# 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,
- Gradient, divergence and curl,
- 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;
- Steady climb & descent;
- Absolute and service ceiling;
- 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 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

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