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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
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Graduate ODE textbook
Teschl's book is a good, modern text on ODEs and is available from the AMS in their GSM series. It blends ODEs and dynamical systems. Bob Devaney updated the classic Hirsch and Smale book some years a …