Syllabus For The Subject DIFFERENTIAL EQUATIONS WITH HIGHER ORDERS

UNIT - 01

INTRODUCTION - HIGHER ORDER EQUATIONS - LINEAR DEPENDENCE - WRONSKIAN

METHOD OF VARIATION OF PARAMETERS.

UNIT - 02

HOMOGENEOUS LINEAR EQUATIONS WITH CONSTANT CO-EFFICIENT - EQUATIONS

WITH VARIABLE CO-EFFICIENT.

UNIT - 03

INTRODUCTION - POWER SERIES SOLUTION - LEGENDRE EQUATION & LEGENDRE

POLYNOMIAL.

UNIT - 04

BESSELS EQUATION AND PROPERTIES.

UNIT - 05

INTRODUCTION - SYSTEMS OF FIRST ORDER EQUATIONS - MODEL FOR ARMS

COMPETITION BETWEEN TWO NATIONS - EXISTENCE AND UNIQUENESS THEOREM.

UNIT - 06

FUNDAMENTAL MATRIX.

UNIT - 07

INTRODUCTION - NON-HOMOGENEOUS LINEAR SYSTEMS - LINEAR SYSTEMS WITH

CONSTANT COEFFICIENTS - LINEAR SYSTEMS WITH PERIODIC COEFFICIENTS.

UNIT - 08

INTRODUCTION - PRELIMINARIES - SUCCESSIVE APPROXIMATIONS - PICARDS THEOREM

- CONTINUATION AND DEPENDENCE ON INITIAL CONDITIONS.

UNIT - 09

INTRODUCTION - STURM LIOUVILLE PROBLEM - GREENS FUNCTION - APPLICATION OF

BOUNDARY VALUE PROBLEMS.

UNIT - 10

PICARDS THEOREM.

UNIT - 11

INTRODUCTION - LEARNING OBJECTIVES - FUNDAMENTAL RESULTS - STURMS

COMPARISION THEOREM - ELEMENTARY LINEAR OSCILLATIONS - COMPARISON

THEOREM OF HILLE - WINTNER.

UNIT - 12

INTRODUCTION - SYSTEM OF EQUATIONS WITH CONSTANT COEFFICIENTS - LINEAR

EQUATION WITH CONSTANT COEFFICIENTS - STABILITY OF QUASI-LINEAR SYSTEMS -

SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS.