,43

thurs % 17.3 p. 1099 ex 3 -19 odds

Week 14, 4/21

Tues % 17.4 p.1096 Ex. 1-17 odds

%17.5 ex 1- 7 odds, 12, 13 - 17 odds, 19 21

.thurs

% 17.7 pp 1126 ex 5- 15 odds

Stokes and divergence theorems

Week15, 4/29

Tues Sample questions for Final Exam ( updated 4/25/2009)

,the work example from p1154Example 2 in maple and pdf

FINALS Week:
5/4 -- 5/8

Final Exam Tuesday May 5, 3:15 -5:15

Solution to final in maple and pdf