高等数学对中学数学教学的指导作用 毕业论文.doc

高等数学对中学数学教学的指导作用 摘要：随着新课程改革的不断进步，中学数学中所涉及的高等数学的知识在高考中所占的比重越来越大，所以，作为一名中学教师，必须认真学习高等数学，用更高的数学知识武装自己，才能更加深刻地理解中学数学教材．这也是提高中学数学教学质量、实施素质教育的条件之一．指导学生学习高等数学与中学数学之间的内在联系，并将高等数学的思想方法渗透到中学数学中去是有重要的现实意义的．本文主论述的高等数学中的方法有微积分法、极限思想方法、概率与统计方法，并以大量详实的中学数学的范例为依据，尤其是近几年来的高考试题，充分说明了高等数学在解决中学数学的相关问题上具有的指导作用． 关键词：高等数学；中学数学；数学思想；数学方法 A Guide of Advanced Mathematics to High School Mathematics Teaching Abstract: With the reform of new course, the knowledge of advanced mathematics in high school mathematics covers larger and larger percentage in College Entrance Examination, so, being a mathematics teacher in high school, we must learn advanced mathematics hard in order to equip ourselves with more advanced knowledge in mathematics and understand high school mathematical books. This is also one of the conditions to improve the teaching quality of high school mathematics and imply the Quality Education. It is of great significance to guide the students to learn the internal relation between advanced mathematics and high school mathematics, and to permeate the high school mathematics with the thought of advanced mathematics. This paper mainly discusses the following methods in advanced mathematics: calculus method, extreme limit though method, probabilistic method, mathematics modeling method, with lots of detailed examples in high school mathematics teaching, which are mainly examples from College Entrance Examination in recent years, those examples prove that advanced mathematics are a good guide in solving related problems of high school mathematics. Key words: advanced mathematics; high school; mathematical thought; mathematical method 目 录 1、引言 1 2、中学数学与高等数学的关系 1 2．1 中学数学与高等数学的概念界定 1 2．1．1 中学数学 1 2．1．2 高等数学 1 2．2 中学数学与高等数学的关系 1 2．3 数学思想在中学数学教育中的地位与作用 2 3、高等数学方法在中学数学中的应用 2 3．1 微积分方法的应用 2 3．1．1 求函数的极值、最值 2 3．1．2 求函数的单调区间 3 3．1．3 求曲边图形的面积 4 3．1．4 利用微积分证明代数式 5 3．2 极限思想方法的应用 5 3．2．1 利用极限解决数列问题 5 3．2．2 双曲线的渐近线 6 3．2．3 利用重要极限证明不等式 7 3．3 概率论的应用 7 3．3．1 概率的应用 7 3．3．2 统计的应用 8