·
Basic
definitions, first order and first degree differential equations (Separable
Equations, Homogeneous and nearly homogeneous equations, Exact equations,
Integrating factors, linear equations, Bernoulli equation, Riccati equation,
brief discussion of existence and uniqueness of a solution, orthogonal
trajectories).
·
Linear
higher order differential equations: theoretical considerations, constant
coefficient case, nonhomogeneous equation (variation of parameters method,
undetermined coefficients method), and Euler’s differential equation.
·
Laplace
transformations and its inverse, calculating Laplace transformation and its
invers, using Laplace transformation on solving linear equations.
·
System
of linear differential equations; solution of differential equations in series;
gamma, beta function, Bessel function, modified Bessel function, Legendre polynomials;
Spherical harmonics, hyper geometric functions.
