Mathematics, Basic Engineering Sciences, Economics, and ME Laws Vocabulary Flashcards

Vocabulary practice flashcards extracted from lecture notes covering Algebra, Geometry, Trigonometry, Calculus, Physics, Mechanics, Engineering Economics, and Laws.

Symmetric Axiom

An algebraic axiom stating that if $a = b$, then $b = a$.

Lemma

An ancillary or proved proposition whose result serves mainly as a preliminary step to the proof of a main theorem.

Postulate

A proposition concerning geometric constructions or objects whose possibility is admitted without proof.

Conjecture

A mathematical statement that has neither been proved nor denied by counterexamples.

Monomial

An algebraic expression consisting of exactly one term.

Complex Fraction

Any fraction containing one or more fractions in either its numerator, denominator, or both.

Perfect Number

An integer that is equal to the sum of all its proper positive divisors, excluding the number itself (e.g., $6$).

Amicable Numbers

A pair of integer numbers in which each is equal to the sum of all the proper positive divisors of the other; also known as friendly numbers.

Goldbach Conjecture

The mathematical conjecture stating that every even integer greater than $2$ can be expressed as the sum of two prime numbers.

Cramer's Rule

A method of solving a system of linear equations with multiple unknowns simultaneously using determinants.

Surd

An irrational number expressed as the root of a positive integer or fraction.

Fibonacci Numbers

An unending sequence of integers ($1, 1, 2, 3, 5, 8, 13, 21, \dots$) formed according to the rule that each number is the sum of the preceding two.

Pascal's Triangle

A triangular array of numbers forming the coefficients of a binomial expansion $(x + y)^n$.

Permutation

An ordered arrangement of a set of objects in a specific sequence.

Ogive

A graph representing a cumulative frequency distribution plotted at class marks and connected by straight line segments.

Asymptote

A straight line that a curve approaches infinitely closely but never touches except at an infinite limit.

Latus Rectum

A chord passing through the focus of a conic section and oriented perpendicular to its axis of symmetry.

Cycloid

The plane curve traced out by a fixed point on the circumference of a circle as the circle rolls without slipping along a straight line.

Point of Inflection

A point on a curve where the second derivative equals zero and the concavity changes from upward to downward or vice versa.

First Proposition of Pappus

Theorem stating that the surface area generated by rotating a plane curve about a non-intersecting axis in its plane equals the arc length multiplied by the distance traveled by its centroid.

Latent Heat of Fusion

The amount of heat required to change a unit mass of a substance from a solid to a liquid state at its melting point.

Bernoulli's Theorem

A fluid dynamics principle stating that for steady, ideal fluid flow along a streamline, the sum of pressure head, elevation head, and velocity head remains constant.

Coefficient of Restitution

The negative ratio of the relative velocity of two colliding bodies after impact to their relative velocity before impact.

Young's Modulus

The ratio of tensile stress to tensile strain within the linear elastic region of a material.

Poisson's Ratio

The ratio of lateral unit strain to longitudinal unit strain in a material subjected to stress within its proportional limit.

Annuity

A series of equal payments or receipts occurring at equal intervals of time.

Depreciation

The decrease in the physical or monetary value of an asset over time due to passage of time, wear, and tear.

Monopoly

A market condition where a single seller controls the supply of a commodity or service offered to many buyers.

Monopsony

A market situation in which there is only one buyer for a product or service with no close substitutes.

Economic Order Quantity (EOQ)

The optimal order quantity that minimizes the total inventory costs per unit time under known demand conditions.