Theory of Ordinary Differential Equations - E. Differential Equations : Theory, Technique and Practice - G. Lagrange's method of solving first order quasi linear equations. Laplace, Wave and the Heat equations, at least in 2 - dimensions. Partial differential equations - elements of partial differential equations and the three equations of physics i.e. Bessel's functions, Legendre polynomials, Gamma functions). Syllabus : Ordinary differential equations - first order equations, Picard's theorem (existence and uniqueness of solution to first order ordinary differential equation), Second order linear equations - second order linear differential equations with constant coefficients, Systems of first order differential equations, Equations with regular singular points, Introduction to power series and power series solutions, Special ordinary differential equations arising in physics and some special functions (eg. For more details on timings and past exams, click here. This is a course for 3rd year B.Math(undergraduate) students.
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