MATHEMATICS-III

Credits	Periods			Exam Hrs.	Sessional Marks	Exam Marks	Total Marks
	Theory	Tutorial	Lab
4	3	1	-	3	30	70	100

1. Vector Calculus 

Differentiation of vectors, curves in space, Velocity and acceleration, Relative

velocity and acceleration,  Scalar and Vector point functions, Vector operator  ∇,  ∇
applied to scalar point functions, Gradient,  ∇ applied to vector point functions,
Divergence and curl, Physical interpretations of ∇, F and ∇ × F, ∇ applied twice to
point functions, ∇ applied to products of point functions, integration of vectors, Line
integral, Circulation, Work, Surface integral-flux, Green’s theorem in the plane,
Stoke’s theorem, Volume integral, Divergence theorem, Irrotational and solenoidal
fields, Green’s theorem, Introduction of orthogonal curvilinear coordinates :
Cylindrical, Spherical and polar coordinates.
2. Introduction of Partial Differential Equations  
Formation of partial differential equations, Solutions of PDEs, Equations solvable by
direct integration, Linear equations of  first order, Homogeneous linear equations
with constant coefficients, Rules for finding the complimentary function, Rules of
finding the particular integral, Working  procedure top solve homogeneous linear
equations of any order, Non-homogeneous linear equations.
3. Applications of Partial Differential Equations
Method of separation of variables, Vibrations of a stretched string-wave equations,
One-dimensional and two-dimensional heat  flow equations, Solution of Laplace’s
equation, Laplace’s equation in polar coordinates.
4. Integral Transforms 
Introduction, Definition, Fourier Integral, Sine and Cosine Integrals, Complex Forms
of Fourier Integral, Fourier Transform, Fourier and Cosine Transforms, Finite
Fourier Sine and Cosine Transforms. Properties of F - Transforms, Convolution
Theorem for F - Transforms, Parseval’s Identity for Fourier Transforms, Fourier
Transforms of the Derivatives of a Function, Applications to Boundary Value
Problems, Using Inverse Fourier Transforms only.
Text Book :  
Higher Engineering Mathematics, Dr. B.  S. Grewal, Khanna Pub. New Delhi, 34th
Edition, 1998.
Reference Books : 
1. A  Text  Book  on  Engineering  Mathematics,  N.  P.  Bali  Etal,  Laxmi  Pub.  Pvt.
Ltd. – New Delhi. 2. Higher Engineering Mathematics, Dr.  M. K. Venkataraman, National Pub.
and Co. – Madras.
3. Advanced Engineering Mathematics, Erwin Kreyszig, Wiley Eastern Pvt. – N.
Delhi.