Fundamental Mathematics/Calculus

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Calculus[edit | edit source]

Mathematical operations perform on function, equation

Calculus mathematics[edit | edit source]

Change in variables[edit | edit source]

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

Derivative1.png

Change in variable x

Change in function f(x)

Rate of change[edit | edit source]

Derivative1.png

Rate of change

Limit[edit | edit source]

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

Differentiation[edit | edit source]

Tangent as Secant Limit.svg

Let be a function. Then

wherever this limit exists.

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

Integration[edit | edit source]

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

Indefinite Integral

Riemann Integration 3.png

Where satisfies

Definite Integral

Riemann Integration 2.png

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 equations[edit | edit source]

Given

In summary[edit | edit source]

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

Solving Ordered Differential Equations[edit | edit source]

1st ordered differential equation[edit | edit source]

Equation of general form

After arrangement, equation above becomes

Where

Equation has a root


2nd ordered differential equation[edit | edit source]

The solution of the 2nd ordered polynomial equation above

One real root
Two real roots
One complex roots

With

Partial Differential Equations[edit | edit source]

Integral Transformation[edit | edit source]

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 Formulas[edit | edit source]

Reference[edit | edit source]