1, Euler identity.
Euler's identity, also known as Euler's formula, is one of the most fascinating formulas in mathematics, which connects several most important constants in mathematics: two transcendental numbers: the base e and pi of natural logarithm, two units: imaginary number unit I and natural number unit 1, and the common 0 in mathematics.
2. Gaussian integration.
Gaussian integral is widely used in the unification of probability theory and continuous Fourier transform. It also appears in the definition of error function. Although the error function has no elementary function, Gaussian integral can be solved analytically by calculus. Gaussian integral, sometimes called probability integral, is the integral of Gaussian function.
3. Fourier transform.
Fourier transform means that functions that meet certain conditions can be expressed as trigonometric functions (sine and/or cosine functions) or linear combinations of their integrals. In different research fields, Fourier transform has many different variants, such as continuous Fourier transform and discrete Fourier transform. Firstly, Fourier analysis is proposed as a tool for thermal process analysis.
Extended data:
The great mathematician Euler:
Leonhard euler (1April 70715 ~1September 783 18) was a Swiss mathematician and natural scientist. 1707 was born in Basel, Switzerland on April 5, and 1783 died in St. Petersburg, Russia on September 8. Euler was born in a priest's family and was influenced by his father since childhood. /kloc entered university of basel at the age of 0/3, graduated from university at the age of 0/5, and obtained a master's degree at the age of 0/6.
Euler is one of the most outstanding figures in the field of mathematics in the18th century. He not only made contributions in the field of mathematics, but also pushed the whole mathematics into the field of physics. He is the most prolific mathematician in the history of mathematics, writing more than 800 pages of papers every year on average. He also wrote a large number of textbooks on mechanics, analysis, geometry and variational methods. Introduction to Differential Analysis, Principles of Differential Calculus and Principles of Integral Calculus have all become classic works in the field of mathematics.
Euler studied mathematics so extensively that important constants, formulas and theorems named after him can often be seen in many branches of mathematics.
References:
Baidu encyclopedia-Euler identity
Baidu Encyclopedia-Gaussian Integral
Baidu Encyclopedia-Fourier Transform