Math 283 Honors Multivariate Calculus (Fall 2009)
| Instructor |
Mark Pernarowski |
| Textbook |
Multivariate Calculus (6th ed.) |
|
James Stewart |
| Office Hours |
Schedule (Wil 2-236) |
| Phone |
994-5356 |
| Classroom |
Wil 1-144 |
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FINAL EXAM: Thursday, Dec 17, 4:00-5:50pm (Wilson 1-144)
(Chapter 15-16 only. Details listed below)
Formulae Summary Sample Review Questions (scan is a bit fuzzy)
- Double Integrals in Cartesian and Polar Coordinates: 15.2, 15.3, 15.4
- Triple Integrals in Cartesian, Cylindrical, Spherical Coordinates: 15.6, 15.7, 15.8
- Line Integrals of Vector Fields: 16.2 (like defn 13, pg 1042 but none any like Eqn 9, pg 1039)
- Line Integrals of Conservative Vector Fields: 16.3
- Curl of a Vector Field: 16.5 (how to compute curl F on page 1062 and Theorem 4 on pg 1063)
- Surface Area, integrals and Flux
integrals of surfaces that can be described by graphs z=f(x,y):
16.6-16.7 (with special attention to Eqn 9 on pg 1077, Eqn 4 on pg
1083, Defn 8 on pg 1087, Eqn 10 on pg 1088).
- Divergence Theorem: 16.9
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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. With the exception
of the Final, all exams will be
given in class. Final - TBA.
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Syllabus: Material covered in text is from:
Chapter 12 Vector Geometry
Chapter 13 Vector Functions
Chapter 14 Parital Derivatives
Chapter 15 Multiple Integrals
Chapter 16 Vector Calculus
See below for the 'anticpated' schedule
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 will be handed out in class
and/or posted on this site.
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Topics and Suggested Homework:
| 12.1 |
7,11,13,15,20 |
Cartesian coordinates, distance, spheres |
| 12.2 |
13,17,19,21,41 |
Vectors, vector addition and length |
| 12.3 |
5,7,9,17,21,23,25,27,35,37 |
Dot product and geometric properties |
| 12.4 |
1,3,15,19,27,31,43 |
Cross product and geometric properties |
| 12.5 |
7,10,11,15,19,23,27,33,35,43,53,55,62,69 |
Equations of lines and planes |
| 12.6 |
none |
Quadratic surfaces |
| 13.1 |
1,7,9,25,27,37h |
Vector functions, curves |
| 13.2 |
3,5,9,11,13,19,21,23,31,33,34 |
Vector function calculus, tangent vectors |
| 13.3 |
1-3,11,13,17,19,21,25,43 |
Arclength, curvature, normal and binormals |
| 13.4 |
3,5,9,15,22,33,35 |
Velocity, acceleration |
| 14.1 |
11,13,39,41,47 |
Functions of several variables, domain, range |
| 14.2 |
7,9,11,15,25,29,33,39 |
Limits and continuity |
| 14.3 |
5,15,17,19,21,25,39,45,47,51,61 |
Partial derivatives, tangents to surfaces |
| 14.4 |
1,3,11,13,21 |
Tangent planes and linear approximations |
| 14.5 |
1,5,7,9,13,15,21,27,31,49 |
Chain rules, implicit differentiation |
| 14.6 |
4,5,7,9,11,21,25,39,41,47,61 |
Gradients, directional derivatives, level sets, geometry |
| 14.7 |
1,5,7,9,11,15,29,31,39,43 |
Maxima, minima, second derivative test |
| 14.8 |
3,5,7,9,25,27,31,33,39 |
Lagrange multipliers, constrained maximization |
| 15.1 |
none |
Double integral definition |
| 15.2 |
1,3,5,7,9,15,25,29 |
Double iterated integrals |
| 15.3 |
1,3,7,13,15,19,21,23,25,39,41,43,45,51 |
Double integrals on regions, reversing integration order |
| 15.4 |
5,7,9,11,13,19,20,25,29,31 |
Double integrals in polar coordinates |
| 15.5 |
none |
Applications of double integrals |
| 15.6 |
3,9,11,13,17,19,21,31 |
Triple cartesian integrals, volumes, mass |
| 15.7 |
1,3,7,9,11,15,17,19,21,23a,27 |
Triple integrals in cylindrical coordinates |
| 15.8 |
1,3,7,9,11,13,21,23,25,27,39 |
Triple integrals in sphereical coordinates |
| 15.9 |
1,3,11,13 |
Double integrals in arbitrary coordinates |
| 16.1 |
11-14 |
Vector fields, gradient fields |
| 16.2 |
1,5,7,9,13,15,19,22,41 |
Scalar and vector line integrals |
| 16.3 |
3,5,9,12,13,14,15,19,21 |
