Natural Blogarithms

We have finally started taking partial derivatives in Calculus IV. This is definitely one of my favorite parts of the entire Calculus sequence. Today, we finished up talking about limits of functions of several variables and the concept of continuity. We, then, introduced the concept of holding one variable fixed and finding the derivative of the function with respect to the remaining variable. After seeing the picture drawn on the board of two curves, or slices of a surface, and identifying the partial derivatives as the “slope” of tangent lines to those two curves, one of the students made a keen observation: [..]

During this morning’s class I surprised the students by letting them know that today was my turn to answer homework questions at the board. As I have mentioned in previous posts, the students are being randomly selected to present some of the homework problems at the board. For many of them this is a considerably stressful event and with today’s assignment being particularly challenging, I noticed that many were very relieved when I offered to answer some of the questions at the board. Plus, it saves me needing to grade those particular problems. [...]