Math
283 Honors Multivariate Calculus (Fall 2011)
| Instructor |
Mark
Pernarowski |
| Textbook |
Calculus Early
Trans. (2nd ed) |
|
Jon Rogawski |
| Office
Hours |
Schedule
(Wil 2-236) |
| Phone |
994-5356 |
| Classroom |
Wil
1-144 |
|
 |
I have old
quizzes and final exams. If you really need them back soon email me.
Otherwise I will keep final
exams for you to pick up in January
Grading: The course % is determined by:
Midterm 1 M1 100
Midterm 2 M2 100
Final F 100
Quizzes Q 100
_________________________________
400
% = (M1+M2+F+HW)/4
The final is not comprehensive.
Six quizzes each worth 20 points
will be given. Your best 5 quiz
scores determine Q above.
Exam and quizz dates are indicated
on the schedule below. Their content
will be announced in class.
All exams and quizzes are closed
book and no electronic devices
are permitted. All exams will be
given in class.
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Syllabus: Material covered in text is from:
Chapter 12 Vector Geometry
Chapter 13 Calculus of Vector Functions
Chapter 14 Parital Derivatives and Optimization
Chapter 15 Multiple Integrals
Chapter 16 Line and Surface Integrals
Chapter 17 Fundamental Theorems of Vector Analysis
Homework: Suggested homework is listed below.
Although the homework is not graded
it is representative of the kinds of
questions which will be on quizzes
and exams.
Some additional problem sets and/or
handouts may be handed out in class
and/or posted on this site.
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Exam
and Quiz Schedule: All
exams and quizzes are closed book. No
electronic devices are permitted.
| Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
| Aug
29 |
30 |
31 |
Sept
1 |
2 |
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| 5 |
6 |
7 |
8 |
9 |
| Labor
Day |
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Quiz 1
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| 12 |
13 |
14 |
15 |
16 |
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19 |
20 |
21 |
22 |
23 |
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Quiz 2 |
| 26 |
27 |
28 |
29 |
30 |
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Midterm 1 |
| Oct
3 |
4 |
5 |
6 |
7 |
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| 10 |
12 |
12 |
13 |
14 |
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Quiz 3 |
| 17 |
18 |
19 |
20 |
21 |
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| 24 |
25 |
26 |
27 |
28 |
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Quiz
4 |
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31 |
Nov
1 |
2 |
3 |
4 |
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Midterm
2 |
| 7 |
8 |
9 |
10 |
11 |
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Veterans Day |
| 14 |
15 |
16 |
17 |
18 |
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Quiz 5 |
| 21 |
22 |
23 |
24 |
25 |
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Thanksgiving |
Thanksgiving |
Thanksgiving |
| 28 |
29 |
30 |
Dec
1 |
2 |
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Quiz 6 |
| 5 |
6 |
7 |
8 |
9 |
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| 12 |
13 |
14 |
15 |
16 |
| Final@8am |
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FINAL
EXAM: Monday, Dec 12, 8:00-9:50am (Wilson 1-144)
Suggested
Homework: (Will evolve
as course develops, H=harder)
| 12.1 |
5,9,11,19,29,31,33,35,37,41,43,55H |
Vectors in the plane |
| 12.2 |
7,9,11,19,25,27,29,33,39,41,43H,47,53H,51H
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Vectors in space and Equations
of lines |
| 12.3 |
1,9,13,15,23,25,29a,33,37,39,43,45,53,60,62,65
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Dot
product and geometric properties |
| 12.4 |
9,15,21,25,30,31H,41,43
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Cross
product and geometric properties |
| 12.5 |
1,11,13,17,21,23,27,29,31,33,37,46,49,51,57,59H,63H |
Equations
of planes |
| 12.6 |
Will cover later in relation to
Ch 13-15 |
Quadratic
surfaces |
| 12.7 |
Will cover later in relation to
Ch 15 |
Cylindrical and Spherical
Coordinates |
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| 13.1 |
1-3, 5, 8H, 13, 15, 17, 21H, 27, 29,
31, 35
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Vector
functions - Curves |
| 13.2 |
1,5,7,9,13,17,19,25,29,31,39,45,49 |
Vector
functions - Calculus |
| 13.3 |
1,3, 5H, 7, 11, 19H, 25H |
Arclength |
| 13.4 |
3,5,7,11,19,43,45,47 |
Curvature |
| 13.5 |
3,5,31,33,37,39 |
Motion in Space |
| 13.6 |
not covered |
Planetary Motion |
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Midterm
1 : Friday September 30 |
On 12.1-12.5 and
13.1-13.5 |
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Some Review
problems. Review HW questions too.
