UNIT — I
Ordinary Differential Equations of First Order : 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.
Linear Differential Equations of Higher Order : Solutions of Linear Homogenous and Non-homogenous 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.
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)(without proof), Recurrence Relations for Legendre’s Polynomials P„ (x), Orthogonal Property of Legendre Polynomials Pn(x).
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(without proof).
UNIT – V
Laplace Transforms: Introduction to integral Transforms, Kernel of Integral Transforms, Laplace Transform, Inverse Laplace Transform, Properties of Laplace and Inverse Laplace transforms , Laplace Transform of Unit step Function, Impulse Function and Periodic Function, Convolution Theorem(without proof), Solution of Ordinary Differential Equations using Laplace Transform.
1) Larry Turyn, “Advanced Engineering Mathematics”, CRC Publications, 2014.
2) R.K.Jain and S.R.K.Iyengar, “Advanced Engineering Mathematics”, Narosa Publications, Fourth Edition, 2014.
3) Srimanta Pal and Subodh C. Bhunia, ” Engineering Mathematics” , Oxford University Press ,2015.
4) Peter V.O’Neil, “Advanced Engineering Mathematics”, CENGAGE Learnig, 7th Edition,2013.
5) Dean G.Duffy 7 Advanced Engineering Mathematics with MALAB” ,Third Edition.
6) Eerwin Kreyszig, “Advanced Engineering Mathematics”, Wiley- India, 9thEdition, 2012