What is Calculus? 

Calculus is a branch of mathematics which deals to find the rate of change from curve. It is also called "infinitesimal calculus".

Calculus was developed at 17th century by two mathematician Sir Isaac Newton and Gottfried Wilhelm Leibniz. Calculus is divided into two branches:

1. Differential Calculus 
2. Integral Calculus 

Topics of Calculus 

Calculus has a lot of topics. Here's a few topics of Calculus:

• Function and Graph
• Limits 
• Continuity and Discontinuity 
• Derivatives 
• Integration 

Overview of Calculus Topics

Function and Graph: Function and Graph is the fundamental topic of Calculus. It's like a vending machine where you put a coin or a dollar and it gives you a item. In function you put a value 'x' into it and get 'y'.We express a function with f(x). Suppose a function $x^2-3$ and I put values {-2,-1,0,1,2} so the function gives me {1,-2,-3,-2,1}

Here's the graph of function $x^2-3$

Limits: Limits is like a function. Limits describe how a function behaves near a point, instead of at that point. Limits play a vital role in calculus and mathematical analysis and are used to define integrals, derivatives, and continuity.Let us consider a real-valued function “f” and the real number “c”, the limit is normally defined as  $ \lim_{x \to c} f(x)$. It is read as “the limit of f of x, as x approaches c equals L”.

Derivatives: A derivative in calculus is the rate of change of a quantity y with respect to another quantity x. The derivative of a function f(x) is usually represented by $ \frac{d}{dx} f(x)$. A derivatives means slope of a curve. Let a curve and two points (x,f(x)) and (x+h,f(x+h)) then the slope of the curve is $ m_{sec} = \frac{f(x + h) - f(x)}{(x + h) - x} = \frac{f(x + h) - f(x)}{h}$. It's derivative is also the same but there's a limit function so the derivative is $\frac{d}{dx} f(x)= \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}$. We can also express derivatives with a  prime(') at top of function like f'(x) which also means the derivatives of the curve.

Integration: Integration is a way of uniting the part to find a whole. In maths they are used to find many useful quantities such as areas, volumes, displacement, etc.  According to Mathematician Bernhard Riemann,

“Integral is based on a limiting procedure which approximates the area of a curvilinear region by breaking the region into thin vertical slabs.” The area of the curved shape is approximated by tracing the number of sides of the polygon inscribed in it. This process known as the method of exhaustion was later adopted as integration. Integration is the inverse of differentiation. To represent the antiderivative of “f'(x)”, the integral symbol “∫” symbol is introduced. The antiderivative of the function is represented as ∫ f'(x) dx. This can also be read as the indefinite integral of the function “f” with respect to x. The antiderivative of f'(x) is $ \int f'(x) \, dx = f(x) + C$

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