analytic method

The Method of Applying Analytic Formula to Solve Mathematical Model

synonym analytical method (Symmetry of "comprehensive method") generally refers to analytical method

This entry is made by Compilation and application of scientific encyclopedia entries of "Science Popularization China" to examine.

Analytic method, also known as analytical method, is a method of solving mathematical models by using analytic expressions. Used in mathematics Analytic expression The method of representing a function or any mathematical object is called analytic method.

Chinese name: analytic method
Foreign name: analytic method

Discipline: mathematics
Definition: The method of using analytic expressions to express functions or arbitrary mathematical objects in mathematics

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Used in mathematics Analytic expression The method of representing a function or any mathematical object is called analytic method.^[1]

Coordinate method

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The steps to solve the problem by using the coordinate method are: first, establish the coordinate system on the plane Track of points Of Geometric conditions Translate into Analytic expression ； And then study it; Finally, the properties of the equation are described in geometric language, and the answer to the original geometric problem is obtained.

The idea of coordinate method urges people to use various analytical expressions to solve geometric problems numerically. Previously regarded as a problem in (European) geometry, once analytic geometry was applied, it became commonplace. Coordinate method Modern mathematics The mechanized proof also provides a powerful tool.^[2]

analytic geometry

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Analytic geometry includes Plane analytic geometry And solid analytic geometry. Plane analytic geometry passing through Rectangular coordinate system , establish a one-to-one correspondence between points and real number pairs, and Curves and Equations One to one correspondence between Analytic expression The geometric problems are studied numerically. Since the 17th century, due to the development of navigation, astronomy, mechanics, economy, military affairs, production, as well as elementary geometry and elementary algebra The rapid development of, promoted the establishment of analytic geometry, and is widely used in various branches of mathematics. Before analytic geometry was founded, geometry and algebra were two independent branches. The establishment of analytic geometry has truly realized the combination of geometric methods and algebraic methods for the first time, and unified form and number, which is a major breakthrough in the history of mathematical development. As the first decisive step in the development of variable mathematics, the establishment of analytic geometry is very important for Calculus The birth of has played an immeasurable role.

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