Linear Algebra: Matrix algebra, systems of
linear equations, eigen values and eigen vectors. Calculus: Functions of single
variable, limit, continuity and differentiability, mean value theorems,
evaluation of definite and improper integrals, partial derivatives, total
derivative, maxima and minima, gradient, divergence and curl, vector identities,
directional derivatives, line, surface and volume integrals. Theorems of Stokes,
Gauss and Green.
Differential Calculus: First order linear
and nonlinear equations, higher order linear ODEs with constant coefficients,
Cauchy and Euler equations, initial and boundary value problems, Laplace
transforms. Partial differential equations and separation of variables methods.
Numerical methods: Numerical solution of
linear and nonlinear algebraic equations, integration by trapezoidal and Simpson
rule, single and multi-step methods for differential equations.
Atmosphere: Properties, standard atmosphere.
Classification of aircraft. Airplane (fixed wing aircraft) configuration and
Airplane performance: Pressure altitude;
equivalent, calibrated, indicated air speeds; Primary flight instruments:
Altimeter, ASI, VSI, Turn-bank indicator. Drag polar; take off and landing;
steady climb & descent,-absolute and service ceiling; cruise, cruise climb,
endurance or loiter; load factor, turning flight, V-n diagram; Winds: head, tail
& cross winds.
Static stability: Angle of attack, sideslip;
roll, pitch & yaw controls; longitudinal stick fixed & free stability,
horizontal tail position and size; directional stability, vertical tail position
and size; dihedral stability. Wing dihedral, sweep & position; hinge
moments, stick forces.
Dynamic stability: Euler angles; Equations
of motion; aerodynamic forces and moments, stability & control derivatives;
decoupling of longitudinal and lat-directional dynamics; longitudinal modes;
Central force motion, determination of trajectory
and orbital period in simple cases. Orbit transfer, in-plane and out-of-plane.
Elements of rocket motor performance.
Basic Fluid Mechanics: Incompressible
irrotational flow, Helmholtz and Kelvin theorem, singularities and
superposition, viscous flows, boundary layer on a flat plate.
Airfoils and wings: Classification of
airfoils, aerodynamic characteristics, high lift devices, Kutta Joukowski
theorem; lift generation; thin airfoil theory; wing theory; induced drag;
qualitative treatment of low aspect ratio wings.
Viscous Flows: Flow separation, introduction
to turbulence, transition, structure of a turbulent boundary layer.
Compressible Flows: Dynamics &
Thermodynamics of I-D flow, isentropic flow, normal shock, oblique shock,
Prandtl-Meyer flow, flow in nozzles and diffusers, inviscid flow in a c-d
nozzle, flow in diffusers. subsonic and supersonic airfoils, compressibility
effects on lift and drag, critical and drag divergence Mach number, wave drag.
Wind Tunnel Testing: Measurement and
Stress and Strain: Equations of equilibrium,
constitutive law, strain-displacement relationship, compatibility equations,
plane stress and strain, Airy's stress function.
Flight Vehicle Structures: Characteristics
of aircraft structures and materials, torsion, bending and flexural shear.
Flexural shear flow in thin-walled sections. Buckling. Failure theories. Loads
Structural Dynamics: Free and forced
vibration of discrete systems. Damping and resonance. Dynamics of continuous
Thermodynamics of Aircraft Gas Turbine engines,
thrust and thrust augmentation.
Turbomachinery: Axial compressors and
turbines, centrifugal pumps and compressors.
Aerothermodynamics of non rotating propulsion
components: Intakes, combustor and nozzle. Thermodynamics of ramjets and
scramjets. Elements of rocket propulsion.