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Math 391 Lecture 17 - Conclusion of higher order equations and Series Solutions to linear ODEs
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We had technical difficulties today :( apparently, the first 5 to 10 minutes of the lecture wasn't recorded. I believe all the worked out examples I did were caught for a short time on camera though.
Anyway, in this lecture we looked over a couple more techniques for solving higher order differential equations (third order or higher), and then moved on to series solutions for second order linear equations (SOLDEs).
We went over some basic concepts and properties of series for most of the remaining lecture. As we had some time left over, I rushed through an example of solving a simple SOLDE via series.
The idea: assume the solution to an ODE takes on the form of a power series. Find the necessary derivatives through term-by-term differentiation, plug into the ODE and obtain a recurrence relation for determining the coefficients of your power series. There are some subtle techniques needed to pull this off, and our short review of series gave us the tools and know how to do this. More examples to come in the next lecture.
Anyway, in this lecture we looked over a couple more techniques for solving higher order differential equations (third order or higher), and then moved on to series solutions for second order linear equations (SOLDEs).
We went over some basic concepts and properties of series for most of the remaining lecture. As we had some time left over, I rushed through an example of solving a simple SOLDE via series.
The idea: assume the solution to an ODE takes on the form of a power series. Find the necessary derivatives through term-by-term differentiation, plug into the ODE and obtain a recurrence relation for determining the coefficients of your power series. There are some subtle techniques needed to pull this off, and our short review of series gave us the tools and know how to do this. More examples to come in the next lecture.
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