Math 629: History of Mathematics
Frank Sottile

• Opening Remarks:
      This week's reading is first on mechanics, which is an important influence of physics on Mathematics. As an algebraist, physics major, and now applied mathemetician, I appreciate these topics. This is slightly out of place, as it predates and motivates the Calculus, but then it continues quite a bit past the time of calculus. Stillwell probably did not want to split this into two chapter, hence the slight mismatch. At any given time, mathematics is being developed along several fronts, and thus a subject-based historical survey will have to jumo around in time a lot.
      The chapter on mechanics covers a lot of history, from the late medieval period until 1900. This begins with relations between velocity, acceleration, and distance, and ends with chaotic motion and fluid mechanics. I suspect that the compression of topics is due to Stilwell's interests, and probably also the need to keep the book from getting too long.
      I am also assigning reading about differential geometry and curvature, but not yet assigning many homework problems from it. This topic naturally follows mechanics and mechanical curves.
  
• Reading:
  • Chapter 13 in Stillwell's book. Pages 262–263 are a bit cumbersome, and Fulling has a succinct and easy summary of d'Alembert's derivation of the wave equation.
  • Watch the Vsauce videa on the Brachistochrome.
  • Watch the 3Blue1Brown video interviewing Steven Strogartz about the Brachistochrome.
  • Chapter 17 in Stillwell's book. While differential geometry is a 19th century topic, this can be read just after Chapter 13 (next week, we do the three in between).
  • Watch the Numberphile video about curvature and eating Pizza.
  • Read the following Here is a handout I created for a course in differential equations at the University of Toronto, when the students needed a proof that mixed partials derivatives commuted. It, like the differential equations course I had in 1982 at Michigan State was proof-based (the instructor gave careful proofs of all results, including existence and uniqueness of solutions to ordinary differential equations.
• Assignment: Due Monday, 28 March 2022. (HW 9)
  Here is a .pdf and a LaTeX source of the assignment.
  To hand in: We are using Gradescope for homework submission.
  1. Exercises 13.5.1 and 13.5.2.
  2. Do the steps in Fulling's explanation of d'Alembert's derivation of the wave equation.
  3. With your second paper coming due, I will not assign problems from Chapter 17, for now.
  4. Do the three problems in the handout on Clairaut's Theorem about mixed partial derivatives.

Last modified: Sun Mar 20 04:32:47 CDT 2022 by sottile