|Course Outline||List Of Formula||Lecture Notes||Past Year Paper|
This is an introductory course on differential equations. Topics include first order ordinary differential equations (ODEs), linear second order ODEs with constant coefficients up to fourth order, the Laplace transform and its inverse, Fourier series, and partial differential equations (PDEs). Students will learn how to classify and solve first order ODEs, use the techniques of undetermined coefficients, variation of parameters and the Laplace transform to solve ODEs with specified initial and boundary conditions, and use the technique of separation of variables to solve linear second order PDEs and the method of d’Alembert to solve wave equation.
On completing the course, students should be able to:
1. Use appropriate techniques to find the solution of first order differential equation.
2. Use the method of undetermined coefficients and the method of variation of parameters to find the solution of second order linear differential equations with constant coefficients up to fourth order.
3. Produce the Laplace transforms and its inverses for standard functions.
4. Solve initial, boundary value problems and system of differential equations using Laplace transforms.
5. Produce Fourier series of given functions.
6. Solve second order heat, wave and Laplace equations using the method of separation of variables and the method of d’Alembert for unbounded wave equations.
7. Communicate effectively in written forms using mathematical language.