Difference between revisions of "General resources"
From UBCMATH WIKI
| Line 6: | Line 6: | ||
*[http://www.youtube.com/watch?v=C4VWwN8kUU0 Fourier series of a function with jumps] | *[http://www.youtube.com/watch?v=C4VWwN8kUU0 Fourier series of a function with jumps] | ||
*Solving the Diffusion equation | *Solving the Diffusion equation | ||
| − | **A video summarizing the steps for solving the Diffusion equation [http://www.youtube.com/watch?v=jsQXv4y33Ho youtube] and a [[Media:solvingDiffEqSummary.pdf|pdf]] of the notes in the video. | + | **A video summarizing the steps for solving the Diffusion equation ([http://www.youtube.com/watch?v=jsQXv4y33Ho youtube]) and a [[Media:solvingDiffEqSummary.pdf|pdf]] of the notes in the video. |
**[[Media:solvingDiffEqEx1.pdf|Non-homogeneous Dirichlet BCs]] with a [http://www.desmos.com/calculator/ewzfwcwn4v Desmos demo] | **[[Media:solvingDiffEqEx1.pdf|Non-homogeneous Dirichlet BCs]] with a [http://www.desmos.com/calculator/ewzfwcwn4v Desmos demo] | ||
**[[Media:solvingDiffEqEx3.pdf|Non-homogeneous Neumann BCs]] with a [http://www.desmos.com/calculator/kb73nivihx Desmos demo] | **[[Media:solvingDiffEqEx3.pdf|Non-homogeneous Neumann BCs]] with a [http://www.desmos.com/calculator/kb73nivihx Desmos demo] | ||
**[[Media:solvingDiffEqEx2.pdf|Non-homogeneous mixed BCs]] with a [http://www.desmos.com/calculator/likxhxmpxj Desmos demo] | **[[Media:solvingDiffEqEx2.pdf|Non-homogeneous mixed BCs]] with a [http://www.desmos.com/calculator/likxhxmpxj Desmos demo] | ||
**[[Media:solvingDiffEqExtensions.pdf|How to extend an IC to satisfy BCs]] | **[[Media:solvingDiffEqExtensions.pdf|How to extend an IC to satisfy BCs]] | ||
| − | **A video explaining why the extension trick works [http://www.youtube.com/watch?v=_8PSM03y_4s youtube], a [[Media:solvingDiffEqWhyExtWorks.pdf|pdf]] of the notes in the video and the [https://www.desmos.com/calculator/xrwvyokj9x Desmos demo]. | + | **A video explaining why the extension trick works ([http://www.youtube.com/watch?v=_8PSM03y_4s youtube]), a [[Media:solvingDiffEqWhyExtWorks.pdf|pdf]] of the notes in the video and the [https://www.desmos.com/calculator/xrwvyokj9x Desmos demo]. |
===Sources where you can find extra problems to work on=== | ===Sources where you can find extra problems to work on=== | ||
*[[Suggested problems]], chapter by chapter from Boyce and DiPrima. | *[[Suggested problems]], chapter by chapter from Boyce and DiPrima. | ||
Revision as of 12:53, 21 April 2015
Contents |
Supplemental videos and notes
- A 2x2 system of ODEs with a repeated eigenvalue - video.
- Inverting $H(s)=\frac{1}{s(s^2+2s+10)}$ - pdf, video (part 1 - partial fraction decomposition), video (part 2 - inverting the parts).
- Fourier series of a function with jumps
- Solving the Diffusion equation
- A video summarizing the steps for solving the Diffusion equation (youtube) and a pdf of the notes in the video.
- Non-homogeneous Dirichlet BCs with a Desmos demo
- Non-homogeneous Neumann BCs with a Desmos demo
- Non-homogeneous mixed BCs with a Desmos demo
- How to extend an IC to satisfy BCs
- A video explaining why the extension trick works (youtube), a pdf of the notes in the video and the Desmos demo.
Sources where you can find extra problems to work on
- Suggested problems, chapter by chapter from Boyce and DiPrima.
- MATH 256 Chem. and Bio. Eng focus (winter 2013) - including solutions to some old assignments problems, old midterms etc. Note that the content this year will be subtly different so some questions might not be relevant this year and some topics covered this year might not appear. Ask me if you want to confirm anything you aren't sure about.
- MATH 256 EE focus (Fall 2013) - same comment as above.
- MATH 256 (Winter 2004) - same comment as above.
- A collection of past exams from all MATH courses. Not all problems on past exams are totally appropriate as practice for this year's exam. Here are some comments on past exams that will help you avoid problems we didn't cover this term.
Demonstrations
Desmos demos
| Chapter | Description | Link |
|---|---|---|
| 3 | Graphs of the solution to the equations for a damped oscillator. | demo. |
| 3 | A series of graphs of the solution to a second order ODE as the eigenvalues go from real to repeated to complex. | demo |
| 3 | Amplitude versus forcing frequency for a forced oscillator, showing resonance. | demo |
| 10 | Fourier series approximation to a step function | demo |
Videos from various online sources
- A numerical simulation of a large system of masses and springs
- A slow motion video of a tuning fork - jump to 1:08 if you don't want to listen to the dorky British guys.
- One tuning fork driving another at resonance.
- Resonance for guitar players
- Can a biologist fix a radio? - Or, what I learned while studying apoptosis. This paper is a great read, either for biologists with a sense of humour or engineers trying to figure out how biologists operate.
