trying to be a mile wide AND a mile deep
Using the ease of moving between geometric series and their sums, plus the fact that for power series the derivative of a series is the sum of the derivatives of each term (and likewise for integrals), we can find a wider range of power series without too much trouble. I like making diagrams so here […]
I learned this visualization of the chain rule from one of my grad school officemates. It draws on the fact that “and” usually goes with multiplication (more on that in its own post eventually). Imagine when you have f(g(x)) that x is a little sealed box. It is inside a second sealed box marked g, […]
One of the main things students struggle with on exams is identifying the method to use on each problem. When they are learned in class, they are segregated by type, and their distinguishing features are not always highlighted. Here’s a brief cheat sheet on related rates and optimization. optimization related rates sample keywords maximize, minimize, […]
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. […]