Fundamental Mathematics/Calculus


CalculusEdit

Mathematical operations that perform on function, equation

Calculus mathematicsEdit

Change in variablesEdit

For any function f(x) . Over the interval of   to  

 

Change in variable x

 

Change in function f(x)

 

Rate of changeEdit

 

Rate of change

 

LimitEdit

 

Finite Limit We call   the limit of   as   approaches   if   becomes arbitrarily close to   whenever   is sufficiently close (and not equal) to   .

When this holds we write

 

or

 


Infinite Limit We call   the limit of   as   approaches infinity if   becomes arbitrarily close to   whenever   is sufficiently large.

When this holds we write

 

or

 

Similarly, we call   the limit of   as   approaches negative infinity if   becomes arbitrarily close to   whenever   is sufficiently negative.

When this holds we write

 

or

 

DifferentiationEdit

 

Let   be a function. Then

  wherever this limit exists.

In this case we say that   is differentiable at   and its derivative at   is   .

IntegrationEdit

Mathematics operation on a continuous function to find its area under graph . There are 2 types of integration

Indefinite Integral

 
 

Where   satisfies  

Definite Integral

 

Suppose   is a continuous function on   and   . Then the definite integral of   between   and   is

 

Where   are any sample points in the interval   and   for   .}}

Solving differential equationsEdit

Given

 
 
 
 
 
 

In summaryEdit

Ordered differential equation Equation of the form Root of equation
1st ordered differential equation    
2nd ordered differential equation    
 th ordered differential equation    

Solving Ordered Differential EquationsEdit

1st ordered differential equationEdit

Equation of general form

 

After arrangement, equation above becomes

  Where  

Equation has a root

 


2nd ordered differential equationEdit
 
 
 
 

The solution of the 2nd ordered polynomial equation above

One real root    
Two real roots    
One complex root    

With

 
 
 
 
 
 

Partial Differential EquationsEdit

 

Integral TransformationEdit

Any function f(t) can be transform into Laplace function or Fourier function by using Laplace transform or Fourier transform

     
     
     
     

Example

     
     
     


Go to the School of Mathematics

Calculus FormulasEdit

ReferenceEdit