General resources
From UBCMATH WIKI
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
