In this unit, the reader will learn some basic definitions of ordinary differential equations. Also the reader will study the existence and uniqueness of solutions of initial value problem and a system of differential equations. In order to fully understand the proofs of these theorems, the reader must be familiar with certain concepts of real function theory.

In this unit, the reader first learn the definitions of linearly independent and linearly dependent set of functions. Then they study the fundamental set of solutions for ordinary differential equations, Wronskian, Adjoint differential equations and Green's formula.

In this unit the reader studies the zeros of solutions of ODE. Sturm's separation theorem. Sturm's comparison theorem , Sturm-Liouville problems. The reader also study the method of variation o f parameters. Eigenvalue problems.

In this unit, the reader studies the power series solution by Frobenius method for Laguerre equation, Hermite differential equation, Chebyshev equation, hypergeometric equation.

The objective of this unit is the study of Non-linear Autonomous system of ordinary differential equations, critical points, path and their nature. The reader also studies the method to find the nature of critical points. stability and paths by Liapunov direct method.

In this unit, the reader studies about introduction and formation of partial differential equation (PDE). They also study the classification of first order PDE and some basic definition pertaining to POE.

In this unit, the reader studies about the Cauchy problem, principle of superposition. They also study the method of characteristics to solve semi-linear, quasilinear and non-linear PDEs.

In this unit the reader studies classification of second order partial differential equation. They also study the method of characteristics and classify the given second order POE to its respective canonical form.