Skip available courses

Available courses

This is the first course of a two semester course sequence. This course covers limits, continuity, differentiation and its applications, integrals and techniques of integration, applications of integrals, early transcendental functions.

The laws of science and engineering are typically expressed in differential equations, which are equations with derivatives in them.  Understanding of differential equations and their solutions is important in the sciences and engineering.  This course deals with: First order differential equations; modeling; second order linear equations; Damped motion in mechanical and electrical systems; System of first order linear equations; Eigenvalues and Eigen vector; Series solutions; Introduction to special functions; Fourier series; Partial differential equations; separation of variables and Sturm-Liouville problems.

Eigen value problems and Sturm-Liouville equations, special functions: Hyper geometric equation, Bessel’s equation, Legendre’s equation, Systems of ordinary differential equations, Well-posed initial value problem (i.e. existence, uniqueness, continuation and continuous dependence); Special linear systems, Laplace transform, Laplace transform method for solving ODEs, Applications

Find symmetries of differential equations manually and by using symbolic packages as well Deduce new solutions from known solutions Solve ODEs and systems of ODEs using Lie symmetries Reduce partial differential equations by reduction of the number of independent variables Linearize differential equations by invertible transformation and exact solutions by using integration strategy Compute first integrals/conservation laws for differential equations and systems of differential equations Construct solutions of ODEs and PDEs by using first integrals/ conservation laws