An interesting multivariable calculus example

Earlier this semester in my Multivariable Calculus course we were discussing the second derivative test. Recall the pesky condition that if is a critical point and , then the test fails. A student emailed me after class and asked the following question. Suppose a function has a critical point at and . Moreover, suppose that…

Parametric curve project for multivariable calculus

I’m teaching two sections of Multivariable Calculus this semester. Each class has 3 hours of lecture and a 1 hour 20 minute lab each week. Last week the students were learning about parametric equations. So in lab I wanted to give them some hands-on experience with 2-dimensional parametric curves. Their assignment was to create a…

Making a hyperboloid out of skewers and rubber bands

George Hart, of the Museum of Mathematics, writes a weekly column at Make Magazine called “Math Monday.” A few weeks ago he showed how to make a hyperboloid of one sheet out of 32 shish kabob skewers and 176 hair rubber bands. (Here is a direct link to the instructions.) We just finished talking about…

Three applets for linear algebra or multivariable calculus

This semester I’m teaching two sections of Calculus III (multivariable calculus) and I happen to be teaching the first four weeks of Linear Algebra. The first couple weeks of both courses cover properties of vectors in Rn. (Of course, just to confuse the instructor and the students who happen to be in both classes, the…

Applets for multivariable calculus

When I was in Portland a few weeks ago for MathFest 2009 I attended the minicourse Creating Demonstrations and Guided Explorations for Multivariable Calculus using CalcPlot3D by Paul Seeburger. Paul has created some applets to be used in calculus classes (mostly, but not exclusively, multivariable calculus). They can be found on his Exploring Multivariable Calculus…