Short Course Description
Credit Points: 3.5
Prerequisites: Differential and Integral Methods, Linear Algebra
Examples from mechanics and electricity of problems involving initial or boundary conditions. First order equations, the existence and uniqueness theorem. Second order linear equations; homogeneous equations and linear independence, the wronksian and lowering the order of an equation, homogeneous equations with constant coefficients. Separation to a homogeneous and an inhomogeneous problem, the method of undetermined coefficients and the method of variation of parameters. One sided Green's function for solving initial value problems. Reaction to constraints and to initial/boundary conditions. Generalization to nth order equations, the case of constant coefficients. Euler's formula, series solutions (Frobenius method), Bessel's function, Legendre's function, Hermite's function, Laguerre's function, regular and singular solutions. The Laplace transform and its applications for solving differential equations, initial and final value theorems, transforms of convolutions. System of first order linear equations. Sturm-Liouville and self-adjoint problems, eigenfunctions and eigenvalues, expansion of functions in eigenfucntions series of Sturm-Liouville problem, the example of Fourier series.
Full syllabus will be available to registered students only
