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

## Daily outline for Fri, Oct 14, 2016 9:10 AM (5 months ago)

### ODE series solution

assigned today:
• standard-ODE series solutions:

I can explain and apply series solutions to ODEs. (chapter 5)

1. Explain how the series solution works and when you need Frobenius instead.
2. Solve a damped harmonic oscillator with a series approach. Verify you get the same result as chapter 2.
3. Solve the quantum harmonic oscillator with a series approach. If you're in the quantum class now, compare and contrast with pp. 51-56 of your quantum book:

$$-\frac{\hbar}{2m}\psi''(x)+\frac{1}{2}k x^2 \psi(x)=E \psi(x)$$

Due today:

# in class

• quiz on two tank problem
• Tom noted that my first try at it was not homogeneous so we made a change
• I said they'd get a 3 if they just set it up and a 4 if they finished
• Talked a long time about how the terms in a polynomial are "orthogonal"
• If $$Ax^3+Bx^2+Cx+D=Fx^3+Gx^2+Hx+J$$ then A=F etc
• can you build a parabola with a Taylor's series that doesn't include the second order
• We took successive derivatives of the polynomials above to show A=F etc
• We tackled the series solution for $$y''+y=0$$ but didn't quit finish
• We talked a little about the need for Frobenius
• We talked about how in Quantum they used Frobenius for the quantum oscillator but that they didn't have to

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