FE Exam key terms

A scalar that, when a square matrix multiplies a particular nonzero vector, produces the same result as multiplying that vector by the scalar. It identifies directions a linear transformation only stretches or shrinks.

The rate of change of a function of several variables taken with respect to one variable while the others are held constant. It underlies optimization, error propagation, and multivariable rate problems.

An expansion that writes a smooth function as an infinite sum of terms built from its derivatives at a single point. Truncated versions supply the linear and quadratic approximations used in analysis.

A numerical integration method that approximates the area under a curve by joining sample points with straight segments and summing the resulting trapezoids. Accuracy improves as the interval width decreases.

A result stating that the mean of many independent random variables tends toward a normal distribution regardless of the underlying distribution, justifying normal-based confidence intervals and control charts.

A range computed from sample data that is expected to contain the true population parameter with a stated probability. Its width narrows as sample size grows or variability falls.

Rejecting a null hypothesis that is actually true, commonly called a false positive. Its probability equals the significance level, alpha, chosen by the analyst before testing.

The equivalent value today of a stream of future cash flows, obtained by discounting each flow at the minimum attractive rate of return. It lets alternatives be compared on a common time basis.

The discount rate at which a project's net present value equals zero. An investment is acceptable when this rate exceeds the minimum attractive rate of return.

The present worth of a project assumed to last indefinitely, computed as the initial cost plus the present worth of a repeating annual cost divided by the interest rate.

The lowest rate of return a firm will accept before committing funds to a project. It reflects the cost of capital plus a margin for the risk of the investment.

A circumstance in which an engineer's financial, personal, or other interest could improperly influence professional judgment, or could appear to do so. It must be disclosed or avoided.

Direct control and personal supervision of engineering work by a licensed professional who reviews the design decisions and accepts accountability for the work of subordinates.

Reporting an employer's or client's illegal, unsafe, or unethical conduct to an authority or the public, typically after internal channels fail. Many jurisdictions protect it when public safety is at stake.

The degree of care and skill a reasonable, prudent engineer with similar training would exercise under comparable circumstances. It is the benchmark used when judging negligence claims.

A sketch of a body isolated from its surroundings that shows every applied force, moment, and support reaction acting on it, used to write equilibrium equations.

The ratio of a member's or material's capacity, such as yield or ultimate strength, to the load or stress expected in service. Values above one indicate margin against failure.

A geometric property describing how an area's points are distributed about an axis. It quantifies resistance to bending, so a larger value corresponds to a stiffer beam.

Describing a structure or member with more unknown reactions than independent equilibrium equations, so compatibility of deformations or member stiffness must be used to solve for the forces.

The stress at which a material begins to deform permanently, marking the end of elastic behavior on a stress-strain curve. It is often estimated by the 0.2 percent offset method.

Progressive failure of a material subjected to repeated or fluctuating stress cycles at levels below its static strength, usually beginning at a stress concentration or existing flaw.

Time-dependent permanent deformation of a material held under constant stress. It becomes significant at elevated temperature and, for some polymers, even at room temperature.

A chart showing which phases of a material system are stable as functions of temperature, composition, and sometimes pressure. It guides alloy design and heat-treatment selection.

A dimensionless ratio of inertial forces to viscous forces in a flow. It indicates whether flow is laminar or turbulent and governs which friction correlation applies.

An energy relation for steady, incompressible, frictionless flow along a streamline: the sum of pressure head, velocity head, and elevation head remains constant.

A fluid property measuring internal friction, that is, resistance of adjacent fluid layers to sliding past one another. Higher values mean greater resistance to flow and larger pressure losses.

Formation and violent collapse of vapor bubbles in a liquid where local pressure falls below vapor pressure, producing noise, vibration, and surface erosion in pumps, valves, and propellers.

The principle of energy conservation applied to a system: heat transferred in equals the change in stored energy plus the work done by the system.

A thermodynamic property measuring how dispersed energy is and how irreversible a process is. It increases for an isolated system whenever a real process takes place.

The maximum thermal efficiency any heat engine can achieve between two reservoirs: one minus the ratio of the colder absolute temperature to the hotter one.

A composite property equal to internal energy plus the product of pressure and volume. It is convenient for analyzing flow devices and constant-pressure heating processes.

Two circuit rules: currents entering a node sum to zero, and the voltage rises and drops around any closed loop sum to zero.

A replacement of a linear two-terminal network by one voltage source in series with one resistance, which produces the same response for any load connected to those terminals.

The ratio of real power to apparent power in an alternating-current circuit, numerically equal to the cosine of the phase angle between voltage and current.

The complex ratio of voltage to current in an alternating-current circuit, combining resistance and reactance and carrying both magnitude and phase information.

A ranking of hazard controls by effectiveness, from elimination and substitution through engineering controls and administrative controls down to personal protective equipment.

A regulatory ceiling on the concentration of a substance in workplace air, averaged over a stated period, to which a worker may lawfully be exposed.

A procedure that isolates and de-energizes equipment and attaches locks and warning tags so machinery cannot be started while servicing or maintenance is under way.