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Math Bits - Series Solutions
Prerequisites
Students should have experience with big sigma notation, especially reindexing a series and writing out several terms to see trends.
In-class Content
- Reading/Lecture: Series Solutions (Lecture: 25 min)
- Series Derivative (SWBQ: 5 min)
- Series Solutions (SGA ) 20 min
Homework for Central Forces
- (Series Solutions One)
Use the power series method to find the first six terms in each of two independent solutions to this differential equation.
Solve this differential equation using a different method and show that your answers are the same as part a.
- (Series Solutions Two)
Use a power series expanded about $x = 0$ to find the first six terms in each of two independent solutions to this differential equation.
For what values of $x$ do each of your power series solutions converge?
Suppose you were to subtract one of your two solutions from the other solution. Is the resulting function still a solution to the original differential equation? Explain.
