《介值定理及其应用》-毕业论文.doc

PAGE l l 邯郸学院本科毕业论文 题 目 介值定理及其应用 学 生 指导教师 教授 年 级 2008级本科 专 业 数学与应用数学 二级学院 数学系 （系、部） 邯郸学院数学系 2012年6月 l 介值定理及其应用 摘　要 介值定理是闭区间上连续函数的重要性质之一，在《数学分析》教材中，一般应用有关实数完备性定理中的确界原理、单调有界定理、区间套定理、有限覆盖定理来证明．本课题通过构造辅助函数，应用区间套定理、致密性定理、柯西收敛准则、确界原理对介值定理进行证明．介值定理应用非常广泛，应用介值定理能很巧妙的解决一些问题．如利用介值定理可证明根的存在性、证明不等式、证明一些等式以及解决实际问题等．此外本文还对介值定理进行了推广，并且列举了一些具体的例题来展示推广的介值定理的应用． 关键词：介值定理 连续函数 根的存在定理 应用 Intermediate value theorem and its application Yao Mei Drected by Professor Wang Shuyun Abstract Intermediate value theorem is a continuous function on a closed interval in an important properties. In mathematical analysis textbook, general application about real number completeness theorem of supremum principle, the monotone bounded theorem, nested interval theorem, finite covering theorem to prove. This topic through the construction of auxiliary function, application of nested interval theorem, compact theorem, Cauchy convergence criterion, principle of supremum and infimum proves that intermediate value theorem. Intermediate value theorem is widely used and this theorem can be very cleverly to solve some problems. Such as the use of intermediate value theorem can be proof of the existence of the root, the proof of inequality, that some equation and solving practical problems. In addition to the intermediate value theorem is generalized and lists some specific examples to demonstrate the wide application of intermediate value theorem. KEY WORDS：Intermediate value theorem Continuous function The existence theorem of root Application 目 录 MACROBUTTON AcceptAllChangesInDoc TOC \o 1-3 \h \z \u HYPERLINK \l _Toc326343888 摘　要 PAGEREF _Toc326343888 \h I HYPERLINK \l _Toc326343889 外文页 PAGEREF _Toc326343889 \h II HYPERLINK \l _Toc326343890 前　言 PAGEREF _Toc326343890 \h 1 HYPERLINK \l _Toc326343891 1 介值定理及其证明方法 PAGEREF _Toc326343891 \h 2 HYPERLINK \l _Toc326343892 1.1 介值定理的内容 PAGEREF _Toc326343892 \h 2 HYPERLINK \l _Toc326343893 1.2 介值定理