# Engineering Mathematics

## Linear Algebra

• Matrix algebra,
• Systems of linear equation,
• eigen values and eigen vectors.

## Calculus

• Functions of single variable, limit, continuity and differentiability,
• Mean value theorems,
• Evaluation of definite and improper integral,
• Partial derivatives,
• Total derivatives,
• Maxima and minima,
• Vector identities,
• Directional derivatives, line, surface and volume integrals,
• Theorems of Stokes, Gauss and Green.

## Differential calculus

• Frist 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

# Flight Mechanics

## Atmosphere

• Properties,
• Standard atmosphere,
• Classification of aircraft,
• Airplane configurations 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;
• Absolute and service ceiling;
• Cruise, climb, endurance or loiter;
• Turning flight,
• V-n diagram;
• Winds: head, tail & cross winds.

## Static Stability

• Angle of attack,
• Sideslip;
• Roll, pitch &yaw control;
• Longitudinal stick fixed & free stability,
• Horizontal tail position and size;
• Directional stability,
• Vertical tail position and size;
• Dihedral stability.
• Wing dihedral, sweep position; hinge movements, stick forces.

## Dynamic Stability

• Euler angles;
• Equations of motion;
• Aerodynamic forces and moments,
• Stability & control derivatives;
• Decoupling of longitudinal and lateral directional dynamics;
• Longitudinal and lateral directional modes.

# Space Mechanics

• Central force motion,
• determination of trajectory and orbital period in simple cases,
• Orbit transfers – in-plane and out-of-plane,
• Elements of rocket motor performance