Difference between revisions of "General resources"
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===Supplemental videos and notes=== | ===Supplemental videos and notes=== | ||
| − | + | ====Euler's formula==== | |
| − | + | ::<youtube>rK4NHHZhWNk</youtube> | |
| − | + | ====Homogeneous second order linear ODEs with constant coefficients - summary and examples==== | |
| − | + | ::<youtube>VJdLywZj9CQ</youtube> | |
| − | **A video summarizing the steps for solving the Diffusion equation [http://www. | + | |
| − | **[[Media: | + | ====A 2x2 system of ODEs with a repeated eigenvalue==== |
| + | ::<youtube>hCShTLmeZN4</youtube> | ||
| + | ====Laplace transforms - inverting $H(s)=\frac{1}{s(s^2+2s+10)}$==== | ||
| + | *Part 1 | ||
| + | ::<youtube>EpkRcG1qzCw</youtube> (part 1 - partial fraction decomposition) | ||
| + | *Part 2 | ||
| + | ::<youtube>pl-Gbe6dZRY</youtube> (part 2 - inverting the parts, [[Media:InverseTransformEx1.pdf|pdf]]). | ||
| + | ====Fourier series of a function with jumps==== | ||
| + | ::<youtube>C4VWwN8kUU0</youtube> | ||
| + | ====Solving the Diffusion equation==== | ||
| + | *Comprehensive notes on the Heat/Diffusion equation | ||
| + | ::[https://www.youtube.com/playlist?list=PLZSePgVChPS6_NVQo2Frg5wmhtRNnZhXK Youtube playlist] (4 videos), [[Media:DiffusionEq.pdf|notes from videos]], [[Media:DiffusionEqExamples.pdf|worked examples from playlist video 4]] | ||
| + | *A video summarizing the steps for solving the Diffusion equation | ||
| + | ::<youtube>jsQXv4y33Ho</youtube> (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: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:solvingDiffEqExtensions.pdf|How to extend an IC to satisfy BCs]] | ||
| + | *A video explaining why the extension trick works | ||
| + | ::<youtube>_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=== | ||
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| − | !style="width: 40px;"| | + | !style="width: 40px;"|Week |
!style="width: 230px;"|Description | !style="width: 230px;"|Description | ||
!style="width: 40px;"|Link | !style="width: 40px;"|Link | ||
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|style="text-align: center;"|3 | |style="text-align: center;"|3 | ||
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|style="text-align: center;"|[https://www.desmos.com/calculator/aqh17ebj1k demo] | |style="text-align: center;"|[https://www.desmos.com/calculator/aqh17ebj1k demo] | ||
|- | |- | ||
| − | |style="text-align: center;"| | + | |style="text-align: center;"|4 |
| + | |Graphs of the solution to the equations for a damped oscillator. | ||
| + | |style="text-align: center;"|[https://www.desmos.com/calculator/psy5r8hpln demo]. | ||
| + | |- | ||
| + | |style="text-align: center;"|4 | ||
|Amplitude versus forcing frequency for a forced oscillator, showing resonance. | |Amplitude versus forcing frequency for a forced oscillator, showing resonance. | ||
|style="text-align: center;"|[https://www.desmos.com/calculator/rbk5vped4d demo] | |style="text-align: center;"|[https://www.desmos.com/calculator/rbk5vped4d demo] | ||
| + | |- | ||
| + | |style="text-align: center;"|6 | ||
| + | |Eigenvectors, eigenvalues and solutions to a 2 variable ODE in the phase plane | ||
| + | |style="text-align: center;"|[https://www.desmos.com/calculator/a8n5yhixfu demo] | ||
|- | |- | ||
|style="text-align: center;"|10 | |style="text-align: center;"|10 | ||
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|} | |} | ||
| + | |||
====Videos from various online sources==== | ====Videos from various online sources==== | ||
*[http://www.youtube.com/watch?v=ib1vmRDs8Vw A numerical simulation of a large system of masses and springs] | *[http://www.youtube.com/watch?v=ib1vmRDs8Vw A numerical simulation of a large system of masses and springs] | ||
| Line 53: | Line 78: | ||
===Resources of potential interest but not directly related to the course=== | ===Resources of potential interest but not directly related to the course=== | ||
*[http://www.cell.com/cancer-cell/retrieve/pii/S1535610802001332 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. | *[http://www.cell.com/cancer-cell/retrieve/pii/S1535610802001332 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. | ||
