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
T.Olson, Fall 2011

Link to the microscope :
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. Divergence is seen as the increase in area, while curl is seen as the rotation. See handout for directions on using the microscope to view divergence and curl.

Course Information

Final exam 5:30-7:30pm, Monday, December 12, 2011, in Fisher 139

Getting Help:

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

The Math Learning Center in Fisher 128
Tami's office hours: M-Tu-Th 10am-noon 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

Study Help

Preparing for Tests

Review questions for test #1 (html)
Review questions for test #2 (html)
Review questions for test #3 (html)
SCOOP (pdf) - to appear
- Test #1, Spring 2009
- Test #1, Spring 2006
  
  Our second test covers Sections 16.1-16.5, which is slightly less than what was covered in "Test #2" below. Relevant questions begin halfway through page 2.
- Test #2, Spring 2009
  Our third test covers Chapters 17, 18, and 19, which is slightly less than what was covered in "Test #3" below.
- *Test #3, Fall 2005
- *Test #3, Spring 2006
- Final Exam, Spring 2006
- *Final Exam, Fall 2005

Labs

Mathematical Sciences Instruction Page
Sign up for a MathLab section during the first week of class. You can do this from your "home" computer or you can go to Fisher 331 and ask a Lab Consultant for help starting Thursday.
How to sign up for a lab section
Mathematica TroubleShooting Tips
Hands-on Start to Mathematica
Hands-on Start to Mathematica, part II
Mathematica 6 Tutorial
Calc.III MathLab Coordinator
Questions about the labs (due dates, grades, registration, etc.) should be addressed to the MathLab Calc.III coordinator, Jack Kelley (calc3cc@mtu.edu).

Other Mathematica Stuff

Help for computing divergence and curl (sections 20.1, 20.3) can be found in sec20_1.nb. (Old version. Does it still work?)
Integration help for the section 19.1 and 19.2 homeworks, can be found in sec19_1.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 . Download this to your account and then run it locally using Mathematica. (old version)
Help in drawing parametric curves is in sec4_8.nb. (old version)
Section 16.5 worksheet help: Use sec16_5.nb to view the 3-D regions on integration on the section 16.5 worksheet.
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 to compute integrals in polar coordinates are in polar_integrate.nb.
Homework help for the section 16.2 homework (double integrals), can be found in sec16_2new.nb. (old version)
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.
A Mathematica notebook, graphs.nb, contains Mathematica commands which can be used to generate 3-D graphs of functions of two variables (i.e., z=f(x,y)) and equations in 3 variables. Download this to your account, then run it locally using Mathematica.
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.

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 microscope 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

trolson@mtu.edu

Multivariable Calculus MA3160, Section R04 T.Olson, Fall 2011