微積分是討論 ”極限(Limit)” 這一觀念的數學。有兩種特定的極限定義，分別稱作微分(Differentiation)和積分(Integration)。本課程之內容即為極限、微分、和積分之觀念及應用。

Calculus was created primarily to treat the major scientific problems of the seventeenth century. There were 4 major types of problems in seventeenth century. They are as follows. 1. Given the formula for the distance a body covers as a function of time, find the body’s velocity and acceleration at any instant; and conversely, given the formula describing the acceleration of a body as a function of time, find the velocity and the distance traveled. 2. The second type of problem was to find the tangent to a curve. 3. The third type of problem was that of finding the maximum or minimum value of a function. 4. The fourth problem was finding the lengths of curves, such as the distance covered by a planet in a given period of time; the areas bounded by curves; volumes bounded by surfaces; centers of gravity of bodies; and the gravitational attraction that an extended body, a planet for example, exerts on another body.

B. Thomas, etc.; Thomas’ calculus: Early Transcendentals; 15th Edition, 2024, Pearson