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 mathemeician, I appreciate these topics. This is slightly out of place, as it predates and motivates the Calculus, but then goes on way past the time of calculus.
      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.
  
• 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.
  • 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).
• Assignment: Due Monday, 26 March 2018. (HW 11)
  To hand in: Email a .pdf to Mehrzad Monzavi Mehrzad@math.tamu.edu.
  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 more problems from Chapter 17, for now.
     Answering Sean's question, 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 ordinaray differential equations; and this was Differential Equations for Engineers.)