多元函数的极值及其应用
摘 要
关键词：
Extreme Value Of Multivariate Function And Its Application
ABSTRACT
Function extreme value has always been an important content of mathematical research, there are many in the science and production practice related to extreme value problem.In mathematical analysis, discussed the the extremum of the extreme value of binary function, necessary and sufficient conditions, conditional extremum and Lagrange multiplier method of conditional extreme value. The extremum of function of many variables and its application are discussed in this paper.In the first chapter, we will discuss formally promotion to the extreme value of binary function on the extreme value of multivariate function is given, the necessary and sufficient conditions for the the extremum of function of many variables.In the second chapter, through specific examples, we summarize the conditional extreme value of multivariate function is discussed, the application of minimal polyomial to have substitution elimination method, the Lagrange multiplier method, gradient method, inequality, quadratic equation discriminant, in combination with number form, such as the five methods, we can see different conditional extreme value problem can have different religion, there are some different in this extremum problems can also be the same, so we need to choose the appropriate method, to master the correct way.In the third chapter, we summarized the extremum of function of many variables, conditional extreme value in the practical application of life, in mathematics, we can be used to prove some inequalities, discuss the circle edge trimming of the large area, etc., in economics, can be used to discuss the problem of optimization, in physics, can be used to discuss the shortest path of the refraction of light, etc., as a result, we can realize how will discuss the problems in the real life into the extremum problems of mathematical model, and we summarize the methods to solve.
Keywords: Multivaria
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