向量的数量积在中学数学中的应用-毕业论文.docx

PAGE I PAGE ii 文档均为word文档，下载后可直接编辑使用亦可打印 摘要 向量融数、形于一体，具有几何与代数的双重特性，是解决数学问题的重要工具。向量数量积在中学数学中不仅作为工具贯穿始终，它还在中学数学各分支领域中具有广泛的应用。对向量的数量积的学习，有利于培养学生快速解题的能力，使其更好地掌握数学运算；有利于改进学生解决问题的方法，拓宽解题角度，降低题目的难度；有利于提高学生逻辑思维能力。本文首先简述了数量积的发展背景并给出了数量积的定义及一些重要性质。然后对相关教材及论文进行深入挖掘分析，用典型例题展现了数量积在等式和不等式、三角函数、函数最值以及几何等方面的应用。等式与不等式中构建向量坐标替代代数式；三角函数中数量积替换三角函数转化；在函数最值求解中应用数量积的不等式性质；在几何问题中借助解析式研究图形常利用数量积。最后，对于如何帮助学生加深对向量数量积的理解和学习，引导学生在学习数量积的过程中，主动归纳总结使用数量积解题的通性通法，以及如何帮助学生在解决数学问题时能够高速准确的判断合适的解题方法，提高学生运用向量的数量积解决数学问题的能力，给出了一些教学建议。 关键词 向量 数量积 解题应用 中学数学 The Application of Vector’s Scalar Product in Middle School Mathematics Abstract Vectors blend numbers and shapes into one, with the dual characteristics of geometry and algebra, and are an important tool for solving mathematical problems. Vector’s scalar product is not only used as a tool throughout middle school mathematics, it also has a wide range of applications in various branches of middle school mathematics. The study of the scalar product of vectors is conducive to cultivating students ability to solve problems quickly; it is conducive to improving students problem-solving methods and reducing the difficulty of the problems. This article first briefly describes the development background of scalar product and gives the definition and some important properties of scalar product, and then conducts in-depth mining and analysis of related textbooks and papers, using typical examples to show the scalar product in equations and inequalities, trigonometric functions Application of function maximum value and geometry. Finally, for how to help students deepen their understanding and learning of scalar products, guide students to actively summarize and summarize the general methods of using scalar products to solve problems in the process of learning scalar products, and how to help students to solve mathematical problems High-speed and accurate judgment of appropriate problem-solving methods, improve students ability to use scalar product to solve