FET flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Newton–Raphson iteration formula

x_{n+1} = x_n − f(x_n)/f′(x_n). It converges quadratically near a simple root but can diverge when the initial guess is poor or the derivative is near zero.

Simpson's 1/3 rule

Numerical integration over an even number of equal subintervals: (h/3)[f₀ + 4f₁ + 2f₂ + … + f_n]. Its truncation error is O(h⁴), making it more accurate than the trapezoidal rule.

Central difference derivative

Approximates a derivative as [f(x+h) − f(x−h)]/(2h). Its truncation error is O(h²), one order better than forward or backward differences at the same step size.

Bayes' theorem

P(A|B) = P(B|A)·P(A)/P(B). It updates a prior probability P(A) into a posterior probability using the likelihood of the observed evidence and its total probability.

Central limit theorem

For independent, identically distributed variables with finite variance, the sample mean approaches a normal distribution as sample size grows, regardless of the shape of the underlying population distribution.

Type I and Type II errors

A Type I error rejects a true null hypothesis with probability α; a Type II error fails to reject a false null with probability β. Statistical power equals 1 − β.

Engineering ethics paramountcy

Professional codes place the public's safety, health, and welfare above loyalty to employer or client; engineers must disclose conflicts of interest and sign only work within their competence.

Capitalized cost formula

For a perpetual uniform series, CC = P + A/i, where A is the recurring annual cost and i the interest rate. It compares alternatives assumed to have infinite lives.

Effective annual interest rate

For a nominal rate r compounded m times per year, i_eff = (1 + r/m)^m − 1. Continuous compounding gives i_eff = e^r − 1.

Parallel axis theorem

I = I_c + A·d², where I_c is the centroidal moment of inertia, A the area, and d the perpendicular distance between the parallel axes. It applies to area and mass moments.

Coefficient of restitution

e = (v₂′ − v₁′)/(v₁ − v₂) along the line of impact. e = 1 for a perfectly elastic collision, e = 0 for perfectly inelastic; kinetic energy is lost unless e equals one.

Work–energy principle

T₁ + V₁ + U_{1→2} = T₂ + V₂ balances initial kinetic and potential energy, work done by non-conservative forces, and final kinetic and potential energy for a particle or rigid body.

Zero-force truss members

At a two-member joint with no external load or support reaction, both members carry zero force. At a three-member joint where two are collinear, the third is zero.

Euler column buckling load

P_cr = π²EI/(KL)², where K depends on end conditions, E is Young's modulus, and I is the minimum moment of inertia. It applies to slender columns buckling elastically.

Torsion shear stress

For a circular shaft, τ = T·c/J, where T is torque, c the outer radius, and J the polar moment of inertia. The angle of twist is θ = TL/(JG).

Stress concentration factor

K_t = σ_max/σ_nom, the ratio of peak local stress at a geometric discontinuity such as a hole or fillet to the nominal stress. It is used in static and fatigue checks.

Transverse shear formula

τ = VQ/(It): V is shear force, Q the first moment of the area above the point about the neutral axis, I the section moment of inertia, and t the width there.

Reynolds number

Re = ρVD/μ = VD/ν, the ratio of inertial to viscous forces. Pipe flow is typically laminar below about 2000 and turbulent above about 4000.

Bernoulli equation

p/γ + z + V²/(2g) = constant along a streamline for steady, incompressible, frictionless flow. It expresses conservation of energy per unit weight of fluid.

Pump affinity laws

For geometrically similar pumps at constant efficiency, flow varies with speed N, head with N², and power with N³. Changes in impeller diameter follow the same proportionalities.

Carnot efficiency

η = 1 − T_L/T_H for a reversible cycle between absolute temperatures T_H and T_L. No real cycle operating between the same two reservoirs can exceed this value.

Overall heat transfer coefficient

1/(UA) = ΣR_th, the sum of conduction and convection thermal resistances in series. The total heat rate is then q = UA·ΔT between the two bulk fluids.

Isentropic ideal gas relation

For an ideal gas with constant specific heats undergoing an isentropic process, T₂/T₁ = (P₂/P₁)^((k−1)/k) and P₂/P₁ = (v₁/v₂)^k.

Thevenin equivalent circuit

Any linear two-terminal network reduces to a voltage source V_th in series with R_th, where V_th is the open-circuit voltage and R_th the resistance seen with sources deactivated.

RLC series resonance

At resonance the inductive and capacitive reactances cancel, so impedance is purely resistive and minimum. The resonant frequency is f₀ = 1/(2π√(LC)).

Three-phase real power

For a balanced three-phase load, P = √3·V_L·I_L·cos φ, where V_L and I_L are line voltage and line current and cos φ is the power factor.

Closed-loop transfer function

For a forward path G and feedback path H with negative feedback, the closed-loop transfer function is G/(1 + GH). Roots of its denominator determine stability.

Second-order percent overshoot

M_p = 100·exp(−πζ/√(1−ζ²)), where ζ is the damping ratio. Lower damping raises overshoot; ζ = 0.707 gives about 4.3% overshoot.

Nyquist sampling criterion

Sample at more than twice the highest signal frequency to avoid aliasing. The minimum is f_s > 2·f_max; practical designs add anti-aliasing filters and often sample faster.

Risk priority number

In FMEA, RPN = severity × occurrence × detection, each scored on a 1–10 scale. Higher RPN prioritizes corrective action, though high severity alone may also drive decisions.

Series system reliability

R_system = ΠR_i, so reliability falls as components are added in series because all must work. Parallel redundant systems give R = 1 − Π(1 − R_i).

Hierarchy of controls

Risk controls ranked from most to least effective: elimination, substitution, engineering controls, administrative controls, then personal protective equipment, which protects only the individual and depends on correct use.