Exclude: (1) a-i, (3) c-d, (4) c-d, (5) h-i
(6) c-d, (8) e.
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| 14.1 |
1,3,5,7,29,31 |
Functions
of several variables, domain, range |
| 14.2 |
1,5,9,15,21,23,24,26 (x=0,y=0),31H
(rationalize bottom) |
Limits
and continuity |
| 14.3 |
3,7,,13,15,17,19,23,25,29,41,43,57,59,61,65 |
Partial
derivatives |
| 14.4 |
3,5,11H,13,23H (use f(x,y)=x^3y^2
near x=2,y=1) |
Tangent
planes and linear approximations |
| 14.5 |
1,5,7,11,19,21,25, 35, 36, 39,41,
43,61H |
Gradients,
directional derivatives, level sets, geometry |
| 14.6 |
1, 3,10, 13,15,23,25,27 |
Chain Rules |
| 14.7 |
1,5,7,9,11,13,19,35H,45H (set V=xyz,
then find ct. pt.) |
Maxima,
minima, second derivative test |
| 14.8 |
1,3,5,7,9,11,16,17,21,31 |
Lagrange
multipliers, constrained optimization |
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Midterm
2: Friday
November 4 |
On 14.1-14.8 |
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Some Review
problems |
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All homework
excluding 14.7#35 |
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There will be an
implicit differentiation question |
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Old Midterms 2a, 2b, 2d are indicative |
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but showing limits
do not exist too. |
| 15.1 |
19,29,31,35 (ln(xy)=ln(x)+ln(y)),37 |
Double
integral definition |
| 15.2 |
3,9 (x^2=x+2), 11H,
17,19,21,25,27,33,45 |
Double integrals on regions |
| 15.3 |
9,11,15 (sub),17, 21,23H (long) |
Triple Integrals - Cartesian |
| 15.4 |
1,3,5H,7,9,27,29,31,41,42,43,45H(sphere
center (0,0,1)) |
Triple Integrals - Cylindrical
and Spherical |
| 15.5 |
will not cover |
Application of Multiple
Integrals
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| 15.6 |
will not cover |
Change of Variables |
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| 16.1 |
Read |
Vector Fields |
| 16.2 |
1,3,5,9,11,19,21,23,25,27,29 |
Line Integrals |
| 16.3 |
1,3,5,7,9,11,13,17,21 |
Conservative Vector Fields |
| 16.4 |
17,18,21,23,25 (use formula 16.4#9 on
each) |
Surface Integrals of Graphs
- handout |
| 16.5 |
5,7,9,11,13 (N=k,z=4),23,25 |
Surface Integrals of Vector
Fields (Flux) |
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| 17.1 |
not covered |
Green's Theorem |
| 17.2 |
covered but not on final |
Stokes's Theorem |
| 17.3 |
7 and 9 (but don't "verify"),
11,13,17,25 |
Divergence
Theorem |
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Final: Monday Dec 12,
8-9:50am in Wil 1-144 |
15.1-15.4,
16.2-16.5, 17.3 |
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Some Review
problems - old but good |
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Some old multivariate exams |
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Final Exam Solution Set |
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Handouts:
- Here are some OLD review sheets I've
given to similar classes that relate to Chapters
12-13, Chapter 14 and Chapter 15-17. They include
handwritten solution sets but were meant to accompany our previous
text. Regardless, they may be of use to you.
- A summary sheet for Chapter 15-17 Integration Formulae
- You can find examples of old exams and
quizzes I've given here.
These were written for previous M283 and M224 multivariate calculus
courses. You'll note each file has a *.tex file. Mathematicians often
have to use a typesetting program called latex to create the nicely
typeset formulae in texts and papers. If you are interested you can
look at the *.tex files used to create those exams (what I have to edit
to make your tests ----ugh)
Other
Stuff:
The
scientific process
Here are some links to a few cool sites related to the content of this
course:
Graphing
Tools
Barbara Koskosz (University of Rhode
Island)
Simple
Calculus
WebMathematics Interactive
Multivariate
Demos
Jonathon Rogness University of Minnesota
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