Definition of Calculus

Before starting my journey in this course, what is the most basic definition of calculus?

I say calculus is the study of motion and time.

You say?

Note: Do not give me a textbook definition.

 

Calculus is the most powerful weapon of thought yet devised by the wit of man.

 

Very good but this is not the definition of calculus. To my understanding, calculus is the study of motion and time?

Yes?

 

Mathematics as a field of study is independent of notions tied to our physical reality, such as space or time.

better to say, calculus help us to describe the motion
here is my other definition:
Calculus is the mathematical study of change

 

Ron Larson stated:

"Calculus is the mathematics of change."

Questions:

1. What change? Change in motion?

2. Change in time?

3. Change in motion in terms of time?

4. Change in time in terms of motion?

Trust me, I really want to "master" Calculus l, ll, and lll. I am not interested in Advanced Calculus.

 

CALCULUS is the branch of mathematics dealing primarily with change. Calculus is the study of how things change. Calculus provides a framework for modelling of systems in which there are changes. It provides means for one to construct simple quantitative models of change and to deduce their consequences.

Before Newton and calculus, the study of the motions of the planets was at best limited to kinematics: you could observe the motions and try to describe them. As to what caused those motions, there could only be speculation.
Newton produced a dynamic theory: some simple physical laws that explained the motions as the result of the same forces that act on an apple falling from a tree. Moreover, with the mathematical techniques of calculus and differential equations (which is basically an extension of the calculus), the resulting motions could be calculated and predicted.
From that time on, most of physical science and engineering has been understood in terms of differential equations. The laws of physics give you differential equations that describe the rates of change of various quantities in a system you are interested in. By solving those differential equations, you can predict how the system changes as time goes on.

 

This is a great reply. Since differential equations is an extension of calculus, I might decide to learn the first course after calculus 3. I think the course is called Ordinary Differential Equations. However, I am not going to learn Partial Differential Equations not am I going to learn advanced calculus. What do I mean by advanced calculus? I am not talking about calculus lll. I am talking about, well, see the video clip below.

The following course is beyond the regular calculus lll we know about:

 

You seem to be confusing mathematics with physics!
The "change" studied in Calculus can be any kind of change that can have numbers assigned to it. For example Calculus is used in Economics and Business Administration to model changes in values and prices that have nothing to do with motion.

 

Thank you for the clarification.

 

No. Calculus can be, and is, applied to problems, in economics for example, that have nothing to do with "motion and time".

Calculus has two great sub-fields, differentiation and integration. Both were studied before Newton and Leibniz but they are considered the founders of Calculus because they recognized that those are "inverse" to each other.

 

I saw a video clip on YouTube where the math teacher stated that Newton and Leibniz didn't get along because they each wanted credit for creating calculus. What about the apple falling on Newton's head? This it really happen? Should we credit the falling apple as the foundation for calculus? When I think of calculus, Newton comes to mind. In what way is Leibniz connected to calculus?

 

And you are writing in English! If you were writing in French, you would think it was Leibniz!

Newton used y' for the derivative of y. It was Leibniz who introduced dy/dx.

 

I prefer y prime over dy/dx. What about you?

Note: I expect to be done with the Ron Larson precalculus textbook by late March or sometime in April 2022. I will now concentrate on the essentials of precalculus and not every problem per section. I love every problem in the book but realistically, there just aren't enough hours in a day to answer every question.