E-mail: yl688 at (university) dot edu
Office: Malott 201
Math 1120: Calculus II, Fall 2015
Notes:
A summary of calculus without limits (i.e., the old-fashioned differentials): calculus.pdf
An unorthodox introduction to calculus by way of an example: Cardioid.pdf
The closest textbook to this approach that I've come across is Calculus Made Easy by Silvanus P. Thompson. The title itself may have turned many mathematicians off, but it's not one of those ... for Dummies books. The full title, as it first appeared in 1910/1 in the UK, was actually Calculus Made Easy: Being a Very-Simplest Introduction to Those Beautiful Methods of Reckoning which Are Generally Called by the Terrifying Names of the Differential Calculus and the Integral Calculus. Most recently it was reissued in the US in 1998, with an introduction by Martin Gardner describing, among other things, the state of calculus teaching that sadly still rings true today.
Huygens principle for the Dunkl wave operator, notes for A exam
I'm experimenting with a wiki 2.0 for mathematical proofs. See a sample at FTC, with the layout proudly stolen from the Stacks Project.
The Brachistochrone, after the video done by 3Blue1Brown and Steven Strogatz.
I started using brilliant.org, and contributed to two wikis: Taylor's theorem (with Lagrange remainder), and analytic continuation that I'm pround of.