UMTYMP Calculus I and III Fall 2005

Website Information

This website is not an official part of your course. In UMTYMP courses we cannot assume students have computers or an internet connections, so you will never be required to access something on this page. For those of you who are online, however, I've placed some materials on this page. For various reasons, Calculus I is much less computerized; exam reviews, for example, are generally assembled with scissors and tape from ITCEP's archive of sample problems. Hence this page includes just a few resources for Calc I students, but quite a bit for people in Calc III.

If you have internet access, the easiest way to reach me is always via email: rogness@math.umn.edu.

Online Resources

As we cover material in class, I will update the following list of tools and websites which might be of interest to you; you'll recognize a few of them from class. These webpages are generally hosted outside of the University of Minnesota.

• Online tutorial of function transformations -- compressions, shifts, etc.
• Function Grapher
• How the coefficients in a polynomial affect the graph.
• Derivative Plotter
• Derivative Puzzles

Homework and Exams

• Exam 1 Review Guide.
• Exam 2 Review Guide.
• Exam 3 Review Guide: (This was assembled with paper and tape. Ask us for a copy.) Download the Solutions

• Region of Integration for 12.7 #30.

Online Examples and Demonstrations

I'll try to post the various demonstrations and interactive examples from class on this page, as well as a few others you might find interesting. Links marked with a (*) are actually examples/demos from a different course here that I've also taught; I'm putting them here because I think they're useful and informative, but beware that the notation can be a little different.

Chapter 10

• Parametrized Surface: A Torus
• Continuously Varying Normal Vectors on a Paraboloid
• Is the cone a smooth surface or not? Watch this animation of the normal vector r_u×r_v on the cone and decide!
• The Moebius Strip,* a nonorientable surface
• Parametrized Surfaces*

Chapter 12

• Estimating Double Integrals
• Change of Variables: Polar to Rectangular Coordinates
  
  • Another example of Rectangular to Polar*
• Change of Variables: A Nonlinear Transfoormation
• Change of Variables in 3D: A Story*

Chapter 13

• The 2D Vector Field Applet we used in class. (External site)
• The 3D Vector Field Applet we used in class. (External site)
• Line integral of a scalar function*
• Line integral of a Vector Field*
• Stokes Theorem: infinitely many surfaces with the same boundary
• Stokes Theorem: infinitely many surfaces with the same boundary (our classroom version)
• Stokes Theorem: surfaces with a vector field G=curl(F): the flux across all of these surfaces is the same!