Multivariable Calculus
MA3160, Section R01
Fall 2006

• Test #3 Feedback
  
  

• Review questions for test #1 (html)
  
  
• Review questions for test #2 (html)
  
  
• Review questions for test #3 (html)
  
  

Course Information

• Course Schedule
  
  
• Course Details
  
  
• Homework Assignments
  
  

Getting Help:

• The Math Learning Center in Fisher 128
  • Walk-in hours:
    Sunday 7pm-9pm
    M-Th 10am-5pm and 7-9pm
    Fri. 10am-3pm
  • Team learning (MA0020) sign up -- it's free!
• Tami's office hours: MW 2:00-3:30pm and F 11am-noon in Fisher 310
• Ask David (dcclark@mtu.edu) or Matt(maamille@mtu.edu), my apprentices
  TA office hours in Fisher 324:
  • Tu/Th 11am-noon (David)
  • Tu/Th 2-3pm (Matt)
• 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

• Study suggestions
• How to read your text
  
  
• Mathematica trouble-shooting guide
  
  
• Computer lab information (probably outdated)

Some formulas you'll be using:

• Differentiation Formulas
• Derivative and Integral Formulas

Helpful References

• 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

• Mathematical Sciences Instruction Page

• Mathematica TroubleShooting Tips

Other Mathematica Stuff

• 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.
  

• A Mathematica notebook, w16_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 for secion 3.8 is in sec3_8.nb.
  

• Homework help for the section 16.3 homework (triple integrals), can be found in sec16_3new.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

• 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:

• 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

• A four-dimensional cube and another
• A five-dimensional cube