APPLIED MATHEMATICS
Total Marks200
PAPER I (Marks100)
Candidates will be asked to attempt any two questions from Section A and
any three questions from Section B.
SECTION A
Vector Analysis
Vector algebra, scalar and vector product of two or
more vectors, Function of a scalar variable, Gradient, divergence and curl,
Expansion formulae, curvilinear coordinates, Expansions for gradient, divergence
and curl in orthogonal curvilinear coordinates, Line, surface and volume
integrals, Green’s,
Stoke’s and Gauss’s theorms
Statics
Composition and resolution of forces, Parallel forces, and couples, Equilibrium
of a system of coplanar forces, Centre of mass and centre of gravity of a
system of particles and rigid bodies, Friction, Principle of virtual work
and its applications, equilibrium of forces in three dimensions.
SECTION B
Dynamics
Tangential, normal, radial and transverse components
of velocity and acceleration, Rectilinear motion with constant and variable
acceleration, Simple harmonic motion, Work, Power and Energy, Conservative
forces and principles of energy, Principles of linear and angular momentum,
Motion of a projectile, Ranges on horizontal and inclined planes, Parabola
of’ safety. Motion under
central forces, Apse and apsidal distances, Planetary orbits, Kepler’s
laws, Moments and products of inertia of particles and rigid bodies, Kinetic
energy and angular momentum of a rigid body, Motion of rigid bodies, Compound
pendulum, Impulsive motion, collision of two spheres and coefficient of restitution.
PAPER  II (Marks  100)
Candidates will be asked to attempt any two questions from Section A. one
question from Section B and two questions from Section C.
SECTION  A
Differential Equations
Linear differential equations with constant and variable coefficients, the
power series method.
Formation of partial differential equations. Types
of integrals of partial differential equations. Partial differential equations
of first order Partial differential equations with constant coefficients.
Monge's method. Classification of partial differential equations of second
order, Laplace’s equation
and its boundary value problems. Standard solutions of wave equation and
equation of heat induction.
SECTION B
Tensor
Definition of tensors as invariant quantities. Coordinate transformations.
Contravariant and covariant laws of transformation of the components of tensors.
Addition and multiplication of tensors, Contraction and inner product of
tensors The Kronecker delta and LeviCivita symbol. The metric tensor in
Cartesian, polar and other coordinates, covariant derivatives and the Christoffel
symbols. The gradient. divergence and curl operators in tensor notation.
SECTION C
Elements of Numerical Analysis
Solution of nonlinear equations, Use of x = g (x)
form, Newton Raphson method, Solution of system of linear equations, Jacobi
and Gauss Seidel Method, Numerical Integration, Trapezoidal and Simpson’s
rule. Regula falsi and interactive method for solving nonlinear equation
with convergence. Linear and Lagrange interpolation. Graphical solution
of linear programming problems.
SUGGESTED READINGS

Title 
Author 
1 
Classical Mechanics 
Goldstein 
2 
Lactures on Ordinary Differential Equations 
Hille, E. 
3 
Lectures on Partial Differential Equations 
Petrovosky, I.G. 
4 
Mechanics 
Symon, G.F. 
5 
Mechanics 
Ghori, Q. K. 
6 
Mathematical Pyysics, An Advanced Course 
Mikhin, S.G. 
7 
Ordinary Differential Equations 
Easthan, M.S.P. 
8 
Principles of Mechanics 
Synge and Griffith 
9 
Principles of Mechanics 
Hauser 
10 
Partial Differential Equations 
Sneddon, I.N. 
11 
Theoratical Mechanics 
Beckker 
12 
Theoratical Mechanics 
Bradsbury 
13 
Theory of Ordinary Differential Equations 
Goddirgton, E.A. and N. Livenision 
14 
Vector and Tensor Methods, Cartesian Tensors 
Charlton Jeffreya 