高等数学讲义 目 录 第一章 函数、极限、连续 ······························································· 1 第二章 一元函数微分学 ··································································· 24 第三章 一元函数积分学 ··································································· 49 第四章 常微分方程 ·········································································· 70 第五章 向量代数与空间解析几何 ··················································· 82 第六章 多元函数微分学 ··································································· 92 第七章 多元函数积分学 ··································································· 107 第八章 无穷级数（数一和数三） ··················································· 129 1 第一章 函数、极限、连续 §1.1 函数 (甲) 内容要点 一、函数的概念 1．函数的定义 2．分段函数 3．反函数 4．隐函数 二、基本初等函数的概念、性质和图象 三、复合函数与初等函数 四、考研数学中常出现的非初等函数 1．用极限表示的函数 (1) )(limxfynn (2) ),(limxtfyxt 2．用变上、下限积分表示的函数 (1) xadttfy)( 其中)(tf连续，则)(xfdxdy (2) )()(21)(xxdttfy 其中)(),(21xx可导，)(tf连续， 则2211[( )]( )[( )]( )dyfxxfxxdx 五、函数的几种性质 1． 有界性：设函数)(xfy 在 X 内有定义，若存在正数 M，使Xx 都有Mxf)(，则称)(xf在 X 上是有界的。 2． 奇偶性：设区间 X 关于原点对称，若对Xx ，都有)()(xfxf，则称)(xf在 X 上是奇...
