FET key terms

A scalar that, when a matrix multiplies a particular nonzero vector, produces the same result as multiplying that vector by the scalar. It identifies natural modes, stability, and vibration frequencies in engineering systems.

An iterative numerical method for finding roots of an equation using tangent-line approximations. Starting from an initial guess, each step updates the estimate until the residual is sufficiently small; convergence depends on the starting point.

A numerical integration technique that approximates the area under a curve by fitting parabolic segments through equally spaced points. It is exact for polynomials up to degree three and generally more accurate than the trapezoidal rule.

A range of values, computed from sample data, that is expected to contain an unknown population parameter with a stated probability. Wider intervals indicate greater uncertainty; the confidence level reflects long-run coverage.

The probability, assuming the null hypothesis is true, of obtaining a test statistic at least as extreme as the one observed. A small p-value suggests the observed result is unlikely under the null hypothesis.

Rejecting a true null hypothesis, often called a false positive. Its probability equals the significance level chosen for the test, so lowering that level reduces Type I errors at the cost of more Type II errors.

A result stating that the distribution of sample means approaches a normal distribution as sample size grows, regardless of the underlying population shape, provided observations are independent and variances are finite. It underpins many statistical procedures.

The principle that a sum of money available today is worth more than the same sum received later, because it can earn interest or be invested. It underlies discounting, compounding, and equivalence calculations.

The equivalent value today of a stream of future cash flows, obtained by discounting each flow at a chosen interest rate. Alternatives are compared by converting all costs and benefits to a common present time.

The discount rate at which a project's net present value equals zero, making discounted benefits equal discounted costs. It is compared with a minimum acceptable rate to judge project attractiveness.

A situation in which a professional's personal, financial, or other interests could improperly influence, or appear to influence, engineering judgments or decisions. It must be disclosed and managed, often by recusal.

A sketch of a body isolated from its surroundings, showing all external forces and moments acting on it, including reactions at supports. It is the essential first step in applying equilibrium equations.

The geometric center of a shape or the point where its area or volume is balanced. For homogeneous bodies it coincides with the center of mass and is used to compute moments of inertia and resultant forces.

A relationship stating that the impulse of a resultant force over a time interval equals the change in momentum of the body. It is useful for problems involving collisions, impacts, and time-dependent forces.

A dimensionless ratio between the maximum friction force that can develop before sliding and the normal force pressing two surfaces together. It depends on the material pair and surface condition.

The internal intensity of force per unit area within a material, used to characterize how heavily a component is loaded. Normal stress acts perpendicular to a section; shear stress acts parallel to it.

A measure of deformation expressed as a change in length or angle relative to an original dimension. Normal strain describes elongation, while shear strain describes angular distortion; both are dimensionless quantities.

The negative ratio of transverse strain to axial strain for a material loaded uniaxially. Typical metals have values near 0.3; the theoretical range for isotropic materials is -1 to 0.5.

Progressive damage and possible fracture caused by repeated or fluctuating stress cycles, even when peak stresses are below the yield strength. Fatigue life depends on stress amplitude, mean stress, and surface conditions.

The ratio of a material's or component's strength or allowable load to the actual expected stress or load. Values above one provide margin against uncertainty, overload, and material variability.

An energy relationship for steady, incompressible, frictionless flow along a streamline, stating that pressure head, velocity head, and elevation head sum to a constant. It is used to analyze nozzles, pipes, and orifices.

A dimensionless ratio of inertial forces to viscous forces in a flow. It indicates whether flow is laminar or turbulent and governs scaling and friction correlations for pipes and immersed bodies.

A statement of mass conservation for a control volume: the mass flow rate entering must equal the rate leaving plus any accumulation. For steady incompressible flow, area times velocity remains constant along a stream tube.

A formula expressing head loss in a pipe as a function of friction factor, pipe length and diameter, and velocity head. The friction factor depends on Reynolds number and relative roughness.

A statement of energy conservation for a system: the net heat added equals the net work done plus the change in internal energy, with mass flows also carrying energy across boundaries.

A thermodynamic property that measures energy dispersal within a system at a given temperature. In an isolated system it increases for irreversible processes; it underlies the second law and sets efficiency limits.

A relationship stating that conductive heat flux is proportional to the negative temperature gradient, with the proportionality constant being the material's thermal conductivity. It is fundamental to steady and transient conduction analysis.

The effective average temperature difference between two flowing streams in a heat exchanger, computed from the terminal differences. It accounts for the reduced driving force in counterflow or parallel-flow arrangements.

A relationship for ideal resistors stating that voltage across a component equals current through it times resistance. In AC circuits it generalizes to impedance, relating phasor voltage and current.

Two circuit rules: the sum of currents entering a node equals the sum leaving it, and the sum of voltage changes around any closed loop is zero. They yield equations for analyzing complex networks.

The ratio of real power to apparent power in an AC circuit, equal to the cosine of the angle between voltage and current. Low values indicate reactive demand and larger currents for the same real load.

A method that replaces a linear two-terminal network with a single voltage source in series with a resistance. It simplifies load analysis by reproducing the original network's terminal current-voltage behavior.

The ratio of the Laplace transform of a system's output to that of its input, assuming zero initial conditions. It characterizes dynamics, stability, and frequency response of linear time-invariant systems.

A feedback controller that combines proportional, integral, and derivative actions; the proportional term responds to current error, the integral removes steady-state offset, and the derivative anticipates trends. Gains are tuned for response and stability.

The process of comparing an instrument's readings with a traceable reference of known accuracy and adjusting or documenting the relationship between indication and true value. It establishes measurement uncertainty over a specified range.

A quantitative estimate of the range within which the true value of a measurement is expected to lie, accounting for instrument errors, environmental effects, and repeatability. It is often expressed as a standard or expanded uncertainty.

A structured reliability technique that identifies potential failure modes, their causes, and effects, and ranks them by severity, occurrence, and detectability. It guides design changes and maintenance planning to reduce risk.

The probability that a component or system performs its required function without failure for a specified period under stated operating conditions. It is often modeled with exponential or Weibull distributions.

A systematic process of identifying hazards, estimating the likelihood and severity of harm, and evaluating whether risk is acceptable. Results inform controls such as design changes, procedures, and protective systems.

A deductive method that starts with an undesired top event and traces combinations of lower-level failures that could cause it, using boolean logic gates. It supports reliability and safety decisions.