I took a break and watched a 45 minute video on Fourier Transforms:
A few take away points for college mathematics instructors:
1. When one talks about the Laplace Transform, one should distinguish between the one sided and two sided transforms (e. g., the latter integrates over the full real line, instead of 0 to .
2. Engineers care about being able to take limits (e. g., using L’Hopitals rule and about problems such as )
3. Engineers care about DOMAINS; they matter a great deal.
4. Sometimes the dabble in taking limits of sequences of functions (in an informal sense); here the Dirac Delta (a generalized function or distribution) is developed (informally) as a limit of Fourier transforms of a pulse function of height 1 and increasing width.
5. Even students at MIT have to be goaded into issuing answers.
6. They care about doing algebra, especially in the case of a change of variable.
So, I am teaching two sections of first semester calculus. I will emphasize things that students (and sometimes, faculty members of other departments) complain about.