# Mathematical and Computational Methods in Physics and Engineering (fall 2016)

## Daily outline for Mon, Nov 28, 2016 9:10 AM (11 months ago)

### Review

assigned today:

Due today:
• standard-PDEs: 1D wave equation:

I can derive and calculate the solution of a 1D wave equation.

1. 12.3.11 (triangle initial conditions)
2. 12.3.14 (non-zero velocity)
3. 12.3. 20 (clamped beam)

# in class

• voted on beam equation one and quantum harmonic oscillator
• We drew one moment in time of a wave
• asked about the curvature and what that meant about the acceleration:

$$\frac{\partial^2 y}{\partial t^2}=c^2\frac{\partial^2 y}{\partial x^2}$$

• talked about how the boundary conditions affect the constant (from separation of variables)
• talked about the determinant approach
• Moved on to the philosophy of the quantum problem
• if you build a cage, you've set some stationary states
• if you break the cage, they're not stationary states any more
• Voted on the initial velocity 1D wave problem
• talked about how the A's are the coefficients of the initial shape and how the B's (times the frequencies) are the coefficients of the initial velocity

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