In May I was in Edinburgh to compete in the Edinburgh marathon. On the day after the marathon I did a sight-seeing tour of Edinburgh. One of the things I saw was a statue to the Scottish mathematical physicist James Clerk Maxwell. The statue is at the Saint Andrew Square end of George Street, abut 300 metres from the famous Princes Street.

James Clerk Maxwell was an important physicist and mathematician. His most prominent achievement was to formulate the equations of classical electromagnetic theory. These four equations are known as Maxwell’s equations. They are shown on a small plaque at the rear of the statue’s plinth.

These equations are written in *differential form*, where the symbol is known as the *vector differential operator*. I will explain the mathematics of vector differential operator, and the meaning of each equation, in a series of future blogs.

The four equations can also be written in *integral form*, which many people find easier to understand. In integral form, the equations become

- Equation (1) (and its integral form, equation (5) ) is usually referred to as
*Gauss’s law*. - Equation (2) (and its integral form, equation (6) ) is usually referred to as
*Gauss’s law for magnetism*. - Equation (3) (and its integral form, equation (7) ) is usually referred to as
*Faraday’s law of induction*. - Equation (4) (and its integral form, equation (8) ) is usually referred to as
*Ampère’s circuital law*.