Théorie analytique de la chaleur
Jean Baptiste Josef Fourier(1768-1830)
 Fourier, Napoleon’s colleague and his governor in Egypt in 1801, was a mathematician who studied heat conduction in solids. Fourier found heat conduction in solids to be a most complicated phenomenon which determined various factors such as differences in temperature between two positions, thermal conductivity and the form of solids.
 For the solution of this problem, Fourier invented a new, useful application of a mathematical analysis. It was a method that enabled complexities to reduce the multiple of a simple problem and by which any complicated periodic motion or function was able to resolve into the lap of simple regular motions or functions. That is, he demonstrated that any function could be expanded in a series which is the linear combination of sine and cosine functions. He expressed heat conduction as a partial differential equation and solved it with this method. Consequently, Fourier established the law of heat conduction in which the amount of transferred heat is proportional to the difference in temperature and depends upon the specific thermal conductivity of the matter. The above mentioned series, the method and the law were named after him and called the Fourier series, the Fourier transform or analysis and Fourier’s law.
 This book contains the most thorough research on heat conduction up to the early nineteenth century. It was also profoundly influential to later scientists because of its methods. Fourier’s mathematical methods were not only applied to all problems of vibration pertaining to heat, sounds, lights, and fluid motion, etc., but also initiated a new, important field of analytics.