WITH EFFECT FROM THE ACADEMIC YEAR 2014 - 2015

MT 102

MATHEMATICS - II

Instruction                                                                                   3 Periods per week

Duration of University Examination                                      3 Hours

University Examination                                                         75 Marks

Sessional                                                                                   25 Marks

UNIT - I

Ordinary Differential Equations of First Order :

Introduction to Differential Equations, Exact First Order Differential Equations , Integrating Factors, Linear First Order Equation , Bernoulli's Equation, Riccati's Equation, Clairaut's Equation, Orthogonal Trajectories of a Given Family of Curves, RL - Circuit,RC - Circuit, Newton's Law of Cooling, Law of Growth and Decay .

UNIT- II

Linear Differential Equations of Higher Order :

Solutions of Linear Homogeneous and Non-homogeneous Differential Equations with Constant Coefficients, Solution of Euler-Cauchy Equation, Linearly Dependence and Independence of Functions, Method of Reduction of Order, Method of Variation of Parameters, Simultaneous Differential Equations.

UNIT - III

Series Solutions of Differential Equations :

Ordinary and Singular Points of an Equation, Power Series Method, Frobenius Method, Legendre's Differential Equation and Legendre Polynomials Pn(x), Rodrigue's Formula, Generating Function for Legendre's Polynomials Pn(x) , Recurrence Relations for Legendre's Polynomials Pn(x), Orthogonal Property of Legendre Polynomials Pn(x), Fourier-Legendre Series.

UNIT - IV

Special functions :

Gamma Function, Beta Function, Relation between Gamma and Beta Functions, Error Function. Bessel's Differential Equation, Bessel's Functions of the First Kind , Derivatives and Integrals of Bessel's Functions, Recurrence Relations for Bessel Functions, Generating Function for Bessel Functions.