数学术语表

A derivative measures the instantaneous rate of change of a function — equivalently, the slope of the tangent line to the function's graph at a single point.

An integral is the continuous analogue of summation — most commonly the area under a curve. Definite integrals produce numbers; indefinite integrals produce antiderivative functions.

A limit describes the value a function approaches as its input gets arbitrarily close to a target — without necessarily reaching it. Limits underpin both derivatives and integrals.

The mean — also called the arithmetic average — is the sum of a set of values divided by the count of values. It is the most common single-number summary of a data set.

The Pythagorean theorem states that in any right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c².

A quadratic equation is a second-degree polynomial equation in one variable, written as ax² + bx + c = 0 with a ≠ 0. Its graph is a parabola.

Sine, cosine, and tangent are the three basic trigonometric functions, defined as ratios of sides in a right triangle and extended to all real numbers via the unit circle.

Standard deviation measures how spread out a data set is around its mean. A small standard deviation means values cluster tightly; a large one means they are scattered.