9: Power series methods
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- 9.1: Power Series
- Many functions can be written in terms of a power series. If we assume that a solution of a diﬀerential equation is written as a power series, then perhaps we can use a method reminiscent of undetermined coeﬃcients. That is, we will try to solve for the coefficients of the expansion . Before we can carry out this process, let us review some results and concepts about power series.
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- 9.3: Singular Points and the Method of Frobenius
- While behavior of ODEs at singular points is more complicated, certain singular points are not especially difficult to solve. Let us look at some examples before giving a general method. We may be lucky and obtain a power series solution using the method of the previous section, but in general we may have to try other things.
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- 9.E: Power series methods (Exercises)
- These are homework exercises to accompany Libl's "Differential Equations for Engineering" Textmap. This is a textbook targeted for a one semester first course on differential equations, aimed at engineering students. Prerequisite for the course is the basic calculus sequence.
Thumbnail: The sine function and its Taylor approximations around \(x_o=0\) of 5 th and 9 th degree.
Contributors and Attributions
- Jiří Lebl ( Oklahoma State University ).These pages were supported by NSF grants DMS-0900885 and DMS-1362337.