Math 2673, Spring Semester, 2009
Class Time Tues and Thurs. 1:00 -2:50
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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
I DO NOT POST GRADES
Upon completing this course the successful Calculus III student will accomplished the following:
Use Green's Theorem.
- Graph and find the equation of a line and plane in space.
- Graph and find the equations of surfaces in space such as cylinders and quadric surfaces.
- Convert between rectangular, cylindrical and spherical coordinates.
- Differentiate and integrate vector-valued functions.
- Find the unit tangent vector and principal unit normal vector of a smooth curve and use to find the arc length .
- Find the tangential and normal components of acceleration for a smooth curve.
- Describe graphs, level curves and level surfaces of functions of several variables and evaluate limits of functions of several variables.
- Discuss the continuity and differentiability of a function of several variables.
- Find partial derivatives, directional derivatives, gradients and differentials of functions of several variables and use them to solve applied problems.
- Find equations of tangent planes and normal lines to surfaces.
- Use the chain rule for functions of several variables (including implicit differentiation).
- Find extrema of functions of several variables using the second partials test and Lagrange multipliers and solve applied problems.
- Evaluate iterated integrals and use them to find the area of plane regions.
- Evaluate multiple integrals in rectangular, polar, cylindrical and spherical coordinates and use them to solve applications involving volume.
- Use a Jacobian to change variables in multiple integrals.
- Identify conservative fields.
- Find the curl and divergence of a vector field and the flux of a field through a surface and solve applied problems.
- Evaluate line integrals and solve applied problems.
- Identify when a line integral is independent of path and use the Fundamental Theorem of Line Integrals.
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
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 1,3,9,13,21,18.104.22.168,45,53,59;
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)
Quadric surfaces maple code, quadric surfaces pdf ,
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
maple code for two and three cylinders maple code in pdf format
Week 4, 2/3/2097
Handout maple code and pdf
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.
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,
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.
Quadratic approximation and critical points., text p969. claimed by team engineer
Rocket science , text p 978. (team of 3)
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)$.
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
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
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
, p. 1040 ex 9 - 27 odds
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
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
% 17.7 pp 1126 ex 5- 15 odds
Stokes and divergence theorems
Tues Sample questions for Final Exam ( updated 4/25/2009)
,the work example from p1154Example 2 in maple and pdf
5/4 -- 5/8
Tuesday May 5, 3:15 -5:15
Solution to final in maple and pdf