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.

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.

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 is mathematics that discusses the concept of "limit". There are two specific definitions of limits, called differentiation and integration. The content of this course is the concepts and applications of limits, differentials, and integrals.

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

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