Introducing Differential Equations

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A topic that some students of maths can find difficult at first simply because of the number of terms involved and the fact that some of these terms will involve derivatives of one of the variables. The dependent variable is usually designated as ‘y’ and will be derived from another
independent variable – ‘x’

Here’s a quick introduction to differential equations –

As you can see the solutions of a differential equation look different from algebraic equations because they don’t just include numbers but will normally have functions in them too. If you’re having difficulty with the concept remember that the differential equation represents the relationship between a quantity which varies and it’s rate of change. This concept is essential in many forms of scientific investigation.

You will come across differential equations in most areas of science, especially in physics, chemistry and engineering. However they are not limited to these areas, ask any economist and they will have used these equations in all sorts of economic projections and research.

Other definitions you might come across are those of ‘ordinary differential equation’ which refers to the function of a single variable only and some of it’s linked derivatives.

With all these equations, the order is important and is stated with regards the highest derivative, the simplest form is the first order differential equation.

You can even express that laws of nature in the form of differential equations, if you learn the techniques and processes they are invaluable in so many areas of science. Fortunately the internet has lots of courses and explanations. Some of the best are on various academic sites and there’s useful introductions on places like the BBC website too. If you are having problems accessing then see some of the useful links below for bypassing filters and region locks which can affect some people depending on the location of their IP address.

Further Reading:

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