Milestone map
Milestone map
2 milestones
Do the problem sets and write them up
7–14 weeks (8–10 hrs/week)
Take Introduction to Partial Differential Equations for free and do the problem sets (heat, wave and Laplace equations, Fourier methods, maximum principles). Write every solution up in LaTeX and keep the source and the PDF in one public repo as you go.
Proof required
Link your public repo with the LaTeX source and the PDF of the problem sets (heat, wave and Laplace equations, Fourier methods, maximum principles), and show your self-check (18.152 exams with solutions).
What gets checked
- Every solution is derived, not quoted.
- Exams are marked against the solutions, with scores shown.
- Uniqueness and energy arguments are complete.
Common mistakes
- Copying posted solutions: verifiers read the reasoning and the history.
- A proof that skips the hard step.
- Asking for review before the self-check.
Powstik Guide
A public repo with your LaTeX write-ups of the problem sets (heat, wave and Laplace equations, Fourier methods, maximum principles).
Steps
- Make a public repo for this course.
- Do one problem set at a time; typeset it in LaTeX and commit.
- Self-check: Take each exam timed, then mark it against the posted solutions.
- Fix what the self-check shows, and say what you fixed.
- Ask three people who know the topic to check it.
Template
README Course: Introduction to Partial Differential Equations (MIT OpenCourseWare) What is here (problem sets, PDF): Self-check result: The hardest proof and why:
What gets sent back
- Answers with no reasoning.
- Photos of handwriting instead of typeset work.
- Self-check not shown.
Resources
Foundationstart here
Depthgo deeper
What a verifier looks for
- Every solution is derived, not quoted.
- Exams are marked against the solutions, with scores shown.
- Uniqueness and energy arguments are complete.
- Pick two proofs and check every step: each argument must be correct and complete, not just present.
- Ask about one step; the answer should be clear.
You'll sign in first, then come straight back here.
Solve the heat equation two ways
1–3 weeks (5–8 hrs/week)
Use what you learned. Make a modelling notebook that solves the heat equation on a rod with a Fourier series and with a numerical scheme, proves the series converges, and compares the two. Typeset it in LaTeX (or a notebook with LaTeX maths) in your public repo.
Proof required
Link a modelling notebook that solves the heat equation on a rod with a Fourier series and with a numerical scheme, proves the series converges, and compares the two, in your public repo.
What gets checked
- The Fourier solution is derived in full.
- The numerical scheme is stable for the step sizes used (shown).
- The two answers agree within a stated error.
Common mistakes
- A gap in the main argument.
- A result stated but not proved.
Powstik Guide
A modelling notebook that solves the heat equation on a rod with a Fourier series and with a numerical scheme, proves the series converges, and compares the two.
Steps
- Write one line: what you will prove or show.
- Draft it, then read it cold the next day.
- Ask someone to read it and mark the first step they doubt.
- Fix it and typeset the final version.
- Ask three people to check it.
Template
Title: What this shows: Main result (statement): Proof: What I would look at next:
What gets sent back
- A main step left unproved.
- Not clearly the person's own work.
- Claims more than it proves.
Resources
Foundationstart here
Depthgo deeper
What a verifier looks for
- The Fourier solution is derived in full.
- The numerical scheme is stable for the step sizes used (shown).
- The two answers agree within a stated error.
- Every argument must be correct and complete; mark the first gap you find.
- Check that the work is the person's own.
You'll sign in first, then come straight back here.