Numerical integration facts for kids
Numerical integration is a way to find an approximate answer for an integral. Think of an integral as finding the total amount or the area under a curve on a graph. Sometimes, it's really hard or even impossible to find the exact answer using regular math. This happens when you have data from measurements, or when the math problem is too complicated.
When we can't find the exact answer, numerical integration helps us get a very close estimate. It's also sometimes called quadrature.
One common way to do this is by using interpolation. This means we use simpler math functions, often polynomials, to connect the known points and then estimate the area.
Many smart people have worked on these methods for years. Some famous formulas include the Gaussian quadrature, named after Carl Friedrich Gauss, and the Newton-Cotes formula, named after Isaac Newton. There's also the Euler-Maclaurin formula, named after Leonhard Euler.
Contents
Understanding Numerical Errors
When we use numerical methods, like numerical integration, we are finding an estimate, not the exact answer. This means there can be small differences, called numerical errors. These errors are a normal part of working with approximations in math.
Famous Mathematicians in Numerical Integration
Many mathematicians have helped us understand and improve numerical integration. Here are a few:
Software for Numerical Integration
You can use special computer programs to perform numerical integration. These tools make it much easier to calculate approximations for complex problems.
- MATLAB and INTLAB are powerful programs often used in science and engineering.
- GNU Octave and Scilab are free, open source versions that work similarly to MATLAB.
- Wolfram Mathematica is another advanced software used for many kinds of mathematical calculations.
See also
In Spanish: Integración numérica para niños
