Applied Mathematics KP PMS Paper I Syllabus
Applied Mathematics
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.
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