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Ordinary Differential Equations (ODE), Partialy Differential Equations (PDE) and Vector Calculus

4 Credit Hour Course
Intended For Level 1 Term 2 Students

Prerequisite: None

Ordinary Differential Equation (ODE): Degree and order of ordinary differential equation; Formation of differential equations; Solution of first order differential equations by various methods; Solution of first order but higher degree ordinary differential equations; Solution of general linear equations of second and higher orders with constant coefficients; Solution of homogeneous linear equations and its applications; Solution of differential equations of higher order when dependent and independent variables are absent. (1.5 credit) Partial Differential Equations (PDE): Introduction; Solution of linear and non-linear PDE of order one; Second order linear PDE: its nomenclature and classifications to standard forms: Parabolic Elliptic and Hyperbolic; Solution of second order linear PDE by separation of variables; Higher order linear PDE with constant coefficients. (1.0 credit) Vector Calculus: Multiple products of vectors; Differentiation and integration of vectors together with elementary applications; Gradient, divergence and curl of point functions; Various formulae; Definition of line, surface and volume integrals; Green’s theorem; Gauss’s theorem; Stoke’s theorem. (1.5 credit)

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