Chapter Review Sheets for
Elementary Differential Equations and Boundary Value Problems, 8e
Chapter
5: Series Solutions of Second Order Equations
Definitions:
•
Radius of Convergence, Interval of Convergence
•
Analytic
•
Recurrence Relation
•
Ordinary Point, Singular Point
•
Regular and Irregular Singular Points
•
Euler Equation, Indicial Equation Exponents of Singularity
•
Chebyshev equation Hermite equation; Bessel Equation
Theorems:
•
Theorem 5.3.1:
Existence of series solutions to linear OBE's near ordinary points, and their convergence
properties.
•
Theorem 5.5.1:
General solutions to Euler equations.
•
Theorem 5.7.1:
Series solutions near regular singular points.
Important Skills:
•
Review power series, how to shift the index of summation, (Example 3, p.247) and tests for
convergence. (Example 2, p.245)
•
Know how to find the interval of convergence for a power series. (Example 2, p.245)
•
Be able to determine all ordinary and singular points for a differential equation. (p. 25051)
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 Spring '10
 DorothyWallace
 Differential Equations, Equations, Recurrence relation, Bessel equation

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