**7. APPLIED MATHEMATICS**

Total Marks – 200

Paper I

Marks – 100

Total Marks – 200

Paper I

Marks – 100

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. Expansion for

gradient, divergence and curl in orthogonal curvilinear coordinates, line, surface and volume integrals,

Green’s, Stoke’s and Gauss’s theorems

Statistics: Composition and resolution of forces, Parallel forces and couples, Equilibrium and 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 law, 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

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, Non-linear

equations, Systems of equations, Variations of parameters and 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 solution of wave equation and equation of heat induction.

Section B

Tensor: Definition of tensors as invariant quantities. Coordinate transformations, Contra variant and

covariant laws of transformation of the components of tensors, addition and multiplication of tensors,

contracts and inner product of tensors, The Kronecker delta and Levi-Civita 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 Numeric Analysis: Solution of non-linear 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 re?? Regula Falsi and iterative method for solving non-linear equation with

convergence, Linear and Lagrange interpolation, graphical solution of linear programming problems.

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