Potentials, path independence and the Fundamental Thm. |
| 16.4 |
1,5,11,13,17 |
Greens Theorem in the plane, |
| 16.5 |
1,3,5,13,17,31,35 |
Curl and Divergence of a Vector Field |
| 16.6 |
1,5,19,23h,37,38,39,41,43,47,59 |
Areas for graphs and parametric surfaces |
| 16.7 |
5,7,11,15,19,22,23,29 |
Surface integrals and Flux |
| 16.8 |
2,3,7,9,11a |
Stokes' Theorem |
| 16.9 |
1,3,5,11,13 |
Divergence Theorem |
Schedule:
| Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
| Aug 31 |
Sept 1 |
2 |
3 |
3 |
| 12.1 |
12.2 |
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12.3
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12.3/12.4 |
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| 7 |
8 |
9 |
10 |
11 |
| Labor Day |
12.4 |
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12.5 |
12.5 |
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Quiz 1 |
| 14 |
15 |
16 |
17 |
18 |
| 12.5 |
13.1/13.2 |
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13.2/13.3 |
13.3 |
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| 21 |
22 |
23 |
24 |
25 |
| 13.3/13.4 |
13.4 |
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14.1/14.2 |
14.2 |
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Quiz 2 |
| 28 |
29 |
30 |
Oct 1 |
2 |
| 14.3 |
14.3 |
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Review |
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Midterm 1 |
| 5 |
6 |
7 |
8 |
9 |
| 14.4 |
14.5 |
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14.5/14.6 |
14.6 |
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| 12 |
13 |
14 |
15 |
16 |
| 14.7 |
14.7 |
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14.7/14.8 |
14.8
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Quiz 3 |
| 19 |
20 |
21 |
22 |
23 |
| 14.8 |
15.1/15.2 |
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15.2/15.3 |
15.3 |
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| 26 |
27 |
28 |
29 |
30 |
| 15.3 |
15.4 |
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15.4 |
15.6 |
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Quiz 4 |
| Nov 2 |
3 |
4 |
5 |
6 |
| 15.6 |
15.6 |
15.7 |
Review |
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Midterm 2 |
| 9 |
10 |
11 |
12 |
13 |
| 15.7 |
15.8 |
Vetran's Day |
15.8 |
15.9 |
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| 16 |
17 |
18 |
19 |
20 |
| 16.1/16.2 |
16.2 |
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16.3 |
16.3 |
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Quiz 5 |
| 23 |
24 |
25 |
26 |
27 |
| 16.4 |
16.5 |
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Thanksgiving |
Thanksgiving |
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| 30 |
Dec 1 |
2 |
3 |
4 |
| 16.6 |
16.6/16.7 |
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16.7 |
16.7
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Quiz 6 |
| 7 |
8 |
9 |
10 |
11 |
| 16.8 |
16.8/16.9 |
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16.9 |
Review |
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| 14 |
15 |
16 |
Final 17 |
18 |
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4-5:50 (Wil1-144)
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FINAL EXAM: Thursday, Dec 17, 4:00-5:50pm (Wilson 1-144)
Handouts:
- Summary of grading and homework policy, anticipated schedule and HW problems
- Review questions and solutions for Chapters 12-13
- Review questions and solutions for Chapter 14
- Summary of integration formulae
- Review questions for Chapter 15-16
Examples of exams and quizzes for the non-honors Multivariate Calculus course (M224) I have taught in past years can be found here. You will note both *.pdf and *.tex files. Mathematicians often use a typsetting 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 for instance).
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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