partial-differential-equations

Solving the vibrating-string problem by separation of variables

taught

Carry out separation of variables on the wave equation and match the resulting series simultaneously to both an initial position and an initial velocity.

Taught in

Separation of variables for the vibrating string
Partial Differential Equations
Initial position and initial velocity together
Partial Differential Equations
Reflections at a boundary
Partial Differential Equations
Forced vibrations and resonance on a bounded domain
Partial Differential Equations

Requires

separation-of-variables-ansatz required

Required by

Energy conservation for the wave equation required
Finite differences for the wave equation required
The vibrating circular drumhead required
The vibrating rectangular membrane required

Local knowledge map

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Solid arrows are required prerequisites; dashed are recommended or helpful. Lower rows are more foundational. Click any box to jump to that concept.