Section1: Engineering Mathematics

**Linear Algebra:** Vector algebra, Matrix algebra, systems of linear equations, rank of a matrix, eigenvalues and eigen vectors.

**Calculus:** Functions of single variable, limits, continuity and differentiability, mean value theorem, chain rule, partial derivatives, maxima and minima, gradient, divergence and curl, directional derivatives. Integration, Line, surface and volume integrals. Theorems of Stokes, Gauss and Green.

**Differential Equations:** First order linear and nonlinear differential equations, higher order linear ODEs with constant coefficients. Partial differential equations and separation of variables methods.

**Special Topics:**

Fourier Series, Laplace Transforms, Numerical methods for linear and nonlinear algebraic equations, Numerical integration and differentiation.

Section 2: Flight Mechanics

**Basics: Atmosphere:** Properties, standard atmosphere. Classification of aircraft. Airplane (fixed wing aircraft) configuration and various parts;

**Airplane performance:** Pressure altitude; equivalent, calibrated, indicated air speeds; Primary flight instruments: Altimeter, ASI, VSI, Turn-bank indicator. Drag polar; takeoff 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;

**Special Topics:**

Dynamic stability: Euler angles; Equations of motion; aerodynamic forces and moments, stability & control derivatives; decoupling of longitudinal and lateral-directional dynamics; longitudinal modes; lateral-directional modes.

Section 3: Space Dynamics

Central force motion, determination of trajectory and orbital period in simple cases.

**Special Topics:**

Orbit transfer, in-plane and out-of-plane.

Section 4: Aerodynamics

**Basic Fluid Mechanics:** Conservation laws: Mass, momentum (Integral and differential form);

Potential flow theory: sources, sinks, doublets, line vortex and their superposition; Viscosity, Reynold’s number.

**Airfoils and wings:** Airfoil nomenclature; Aerodynamic coefficients: lift, drag and moment; Kutta-Joukoswki theorem; Thin airfoil theory, Kutta condition, starting vortex; Finite wing theory: Induced drag, Prandtl lifting line theory; Critical and drag divergence Mach number.

**Compressible Flows:** Basic concepts of compressibility, Conservation equations; One dimensional compressible flows, Fanno flow, Rayleigh flow; Isentropic flows, normal and oblique shocks, Prandtl-Meyer flow; Flow through nozzles and diffusers.

**Special Topics:**

Elementary ideas of viscous flows including boundary layers; Wind Tunnel Testing: Measurement and visualization techniques.

Section 5: Structures

**Strength of Materials:** States of stress and strain. Stress and strain transformation. Mohr’s Circle. Principal stresses. Three-dimensional Hooke’s law. Plane stress and strain; Failure theories: Maximum stress, Tresca and von Mises; Strain energy. Castigliano’s principles. Analysis of statically determinate and indeterminate trusses and beams. Elastic flexural buckling of columns.

Flight vehicle structures: Characteristics of aircraft structures and materials. Torsion, bending and flexural shear of thin-walled sections. Loads on aircraft.

**Structural Dynamics:** Free and forced vibrations of undamped and damped SDOF systems. Free vibrations of undamped 2-DOF systems.

**Special Topics:**

Vibration of beams.

Theory of elasticity: Equilibrium and compatibility equations, Airy’s stress function.

Section 6: Propulsion

**Basics:** Thermodynamics, boundary layers and heat transfer and combustion thermochemistry.

Thermodynamics of aircraft engines: Thrust, efficiency and engine performance of turbojet, turboprop, turbo shaft, turbofan and ramjet engines, thrust augmentation of turbojets and turbofan engines. Aerothermodynamics of non-rotating propulsion components such as intakes, combustor and nozzle.

**Axial compressors:** Angular momentum, work and compression, characteristic performance of a single axial compressor stage, efficiency of the compressor and degree of reaction.

Axial turbines: Axial turbine stage efficiency

Centrifugal compressor: Centrifugal compressor stage dynamics, inducer, impeller and diffuser.

**Rocket propulsion:** Thrust equation and specific impulse, vehicle acceleration, drag, gravity losses, multi-staging of rockets. Classification of chemical rockets, performance of solid and liquid propellant rockets.

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