- Gower Twitter thread on thinking you've found a great result, but you made a mistake (2021).
- Shannon's math camp notes on analysis, etc.
- My StackExchange question on synthetic division and whether it is every useful for anything.
- I read that Kronecker opposed the use of irrational numbers because they can't be constructed from integers by a finite number of steps. But you can construct pi as the ratio not only as an infinite series, but as the ratio of circumference to diameter. What's wrong with that?
I should set up a latex file in a rasmapedia directory to explain line integrals.
They are really "curve integrals".
1. You want to integrate x^2 over all points between 2 and 6.
2. You want to integrate x^2 + y^2 over all points between y=0, x in [2,6].
3. You want to integrate x^2 + y^2 over all points on the straight line between (2,2) and (6,6) (not intervals now--- vectors).
4. You want to integrate x^2 + y^2 over all points on the curve y = x^3 between (2,8) and 3,27). This is the real stuff.
5. You want to integrate x^2 + y^2 over all points in the area bounded by (0,0) and (0,2) and (2,0) and (2,2).
6. You want to integrate x^2 + y^2 over all points in the area bounded by y = x^3 and y = log x (or some two curves that cross).