Piazza Class page.
You do need to finish your Second Paper this week.
I will be putting up information about your term paper later this month.
Rough instructions are:
This should be about 2500-3000 words, or a comparable project in another medium.
The topic is your choice, but (like the book) it should involve a nontrivial amount of history and a nontrivial amount of mathematics.
Note that contemporary topics are OK.
If you already have ideas, or want to discuss this, feel free to write me on Piazza.
Week 9: 9 March 2020.
- 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 continues quite a bit 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.
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.
- Reading:
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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.
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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.
Here in Berlin, I eat Pizza with a sharp knife and a fork, as it is served, uncut, on a plate at Italian restaurants.
- Assignment: Due Monday, 23 March 2020. (HW 10)
To hand in: We are using E-campus for homework submission.
- Exercises 13.5.1 and 13.5.2.
- Do the steps in Fulling's explanation of d'Alembert's derivation of the wave equation.
- With your second paper coming due, I will not assign more problems from Chapter 17, for now.
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.)
Last modified: Sat Mar 14 12:53:30 CDT 2020