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. 250-51)
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