ME 12: Numerical Methods for Engineers

Proof required

Link the public repo with 2.086 Assignment 1 and the Quiz 1 sample problems written up (a typeset PDF, LaTeX source or notebook), and show the self-check: which answers matched and how you fixed the ones that did not.

What gets checked

• Each method's error is shown to shrink at its expected order.
• Code results are checked against an exact answer on a test function.
• The sample problems match their solutions, and misses are reworked.

Common mistakes

• Answers copied from a solution with no working.
• Missing units, or a free-body diagram or sign convention left out.

Powstik Guide

A public write-up of 2.086 Assignment 1 and the Quiz 1 sample problems, with the self-check shown.

Steps

1. Study the linked course material.
2. Solve the problems on your own first.
3. Check them against the self-check and rework the misses.
4. Typeset the write-up (LaTeX or a notebook) in a public repo.
5. Ask someone who knows the subject to check it.

README
ME 12: Numerical Methods for Engineers, unit 1: Interpolation, differentiation and integration
Problems:
Self-check result (matched / reworked):
What I got wrong first and why:

What gets sent back

• No working shown.
• The self-check result is missing.

Resources

What a verifier looks for

• Each method's error is shown to shrink at its expected order.
• Code results are checked against an exact answer on a test function.
• The sample problems match their solutions, and misses are reworked.
• Is the engineering right, not just the final number?

You'll sign in first, then come straight back here.

Proof required

Link the public repo with 2.086 Assignments 2, 3 and 5 and the Quiz 2 and 3 sample problems written up (a typeset PDF, LaTeX source or notebook), and show the self-check: which answers matched and how you fixed the ones that did not.

What gets checked

• Linear solves check the residual and the condition number.
• Regression answers report the fit's uncertainty, not just the line.
• The sample problems match their solutions, and misses are reworked.

Common mistakes

• Answers copied from a solution with no working.
• Missing units, or a free-body diagram or sign convention left out.

Powstik Guide

A public write-up of 2.086 Assignments 2, 3 and 5 and the Quiz 2 and 3 sample problems, with the self-check shown.

Steps

1. Study the linked course material.
2. Solve the problems on your own first.
3. Check them against the self-check and rework the misses.
4. Typeset the write-up (LaTeX or a notebook) in a public repo.
5. Ask someone who knows the subject to check it.

README
ME 12: Numerical Methods for Engineers, unit 2: Linear systems, least squares and regression
Problems:
Self-check result (matched / reworked):
What I got wrong first and why:

What gets sent back

• No working shown.
• The self-check result is missing.

Resources

What a verifier looks for

• Linear solves check the residual and the condition number.
• Regression answers report the fit's uncertainty, not just the line.
• The sample problems match their solutions, and misses are reworked.
• Is the engineering right, not just the final number?

You'll sign in first, then come straight back here.

Proof required

Link the public repo with 2.086 Assignment 4 and the Quiz 4 sample problems written up (a typeset PDF, LaTeX source or notebook), and show the self-check: which answers matched and how you fixed the ones that did not.

What gets checked

• Stability limits are worked out for each explicit method used.
• Convergence order is shown on a log–log error plot.
• The sample problems match their solutions, and misses are reworked.

Common mistakes

• Answers copied from a solution with no working.
• Missing units, or a free-body diagram or sign convention left out.

Powstik Guide

A public write-up of 2.086 Assignment 4 and the Quiz 4 sample problems, with the self-check shown.

Steps

1. Study the linked course material.
2. Solve the problems on your own first.
3. Check them against the self-check and rework the misses.
4. Typeset the write-up (LaTeX or a notebook) in a public repo.
5. Ask someone who knows the subject to check it.

README
ME 12: Numerical Methods for Engineers, unit 3: ODEs and time stepping
Problems:
Self-check result (matched / reworked):
What I got wrong first and why:

What gets sent back

• No working shown.
• The self-check result is missing.

Resources

What a verifier looks for

• Stability limits are worked out for each explicit method used.
• Convergence order is shown on a log–log error plot.
• The sample problems match their solutions, and misses are reworked.
• Is the engineering right, not just the final number?

You'll sign in first, then come straight back here.

Proof required

Link the public repo with the code or model files, the one command that reruns it, the convergence (mesh or step-size) study and the hand-calculation check, and a README that says how to rerun it and what limits the result.

What gets checked

• The drag-free case matches the exact range within 0.1% at the finest step.
• The log–log plot shows the expected orders, with the fitted slopes stated.
• The final range is given with a numerical uncertainty from the step-size study, and the code reruns from the repo.

Common mistakes

• A result that nobody else can rerun from the repo.
• A table with no explanation of the gaps.

Powstik Guide

A simulation of a ball thrown with quadratic air drag, solved with Euler and fourth-order Runge–Kutta, in a public repo.

Steps

1. Write down what you expect before you start.
2. Check the code first with drag set to zero against the exact projectile range. Then add drag, F = ½ρC_dAv², for a stated ball (for example a tennis ball). For the order study, measure the position error at a fixed time that every step size reaches, against a reference RK4 run with a step 16 times smaller than your finest. Halve the step at least five times for both methods, and plot error against step size on log axes. Show Euler converges at order 1 and RK4 at order 4, ignoring points at the round-off floor. Report the range with drag and its numerical uncertainty, finding the landing point by interpolation.
3. Fill the predicted-vs-measured (or hand-vs-simulated) table.
4. Explain every gap with a cause someone can check.
5. Write the README and ask someone who knows the subject to check it.

README
ME 12: Numerical Methods for Engineers — Simulate a projectile with drag and prove it converges
What I expected:
How to rerun it:
Predicted vs measured:
Why they differ:
Safety: hand tools and eye protection only

What gets sent back

• No convergence study, or no hand calculation that checks it.
• Machine tools, welding, pressure vessels, combustion, or springs and flywheels storing dangerous energy without a trained supervisor.

Resources

What a verifier looks for

• The drag-free case matches the exact range within 0.1% at the finest step.
• The log–log plot shows the expected orders, with the fitted slopes stated.
• The final range is given with a numerical uncertainty from the step-size study, and the code reruns from the repo.
• Check the engineering and the numbers, not just that it exists: do the units, the hand calculation and the table agree?
• Build photos show hand tools only and eye protection worn: no machine tools, welding, pressure vessels, combustion, or springs and flywheels storing dangerous energy (unless a trained supervisor and a proper workshop are shown).

You'll sign in first, then come straight back here.