My thoughts on calculus

A Lot of people struggle with math because they don't have the proper background knowledge to grasp what is going on. For the duration of this post I will be explaining the fundamentals of calculus, mostly the concepts, however to understand calculus you will need to understand algebra. Algebra is the system of mathematics that allows numbers to be modified by other numbers in many ways(addition, subtraction, multiplication, and division) along with how to undo what was done to the original to gain values in a system(like the one and two step equations you likely have done in school). In algebra there are some limitations, for instance algebra primarily works with linear numbers(variables that have an exponent of 1). Calculus on the other hand is designed to handle the limitations from algebra. For example in algebra the standard formula to make a line is y = mx + b, m being the slope. Hypothetically what is the slope of the formula y = x^2(this makes a curve)? The answer is that it depends on the point in the function. The slope will change over time(you can test this with secant lines to approximate the slope but the slope formula of x^2 is 2x if you want exact values). Derivatives are formulas that match the exact slope to the current point in the function. Calculus can be used to get values from functions with holes(values in function that cannot be computed due to math operations limitations like log(negative) or dividing by 0) in them. Calculus can help us find these values using limits. Fun Fact you can use the squeeze method to find most limits; it's simply the formula (F(x + e) + F(x - e)) / 2, e being a very small constant. For this next problem I recommend using an integration formula sheet. It will help. Hypothetically if you had the formula y = 4x + 5 how much is every number added from x = 0 to x = 4? Intuitively the solution seems like we have to add every decimal and whole number between 0 and 4 then match each number into the formula to get the result. For centuries we have done this in mathematics, however this creates an approximation by definition because it is impossible to add every number because numbers are infinite even in between 2 numbers. Over time humanity found an understanding of “integration”. Integration is a technique that modifies the original formula to convert it to keep track of the exact summation of the original formula. To answer the original question using integration the modified formula in this case is y = 2x^2 + 5x so if x = 4 then y = 52 and if x = 0 they y = 0 so 52 - 0 equals 52 then the answer is 52. So why is this important? Derivatives can help us understand non linear growth patterns in data. Integration can help us understand how much stuff is in a non linear gap between 2 numbers. Limits allow us to break some rules in algebra like calculating what 1 / 0 approaches(the answer is “does not exist” but if you approach from the right it is positive infinity and the left is negative infinity). Over all calculus can be used for systems that have numbers that are non linear. I hope you have enjoyed this read i hope it helped you with calculus