MATH 129 Course Outline

 Math

 Ordinary and Partial Differential Equations and Laplace Transforms

3.00 Contact Hour 3.00 Credit Hour

SECTION-A (ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS)

a. Ordinary Differential Equations. Formulation of Differential Equations, Solution of first order but higher degree differential equations, Solution of first order differential equations by various methods, Solution of general linear equations of second and higher orders with constant co-efficient, Solution of Homogeneous linear equations and its applications, Solution of differential equations by the methods based on the factorization of the operators.

b. Partial Differential Equations. Introduction, Linear and non linear first order equations, Standard forms of linear equations of higher order, Equation of second order with variable coefficients.

SECTION-B (LAPLACE TRANSFORM)

Definition. Laplace transforms of some elementary functions. Sufficient conditions for existence of Laplace transform, Inverse Laplace transforms. Laplace transforms of derivatives. The unit step function. Periodic function, some special theorems on Laplace transform, Partial fraction. Solutions of differential equations by Laplace transform. Evaluation of improper integral.

Text and Ref books:

1. Ordinary and Partial differential Equations – M. D. Raisenghania.

2. Differential Equations – M. L. Khanna.

3. Differential Equations – B. D. Sharma.

4. Differential Equations – P. N. Chatterjee.