| + | |||
| + | ===A list of Desmos demos=== | ||
| + | |||
| + | *[https://www.desmos.com/calculator/xrwvyokj9x Mixed BCs and zero FS coefficients] | ||
| + | *[https://www.desmos.com/calculator/kb73nivihx Diffusion, non-homo. Neumann] | ||
| + | *[https://www.desmos.com/calculator/likxhxmpxj Diffusion, non-homo. mixed] | ||
| + | *[https://www.desmos.com/calculator/ewzfwcwn4v Diffusion, non-homo. Dirichlet] | ||
| + | *[https://www.desmos.com/calculator/wpiohhmbeu Integral with symmetry about L] | ||
| + | *[https://www.desmos.com/calculator/4zfnnhpjmb Fourier for mixed boundary conditions] | ||
| + | *[https://www.desmos.com/calculator/rhwwmbuacw Resonance with Fourier series forcing 2] | ||
| + | *[https://www.desmos.com/calculator/vy9gdvrse1 Fourier series example] | ||
| + | *[https://www.desmos.com/calculator/swiwnuvstr Resonance with Fourier series forcing] | ||
| + | *[https://www.desmos.com/calculator/xzagakgd6b Resonance graphing] | ||
| + | *[https://www.desmos.com/calculator/cfjfpxef1w Beats] | ||
| + | *[https://www.desmos.com/calculator/0pmhez6y6y Mass-spring resonance] | ||
| + | *[https://www.desmos.com/calculator/symfd49z0n Pulsatile drug ODE] | ||
| + | *[https://www.desmos.com/calculator/hfxs1kuebw Real distinct evalues to vector field] | ||
| + | *[https://www.desmos.com/calculator/uaojf4tfkc Complex evalues to vector field] | ||
| + | *[https://www.desmos.com/calculator/mgkfg3ol3o Diffusion Eq - linear IC, Dirichlet] | ||
| + | *[https://www.desmos.com/calculator/cocvgmka4u Wave equation] | ||
| + | *[https://www.desmos.com/calculator/uyaqt329t7 Diffusion Eq - linear IC, Neumann] | ||
| + | *[https://www.desmos.com/calculator/98fulaxgt5 Diffusion Eq - const IC, Dirichlet] | ||
| + | *[https://www.desmos.com/calculator/fwfdhqyj7i Fourier - tent function] | ||
| + | *[https://www.desmos.com/calculator/94lluim82q Fourier - step function] | ||
| + | *[https://www.desmos.com/calculator/yy2uenvb2b Matrix to vector field] | ||
| + | *[https://www.desmos.com/calculator/s1brxuqr2n ODE solution with delta-function jump] | ||
| + | *[https://www.desmos.com/calculator/ovrpswjkq5 Second Order ODE with On/Off Forcing] | ||
| + | *[https://www.desmos.com/calculator/dr2r2du0qi Damped oscillations] | ||
Latest revision as of 16:58, 6 April 2017
Supplemental videos and notes
Euler's formula
Homogeneous second order linear ODEs with constant coefficients - summary and examples
A 2x2 system of ODEs with a repeated eigenvalue
Laplace transforms - inverting $H(s)=\frac{1}{s(s^2+2s+10)}$
- Part 1
- (part 1 - partial fraction decomposition)
- Part 2
- (part 2 - inverting the parts, pdf).
Fourier series of a function with jumps
Solving the Diffusion equation
- Comprehensive notes on the Heat/Diffusion equation
- A video summarizing the steps for solving the Diffusion equation
- (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
- ,
- 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
| Week | Description | Link |
|---|---|---|
| 3 | A series of graphs of the solution to a second order ODE as the eigenvalues go from real to repeated to complex. | demo |
| 4 | Graphs of the solution to the equations for a damped oscillator. | demo. |
| 4 | Amplitude versus forcing frequency for a forced oscillator, showing resonance. | demo |
| 6 | Eigenvectors, eigenvalues and solutions to a 2 variable ODE in the phase plane | 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.
A list of Desmos demos
- Mixed BCs and zero FS coefficients
- Diffusion, non-homo. Neumann
- Diffusion, non-homo. mixed
- Diffusion, non-homo. Dirichlet
- Integral with symmetry about L
- Fourier for mixed boundary conditions
- Resonance with Fourier series forcing 2
- Fourier series example
- Resonance with Fourier series forcing
- Resonance graphing
- Beats
- Mass-spring resonance
- Pulsatile drug ODE
- Real distinct evalues to vector field
- Complex evalues to vector field
- Diffusion Eq - linear IC, Dirichlet
- Wave equation
- Diffusion Eq - linear IC, Neumann
- Diffusion Eq - const IC, Dirichlet
- Fourier - tent function
- Fourier - step function
- Matrix to vector field
- ODE solution with delta-function jump
- Second Order ODE with On/Off Forcing
- Damped oscillations
