Math 322 Exam 2 Preparation
- Series Solutions to differential equations.
- Determine whether a point is an ordinary point or a singular point for an ODE. If it is a singular point, determine whether it is regular.
- Determine the radius of convergence of a power series solution about an ordinary point. Determine the interval of convergence.
- Find a power series about an ordinary point. Note: This involves guessing a normal power series as a solution, and is not the method of Frobenius.
- Change indices of summation as needed to combine sums.
- Obtain a recurrence relation to find subsequent coefficients.
- Find enough coefficients to identify any obvious patterns.
- Give the final solution or solutions.
- Apply the method of Frobenius to find a series solution about a regular singular point.
- Change indices of summation as needed to combine sums.
- Obtain a recurrence relation to find subsequent coefficients.
- Find and solve the indicial equation.
- Determine whether any coefficients must be zero.
- Find enough coefficients to identify any obvious patterns.
- Give the final solution or solutions.
- Systems of Differential Equations
- Find the homogeneous solution to a system of differential equations. This was tested on Exam 1, but is needed again here.
- Sketch the phase portrait for a homogeneous system of two first order ODEs.
- Determine whether the origin is a nodal sink, nodal source, spiral sink, spiral source, saddle point or center for a system of two first order ODEs. (You do not have to classify the type of node if the origin is a node.) Determine whether a system is unstable, neutrally stable or asymptotically stable.
- Find a particular solution to a system of ODEs using
- the method of undetermined coefficients, with the guess for the particular solution given
- the method of variation of parameters
- Solve a non-homogeneous system or an IVP for a non-homogeneous system.
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