And I will be able to use this to some worthwhile end? Okay, probably not. But you might. And also you might be provoked to learn more about the systems you want to study or about mathematics, to improve your chances to do so. And the details of calculus involve the interrelations between the concepts exemplified by speed and acceleration and that represented by position. So what does one study in learning about calculus? To begin with you have to have a framework for describing such notions as position speed and acceleration. (We add a sign to this distance, which will be negative if the object is behind the origin.) The motion of the object is then characterized by the set of its numerical positions at relevant points in time. The study of calculus is normally aimed at giving you the "mathematical sophistication" to relate to such more advanced work. So why this nonsense about empowerment? This course will try to be different and to aim at empowerment as well as the other usual goals.
How to find the instantaneous change (called the "derivative of various functions. (The process of doing so is called "differentiation".) 2. How to use derivatives to solve various kinds of problems.
When we deal with an object moving along a path, its position varies with time we can describe its position at any time by a single number, which can be the distance in some units from some fixed point on that path, called the "origin" of our coordinate system.