Differential Equations:
Basic Definitions and Terminology: differential equation (de), classifications of de, formation and solution of a de and further terminology, Ordinary de (ode), des of the first order and first degree: variable separable, homogeneous equations, exact equations, linear equations, Linear Equations with constant coefficients: linear and nonlinear de, solution of linear de, 2nd order des, 2nd and higher order homogeneous des, Method of Variation of Parameter; Method of undetermined coefficients; System of Linear de: operator method matrices and system of linear first order equations, homogeneous linear systems, undetermined coefficients, variation of parameters, Solution by Series.
Numerical Analysis:
Errors in Numerical Calculations: numbers and their accuracy, errors and their computation, a general error formula, error in a series approximation, Solution of Algebraic and Transcendental Equations: bisection, iteration, false position, Newton-Raphson methods, Interpolation: finite difference, forward, backward and central differences, Newton’s formula for interpolation, Stirlings formula, Lagrange’s interpolation formula, divided differences and their properties, Numerical Differentiation and Integration, Matrices and Linear Systems of Equations, Numerical Solution of Ordinary Differential Equations.