trying to be a mile wide AND a mile deep
As with related rates, optimization is sometimes approached with some dread. Fortunately, although the calculus has more steps than in related rates, the process is somewhat more cut and dried. A. Make two-word phrase of goal, where first word is minimize or maximize and second word is the name of a quantity. B. Name quantities […]
These are perhaps the epitome of the dreaded “word problem.” Fortunately there is a step by step method for solving them. A. Assign variables to your quantities and find relationship equations for them. B. If relevant, simplify the equations to remove extraneous variables. C. Express given and asked-for rates of change in terms of d/dt. […]
Parametrization is applied when an object is “really” of lower dimension than the space it lives in. Curves, whether they live in 2D or 3D, are really only one-dimensional. A surface, which might live in 3D (such as a sphere), is really only two-dimensional. The “really” is made rigorous by our ability to represent such […]
Here are a few handouts I’ve used in the past to teach parts of calculus. Relating latitude and longitude to spherical coordinates. Bonus appendix about great circles. Trigonometry review for calculus students. A guide to curve sketching. Painfully detailed examples of surface integration.