Differential Equations › Section F · Series solutions › Topic F.1
Review: power series and Taylor series
Equations with variable coefficients usually have no solution built from familiar functions, but they can often be solved one coefficient at a time as a power series. This review gathers the series skills that method depends on, with extra practice in the bookkeeping it needs.
In this topic
- Why series come back now
- Power series and the radius
- Adding series and moving factors inside
- Differentiating term by term
- Shifting the index
- Worked example: one single series
- When a series is zero everywhere
- Taylor series, briefly
- Worked example: a polynomial about a new centre
- Analytic functions
- Common mistakes to avoid
- Key takeaways
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