B.E. 301 - ENGINEERING MATHEMATICS II

Unit I

Fourier Series: Introduction of Fourier series , Fourier series for Discontinuous functions, Fourier series

for even and odd function, Half range series Fourier Transform: Definition and properties of Fourier

transform, Sine and Cosine transform.

Unit II

Laplace Transform: Introduction of Laplace Transform, Laplace Transform of elementary functions,

properties of Laplace Transform, Change of scale property, second shifting property, Laplace transform

of the derivative, Inverse Laplace transform & its properties, Convolution theorem, Applications of L.T.

to solve the ordinary differential equations

Unit III

Second Order linear differential equation with variable coefficients : Methods one integral is known,

removal of first derivative, changing of independent variable and variation of parameter, Solution by

Series Method

Unit IV

Linear and Non Linear partial differential equation of first order: Formulation of partial differential

equations, solution of equation by direct integration, Lagrange’s Linear equation, charpit’s method.

Linear partial differential equation of second and higher order: Linear homogeneous and Non

homogeneous partial diff. equation of nth order with constant coefficients. Separation of variable method

for the solution of wave and heat equations

Unit V

Vector Calculus: Differentiation of vectors, scalar and vector point function, geometrical meaning of

Gradient, unit normal vector and directional derivative, physical interpretation of divergence and Curl.

Line integral, surface integral and volume integral, Green’s, Stoke’s and Gauss divergence theorem

References:

(i) Advanced Engineering Mathematics by Erwin Kreyszig, Wiley India

(ii) Higher Engineering Mathematics by BS Grewal, Khanna Publication

(iii) Advance Engineering Mathematics by D.G.Guffy

(iv) Mathematics for Engineers by S.Arumungam, SCITECH Publuication

(v) Engineering Mathematics by S S Sastri. P.H.I.