Milestone map
Milestone map
2 milestones
Do the problem sets and write them up
7–14 weeks (12 hrs/week)
Take Differential Equations for free and do the problem sets for all four units (first-order, second-order, Fourier and Laplace, systems). 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 for all four units (first-order, second-order, Fourier and Laplace, systems), and show your self-check (Unit exams and final exam with solutions).
What gets checked
- Every solution shows the method, not just the answer.
- Each unit exam is marked against the solutions, with the score shown.
- A sample of answers is checked by plugging back in or by a numerical solver.
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 for all four units (first-order, second-order, Fourier and Laplace, systems).
Steps
- Make a public repo for this course.
- Do one problem set at a time; typeset it in LaTeX and commit.
- Self-check: Each unit ends with an exam and its solutions. Take it timed, then mark it against the 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: Differential Equations (MIT OpenCourseWare Scholar) 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 shows the method, not just the answer.
- Each unit exam is marked against the solutions, with the score shown.
- A sample of answers is checked by plugging back in or by a numerical solver.
- 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.
Model something real with an ODE
1–3 weeks (5–8 hrs/week)
Use what you learned. Make a modelling notebook that sets up a differential equation for something real (cooling coffee, a spring, a population), solves it by hand and numerically, and compares both with data or a sanity check. Typeset it in LaTeX (or a notebook with LaTeX maths) in your public repo.
Proof required
Link a modelling notebook that sets up a differential equation for something real (cooling coffee, a spring, a population), solves it by hand and numerically, and compares both with data or a sanity check, in your public repo.
What gets checked
- The model's assumptions are stated.
- The exact and numerical solutions agree.
- The argument from model to answer is complete.
Common mistakes
- A gap in the main argument.
- A result stated but not proved.
Powstik Guide
A modelling notebook that sets up a differential equation for something real (cooling coffee, a spring, a population), solves it by hand and numerically, and compares both with data or a sanity check.
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 model's assumptions are stated.
- The exact and numerical solutions agree.
- The argument from model to answer is complete.
- 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.