Gate Syllabus

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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