Everything here is subject to revision. Changes will be announced in class and/or by email.
Please report any mistakes to trolson@mtu.edu

Multivariable Calculus
MA3160, Section R04
Fall 2007

Link to the microscope for Wednesday 12/5:
A vector-field microscope to visualize derivatives, including a flow program that lets you see how polygons distort under the flow of a vector field.

Course Information

Getting Help:

If you can't get your questions answered during the "activity" part of classtime, try these resources:

The Math Learning Center in Fisher 128
- Walk-in hours:
  Sunday 7pm-9pm
  M-Th 10am-5pm and 7-9pm
  Fri. 10am-noon
- Team learning (MA0020) sign up -- it's free!
Tami's office hours: Tu/Th 10am-noon and Fri 1:30-3:00pm in Fisher 310
Send email to trolson
(ask a specific question, or schedule an appointment to meet with me.)
Use your lab TA and fellow students

Informative Handouts

Some formulas you'll be using:

Helpful References

Click here for instructions on how to edit your Netscape Preferences in order to view postscript documents (like some of these below) directly from Netscape.

Vector Facts (postscript)
Review questions for test #1 (html)
Review questions for test #2 (html)
Review questions for test #3 (html)
SCOOP
Try the scoop on electronic reserve. Searching under "Olson" will get you tests/finals from 2000 and 2003. (In addition, copies of some tests and answers are available at the reserve desk in the library.)
Our first test covers chapters 12-14, which is more that what was on the first test in Fall '00. So some of the questions on the Fall '00 Test #2 will be covered in our Test #1.

or look at the following postscript files:
- *Test #1, Spring 2006 OR PDF
- Test #2, Spring 2006 OR PDF
- *Test #3, Spring 2006 OR PDF
- *Final Exam, Spring 2006 OR PDF
- Test #1, Fall 2005 OR PDF
- Test #2, Fall 2005 OR PDF
- *Test #3, Fall 2005 OR PDF
- Final Exam, Fall 2005 OR PDF
Link to the microscope for chapter 12:
A vector-field microsccope to visualize derivatives, including a flow program that lets you see how polygons distort under the flow of a vector field. Divergence is seen as the increase in area, while curl is seen as the rotation.

Labs

Other Mathematica Stuff

Download these notebooks by holding the Shift key while you click the left mouse button on the link.

Help for computing divergence and curl (sections 20.1, 20.3) can be found in sec20_1.nb.
Integration help for the section 19.2 homework, can be found in sec19_2.nb.
Help in computing line integrals for secion 18.2 is in sec18_2.nb.
For Chapter 17: w17_1.nb contains Mathematica commands which can be used to generate parametric plots . To download this to your account, hold the Shift key while you click the left mouse button.
Help in drawing parametric curves is in sec3_8.nb.
Homework help for the section 16.3 homework (triple integrals), can be found in sec16_3new.nb.
Section 16.4: The Mathematica commands Tami used in class are in polar_integrate.nb.
Homework help for the section 16.2 homework (double integrals), can be found in sec16_2new.nb.
To check your answers to section 15.3 homework (Lagrange multipliers), use sec15_3.nb.
Use sec15_1.nb to check your answers to section 15.1 homework.
A Mathematica notebook, w15_1.nb, contains Mathematica commands which can be used to generate graphs for the Play-Doh worksheet (section 15.1). It also has a cute little animation that shows how to deform a Play-Doh bowl into a graph for problem 15. To download this to your account, hold the Shift key while you click the left mouse button.
Use partials.nb to generate the graphics Tami used for illustrating partial derivatives and their relationship to cross-sections (section 14.1).
Use sec12_5.nb to generate the graphics Tami used for graphing slices of functions of three variables (section 12.5).
Use ans12_3.nb to generate pictures illustrating the answers to the contours worksheet.
If you have not used Mathematica before, you should work through Lab Project 1 and Lab Project 2.
This introduction to 3-D graphs is a Mathematica notebook with simple instructions for making all kinds of graphs which will be useful in this class.
A Mathematica notebook, graphs.nb, contains Mathematica commands which can be used to generate 3-D graphs. To download this to your account, hold the Shift key while you click the left mouse button.

Possibly useful calculus links

(These haven't been updated in a long time.)
(I count on my students to tell me if the links aren't working or if there's a new link I should include.)

Units and conversions
Cylindrical and Spherical Coordinates
Spherical Coordinates
MathWorld
Cylindrical Coordinates
Practice quizzes from Terence Gaffney at Northeastern University
Visualize divergence and curl. See how a rectangle flows in a vector field ... divergence is the change in area and curl is the rotation
A vector-field microsccope to visualize derivatives, along with a ``rectangle flow'' similar to the previous link (but here you can enter any vector field you want!)
Vector field flows and divergence interpreted in terms of population migration and population densities
More divergence stuff, including:
- ``Divergence'' of a function of one variable modeling traffic flow and traffic jams
- Divergence in 1,2,3 dimensions modeling population migration and heat flow
- The divergence theorem in terms of population migration

Possibly useful study links

The MTU Math Learning Center in Fisher 128
- Walk-in help: ??3-5pm?? M-Th and ??7-9pm?? Su-Th
David Olson's Study Skills Links
Felder and Stice's "Tips on Test Taking"
Felder Tips on "How to Survive Engineering School"

Calculator links:

(Not all links have been tested -- let me know if some aren't working.)
(And let me know which ones are useful!)

Riemann Sums for HP, TI, Casio, Sharp, from John Courtney at MSU
TI: TICalc.org, Tutorials for TI's, TI Student Page, TI Homepage
Casio

Some pictures

trolson@mtu.edu

Multivariable Calculus MA3160, Section R04 Fall 2007