Associated Topics || Dr. Math Home || Search Dr. Math

### What is Nonlinear Math?

```
Date: 10/02/97 at 17:25:41
From: Andy Jones
Subject: Nonlinear math

I have been wondering for a while what exactly nonlinear math is and
what it is used for.  I have heard of things such as the fractal curve
and I know it is mostly theories. I was just wondering if you could
explain some of the facts about it to me.  If you can help, I'll
appreciate it. Thank you.
```

```
Date: 10/02/97 at 18:58:51
From: Doctor Anthony
Subject: Re: Nonlinear math

The word 'LINEAR' appears in many guises in mathematics.  A linear
equation like ax + by + c = 0 represents a straight line, but you also
get linear differential equations like

a(d^2y/(dx)^2 + b(dy/dx) + cy = f(x)

and linear combinations of vectors. A non-linear differential equation
would have the constants a, b, c replaced by functions of x or y.

We also talk of linear algebra, which deals with the mathematics of
linear equations, matrices, determinants, and vector spaces. I suppose
the single defining property of linearity is that if you superimpose
two solutions you get another solution.

Non-linear equations can be extremely difficult, and are often
insoluble. For example the long-term behaviour of three bodies moving
under gravity cannot be solved mathematically, though we can work a
long way into the future. Unfortunately, non-linear, partial
differential equations are exactly the equations that describe most
real-life situations, like weather systems, frictional or turbulent
motion, and so on. Before computers came along these equations were
handled by making sweeping simplifications - the trick was to know
which simplifications were justified. Although we still can't SOLVE
the equations we can run computer models which give a very good idea
of what will actually happen.

The fact that we now tackle such problems is one reason why chaos
theory and complexity have become such popular fields of study.  In
the past the non-linear world was largely ignored - it was just too
difficult.

-Doctor Anthony,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Calculus
High School Linear Algebra
High School Linear Equations

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search