# Differentiation Data and Integration Data

"Acceleration, speed and distance". These are differentiated or integrated each other by "time".

"Length, area and volume". These are differentiated or integrated each other by "length".

These stories are known many people who studied mathematics.
But people who need such knowledge in daily works are not many.

By the way, such knowledge could be powerful and needed in the data analysis.

##
Differentiation and Integration in Data Analysis

The main part of differentiation and integration in the study of mathematics is the change of formulation.
But in the data analysis, the main part is the handling of real data.

Examples in this page are the simple ways of differentiation and integration in data analysis.
But in the fields of
Differential Equation Model
and
Numerical Integration
, more difficult calculations are developed.

###
Sinple Examples of Differentiation

If there is the data of distance by 1 hour.
Difference from privious time is the speed.

###
Sinple Examples of Integration

If there is the data of speed by 1 hour and it is 5 (km/hour) from 7 to 9 o'clock, the distance is 10 (km).
Because

5 * ( 9 - 7 ) = 5 * 2 = 10

##
Power of Differentiation and Integration

The selection in differentiation and integration by "what" have success,
"useless data" changes "precious data".

For example, even if there is not the data of the volume of water in the dam,
we can estimate the data by flow rate data by integration.

##
Way to Use Differentiation and Integration

The goal image of
Analysis of Type 2
or
Analysis of Type 3
, is the hint to find the way to use differentiation and integration in the data analysis.

In
Sensor Data Analysis
, "time" is the key parameter.

Gap between Models of Statistics and Real

Linking different source data

Mathematical Modeling

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