凸函數(shù)、琴生不等式及其在中學(xué)數(shù)學(xué)中的應(yīng)用
[Abstract]:Convex function is not only a kind of very important function, but also a typical function that gathers many excellent properties. For the research of function convexity, it has very important applications in many fields and branches of mathematics. In particular, convex functions play a very important role in the derivation of inequalities, the problem of finding the maximum value and the range of values, and the trigonometric function problem. In addition, convex functions also involve many mathematical concepts, properties, theories, propositions and applications, and convex functions also have extremely important theoretical and applied value in college entrance examination and mathematics competitions. In this paper, the definition of convex function, geometric meaning, equivalent definition, property, judgment and proof, deformation and generalization of Qin Sheng inequality are introduced briefly. Finally, the application of convex function and Qinsheng inequality in middle school mathematics is systematically, comprehensively and clearly divided. For example, a unified method for solving similar problem types is given, which simplifies the proof process and opens up the students' thinking of solving problems. For some problem types, it also gives corresponding generalizations, such as "solving the inner connection of the circle," The problem of the minimum value of the area of a tangent polygon is extended to "solving the problem of the interior connection of an ellipse and the area of an outer polygon". Through systematic, comprehensive and definite arrangement, it is helpful for students to have a deeper understanding of the related question types involved in this part of knowledge, and to learn to use the properties of convex functions and Qin Sheng's inequality to solve the related problems more conveniently and simply. At the same time for students to provide some new ideas and skills to solve problems.
【學(xué)位授予單位】:西北大學(xué)
【學(xué)位級別】:碩士
【學(xué)位授予年份】:2016
【分類號】:G633.6
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