Worked Examples

PHY621's methods only become convincing when you watch one of them produce an answer you could also have got another way — and then produce an answer you could not. Each example below does both: it solves a problem twice where possible, and checks the two against each other.

• The driven oscillator via its Green's function — build \(G\) from a unit kick, convolve, and confirm it against the elementary solution
• Cooling a rod — separation of variables, a Fourier series, and the question of how many terms you actually need

Related tools

The normal modes lab solves the eigenvalue problem these methods lean on; the Fourier series builder shows the convergence behaviour that the second example depends on.

The habit these are teaching

Every transform method in this course converts a hard operation into an easy one in another representation — differentiation into multiplication, convolution into a product, a PDE into a family of ODEs. The work is always in getting back. Notice, in each example, where the difficulty moved to.