Introductory Calculus

Calculus is a major part of mathematics that studies change. There are two major branches, namely Differential Calculus and Integral Calculus which are linked together by the Fundamental Theorem of Calculus.

Differential Calculus
Differential Calculus is the study of the rates at which a function changes. In a straight line graph, this would be the gradient, but in curves, it would be the gradient of the tangent at particular points. We find the gradient of these tangents through a process called differentiation. The derivative of a function (function after differentiation) can be written as

There are a few rules for differentiating:

1. Power Rule
   
   
   
   
   
   
   
   
   
   
   
   
2. Product Rule: The y is a product of two functions, then the derivative is:
   
   
   
   
   
   
   
   
3. Quotient Rule: if y is a function divided by another function, then the derivative of y is:
   
   
   
   
4. Chain Rule/Function of a Function:
   
   
   
   
   
   
   
   
   
   
   
   
   
5. Differentiation by first principles: The original but long method
   

Integral Calculus
Integral Calculus is the study of areas under functions. In a straight line graph, this would be a trapezium, but in curves it can be very hard to find the exact value, integral calculus can give the exact value. There are two different types of Integrals (Function after integrating). They are the Indefinite (also the antiderivative, opposite of derivative) and Definite (which give the area between the curve and the x axis within the boundaries).

The integral of a function is:

Hope you have learnt something!