ABSTRACT
Jean Baptiste Joseph Fourier methods or Fourier analysis constitute a branch of mathematics developed formally some 150 years after Newton's and Leibniz' calculus and heavily depend on integral and differential calculus. Fourier was born in 1768 in Auxerre, a town between Paris and Dijon. After the French Revolution, Fourier taught in Paris, then accompanied Napoleon to Egypt and served as permanent secretary of the Institute of Egypt. He wrote a book on Egypt and in certain quarters he is famous more as an Egyptologist than for his contributions to mathematics and physics. Fourier showed how these, periodic functions, non-periodic functions, mathematical tools can be used to study natural phenomena such as heat diffusion, making it possible to solve equations that had until then remained intractable. Under the action of the Fourier transform, derivatives are transformed into multiplications, thus turning differential equations into equations containing algebraic expressions.
