# TRB Teachers Recruitment Board

## MATHEMATICS UNIT 1: REAL ANALYSIS

### Linear programming: Formulation and graphical solutions – Simplex method – Transportation and Assignment problems – Advanced linear programming: Duality – Dual simplex method – Revised simplex method – Bounded variable technique – Integer programming: Cutting plane algorithm – Branch and bound technique – Applications of integer programming – Non-linear programming: Classical optimization theory Unconstrained problems – Constrained problems – Quadratic programming – Dynamic programming: Principle of optimality – Forward and backward recursive equations – Deterministic dynamic programming applications. FLUID DYNAMICS: Kinematics of fluids in motion : Real and ideal fluids – Velocity – Acceleration – Streamlines – Pathlines – Steady and unsteady flows – Velocity potential – Vorticity vector – Local and particle rates of change – Equation of continuity – Conditions at a rigid boundary – Equations of motion of a fluid : Pressure at a point in a fluid – Boundary conditions of two inviscid immiscible fluids – Euler’s equations of motion – Bernoullt’s equation – Some potential theorems – Flows involving axial symmetry – Two dimensional flows : Two-dimensional flows – Use of cylindrical polar coordinates – Stream function, complex potential for two-dimensional flows, irrotational, incompressible flow – Complex potential for standard two-dimensional flows – Two dimensional image systems – Milne – Thomson circle theorem – Theorem of Blasius – Conformal transformation and its applications : Use of conformal transformations – Hydro-dynamical aspects of conformal mapping – Schwarz Christoffel transformation – Vortex rows – Viscous flows : Stress – Rate of strain – Stress analysis – Relation between stress and rate of strain-Cofficient of viscosity – Laminar flow – Navier – Stokes equations of motion – Some problems in viscous flow.

Call Us For More....