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 […]
There are basically 4 techniques for solving an indefinite integral. Directly/by rules. After algebraic manipulation. Using substitution. By parts. Using limits for improper bounds or internal discontinuities should be mentioned here, but it’s not really in the same category since you don’t use the limit to find an antiderivative. is the method you learn first. […]
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.