[Edit this paragraph]
Jean Baptiste Joseph (1768- 1830) is a French mathematician and physicist.
Resume1768 Born in Oszer on March 2 1 and died in Paris on May 1830. At the age of 9, his parents died and he was adopted by the local church. /kloc-when he was 0/2 years old, he was sent to the local military school by a bishop. 17 (1785) returned to his hometown to teach mathematics, 1794 went to Bali, became the first batch of students in higher normal schools, and taught at Paris Polytechnic the following year. 1798 went on an expedition to Egypt with Napoleon, and later served as the secretary of the Institute of Military Literature and Egypt. 180 1 returned to China and served as the local governor of Izel province. 18 17 was elected as an academician of the academy of sciences, 1822 served as the lifelong secretary of the academy of sciences, and later served as the lifelong secretary of the French Academy and the chairman of the Council of the University of Science and Technology.
Main contribution
■ Mathematical aspects
The main contribution is to establish a set of mathematical theories when studying the spread of heat. 1807 submitted the paper "Heat Propagation" to the Paris Academy of Sciences, and deduced the famous heat conduction equation. When solving this equation, it is found that the solution function can be expressed in the form of series composed of trigonometric functions, thus it is proposed that any function can be expanded into infinite trigonometric function series. Fourier series (that is, trigonometric series), Fourier analysis and other theories were founded.
Other contributions include: the earliest use of definite integral symbols, the improvement of the proof of symbolic rules of algebraic equations and the discrimination of real roots.
The basic idea of Fourier transform was first put forward by Fourier, so it was named after it to commemorate it.
From the point of view of modern mathematics, Fourier transform is a special integral transform. It can represent a function satisfying certain conditions as a linear combination or integral of sine basis functions. In different research fields, Fourier transform has many different variants, such as continuous Fourier transform and discrete Fourier transform.
Fourier transform belongs to harmonic analysis. The word "analysis" can be interpreted as in-depth research. Literally, the word "analysis" is actually "piecemeal analysis". It realizes in-depth understanding and research of complex functions through "piecemeal analysis" of functions. Philosophically, "Analyticism" and "Reductionism" aim to improve the understanding of the essence of things through proper analysis. Modern atomism, for example, tries to analyze the origin of all substances in the world as atoms, but there are only a few hundred atoms. Compared with the infinite richness of the material world, this analysis and classification undoubtedly provide a good means to understand the various attributes of things.
In the field of mathematics, the same is true. Although Fourier analysis was originally used as an analytical tool of thermal process, its thinking method still has the characteristics of typical reductionism and analytical theory. Any function can be expressed as a linear combination of sine functions through a certain decomposition, and sine functions are relatively simple functions that have been fully studied in physics. How similar this idea is to that of atomism in chemistry! Strangely, modern mathematics has found that Fourier transform has very good properties, which makes it so easy to use and useful that people have to sigh the magic of creation:
1. Fourier transform is a linear operator, and it is also a unitary operator if a proper norm is given;
2. The inverse transform of Fourier transform is easy to find, and the form is very similar to the forward transform;
3. Sine basis function is the inherent function of differential operation, so that the solution of linear differential equation is transformed into the solution of algebraic equation with constant coefficient. In a linear time-invariant physical system, frequency is an invariable property, so the response of the system to complex excitation can be obtained by combining its responses to sinusoidal signals with different frequencies.
4. The famous convolution theorem points out that Fourier transform can transform complex convolution operation into simple product operation, thus providing a simple means to calculate convolution;
5. Discrete Fourier transform can be quickly calculated by digital computer (its algorithm is called FFT).
Because of the above good properties, Fourier transform is widely used in physics, number theory, combinatorial mathematics, signal processing, probability, statistics, cryptography, acoustics, optics and other fields.
■ Physical aspects
He is the founder of Fourier law. In 1822, his masterpiece "Analysis Theory of Heat" solved the problem of heat distribution and propagation in non-uniform heated solids, which became one of the earliest examples of the application of analysis in physics and had a far-reaching impact on the development of theoretical physics in19th century.
Introduction to Fourier Law
English name: Fourier law
Fourier law is a basic law in heat transfer. It can be used to calculate heat conduction.
The related formulas are: φ =-λ a (dt/dx) and q =-λ (dt/dx).
Where φ is the thermal conductivity in W, λ is the thermal conductivity, A is the heat transfer area in M 2, T is the temperature, K is the unit, X is the coordinate on the heat transfer surface, M is the heat flux, and Q is W/M 2. The negative sign indicates that the heat transfer direction is opposite to the temperature gradient direction, and λ is a physical parameter indicating the thermal conductivity of the material (the greater λ is, the better the thermal conductivity is).