Mathematics and Basic Engineering Sciences
This domain tests whether you can translate an engineering description into a correct mathematical model and carry the numbers through to a defensible answer. Expect calculus, linear algebra, differential equations, probability, and the mechanics, thermodynamics, fluid and electrical fundamentals behind aircraft systems.
Core rules
- Model before computing: define the independent variable, the state variables, and the sign convention first.
- Eigenvalues decide stability. Repeated negative real roots mean critical damping; any positive real part means divergence.
- Pressure discipline: keep gauge and absolute values separate, and state the density assumption before combining the ideal gas law p = ρRT with Bernoulli's equation.
- Convert to coherent SI units at the start; kPa fed into a kg/m³ density scales an answer by 1000.
- For statistics, distinguish sample from population variance and remember reliability needs a distribution, not just a mean.
Worked example
Solve y″ + 4y′ + 4y = 0 with y(0)=1, y′(0)=0. The characteristic equation r²+4r+4=(r+2)² gives the repeated root r=−2, so y=(C₁+C₂t)e^{−2t}. From y(0)=1, C₁=1. Differentiating, y′=(C₂−2C₁−2C₂t)e^{−2t}; at t=0, y′(0)=C₂−2=0, so C₂=2 and y=(1+2t)e^{−2t}. The negative repeated root means stable, critically damped motion: no overshoot, monotonic decay after the initial rise. Checking the limits y(0)=1 and y→0 confirms the solution.
Traps
- Superposing solutions of a nonlinear equation.
- Mixing degrees and radians.
- Quoting a time constant or eigenvalue without units.
- Treating a small-sample mean as the population value.