Estb. 1882

University of the Punjab
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MATH-312 Ordinary Differential Equations

First and Second Order Differential Equations  Review of ordinary differential equations
 Techniques of solving second and higher differential equations Sturm Liouville Systems
 Some properties of Sturm-Liouville equations
 Regular, periodic and singular Sturm-Liouville systems and its applications Series Solutions of Second Order Linear Differential Equations
 Review of power series
 Series solution near an ordinary point
 Series solution near regular singular points. Series Solution of Some Special Differential Equations  Hypergeometric function F(a, b, c; x) and its evaluation
 Series solution of Bessel equation
 Expression for Jn(X) when n is half odd integer, Recurrence formulas for Jn(X)
 Series solution of Legendre equation
 Rodrigues formula for polynomial Pn(X)
 Generating function for Pn(X)
 Recurrence relations, orthogonal polynomials
 Orthogonality of Bessel functions
 Expansions of polynomials
 The three term recurrence relation
Credit hours/ Marks:- 3

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