1, piano's definition of Taylor formula.
Taylor formula of piano remainder, also known as Taylor formula or Taylor series, is an expansion in mathematics, which is used to approximately represent the value of a function at any point in its definition domain. It constructs the expansion based on the derivative of the function at a certain point, and adds a piano remainder to consider the higher-order error.
2. The application of piano Taylor formula.
Piano's Taylor formula is widely used in mathematics, physics and engineering. For example, in calculus, it can be used to solve the approximate value of a function, approximately calculate the zero point of a function and discuss the extreme value of a function. In physics, it can be used to approximately describe the laws of physical phenomena, such as elastic modulus in elasticity and viscous resistance in fluid mechanics.
3. The relationship between piano remainder and other mathematical concepts.
Taylor formula of piano remainder is closely related to some important mathematical concepts and theorems. For example, it is related to Lagrange mean value theorem (English: Lagrange mean value theorem or Lagrange mean value theorem, also known as Lagrange theorem and finite increment theorem).
Development history
1, put forward
Taylor formula of piano remainder, also known as Taylor series or Taylor series expansion, is a mathematical formula used to approximate the value of a function at any point in its definition domain. This formula was first proposed by British mathematician Taylor in the18th century, and has been widely used in various mathematical and scientific problems.
2. Development
After piano's Taylor formula was put forward, mathematicians began to study and improve it. Among them, the French mathematician piano put forward a new form of remainder at the end of 19, which is called piano remainder.
3. Application
With the development of mathematics and science, the application scope of piano's Taylor formula has gradually expanded to other fields. For example, in physics, piano remainder can be used to describe the approximate laws of physical phenomena, such as elastic modulus in elasticity and viscous resistance in fluid mechanics.