University · Mathematics · Ordinary Differential Equations
Series Solutions and Special Functions
Develops the power series method for solving second-order linear ODEs about ordinary points, including how substitution of a trial series yields a recurrence relation for the coefficients, works a fully verified example recovering the hyperbolic sine and cosine functions from the equation y'' - y = 0, and introduces singular points, the method of Frobenius, and the special functions -- Legendre polynomials and Bessel functions -- that arise as series solutions to two classical named equations.
Inhaltsübersicht
- The Power Series Method and Ordinary Points
- Worked Example: Solving y'' - y = 0 by Power Series
- Singular Points and the Method of Frobenius
- Special Functions: Legendre Polynomials and Bessel Functions
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