Lesson 1: Introduction to Calculus

Hello and welcome to the next chapter of ur mathmatical life. Calculus; this name may frighten you, but let's take a look at the its goal, why was it invented, and why is it important today.

Issac Newto Absolute cinema

The guy who invented Calc, Sir Issac Newton, was one brillient man, in just 2 years he descovered his infamous Three laws, which are fundemental in Mechanics. Additionally, He invented the Universal law of gravitation, which explains the gravitational fields of all planetary objects. Moreover, He created color theory and the color wheel. However, he was suffering from a problem. "I can meuasure the average velocity of an object in a small period of time," said Newton, "But I can never know what is its instantainious velocity" this is the problem that tackelled scientist for centries, because how could anybody calculate te instantainious velocity when velocity is the slope of 2 points on the position time graph (AKA \(\frac{\Delta x}{\Delta t}\)). But then, Newton's brillient mined had an Idea: "Lets decrease the distance between those 2 points until they approach 1 point, they transform from the difference in x (\( \Delta x\)) into the DIFFERENTIAL ELEMENT OF x (\(dx\)) I distance so small that the 2 points become 1, and I can achieve my master plan THE SLOPE OF 1 POINT (aka derivative), and to reverse it, since the slope is the opposite of the area I can take the area under the curve: BY DIVIDING THE x AXIS INTO THE SAME DIFFERENTIAL ELEMENT OF x (\(dx\)) and multiplying them by the y value of f(x), I can get THE AREA OF AN INTERVAL OF LINES UNDER A CURVE (aka integrals)." and the rest was history... litrally, I mean almost all general formulas in physics rely on integral and differential Calculus. To the point that the scientific method to derive any formula must use integration.