第一章函数与极限......................................................................................................1
§1函数.................................................................................................................1
§2极限.................................................................................................................6
§3函数的极限.....................................................................................................8
§4无穷大与无穷小.............................................................................................9
§5极限的运算法则...........................................................................................11
§6极限存在准则两个重要极限.......................................................................12
§7无穷小的比较...............................................................................................13
§8函数的连续性与间断点...............................................................................14
§9连续函数的运算与初等函数的连续性.......................................................15
§10闭区间上连续函数的性质.........................................................................16
第二章导数与微分....................................................................................................17
§1导数概念.........................................................................................................17
§2函数的求导法则.............................................................................................20
§3高阶导数.........................................................................................................23
§4隐函数及由参数方程所确定的函数的导数.................................................24
§5函数的微分.....................................................................................................26
第三章微分中值定理及导数的应用........................................................................28
§1微分中值定理..............................................................................................28
§2洛必达法则.....................................................................................................30
§3泰勒公式.........................................................................................................32
§4函数的单调性与曲线的凹凸性.....................................................................34
§5函数的极值与最大最小值.............................................................................36
§6函数图形的描绘.............................................................................................39
第四章一元函数不定积分........................................................................................41
§1不定积分的概念与性质..............................................................................41
§2换元积分法..................................................................................................44
§3分部积分法..................................................................................................46
§4有理函数的积分..........................................................................................47
第五章定积分............................................................................................................50
§1定积分的概念与性质..................................................................................50
§2微积分基本公式..........................................................................................52
§3定积分的换元法和分部积分法..................................................................54
§4反常积分......................................................................................................55
第六章定积分的应用................................................................................................58
§1定积分的元素法..........................................................................................58
§2定积分在几何学上的应用..........................................................................59
第七章微分方程........................................................................................................62
§1微分方程的基本概念..................................................................................62
§2可分离变量的微分方程..............................................................................63
§3齐次方程......................................................................................................63
§4一阶线性微分方程......................................................................................64
§5可降阶的高阶微分方程..............................................................................65
§6高阶线性微分方程......................................................................................66
§7常系数齐次线性微分方程............................................................................68
§8常系数非齐次线性微分方程........................................................................70
第八章向量代数和空间解析几何............................................................................71
§1向量及其线性运算.........................................................................................71
§2数量积向量积混合积.................................................................................77
§3曲面及其方程..............................................................................................80
§4空间曲线及其方程......................................................................................84
§5平面及其方程..............................................................................................85
§6空间直线及其方程.........................................................................................87
第九章多元函数微分学............................................................................................90
§1多元函数的基本概念.....................................................................................90
§2偏导数.............................................................................................................92
§3全微分.............................................................................................................94
§4多元复合函数的求导法则.............................................................................96
§5隐函数的求导公式.........................................................................................98
§6多元函数微分学的几何应用.........................................................................99
§7方向导数与梯度...........................................................................................101
§8多元函数极值及其求法...............................................................................103
第十章多元函数积分..............................................................................................106
§1二重积分的概念与性质............................................................................106
§2二重积分的计算........................................................................................108
§3三重积分....................................................................................................111
§4重积分的应用............................................................................................115
第十一章曲线积分与曲面积分..............................................................................118
§1对弧长的曲线积分.......................................................................................118
§2对坐标的曲线积分.......................................................................................119
§3格林公式及其应用.......................................................................................122
§4对面积的曲面积分.......................................................................................124
§5对坐标的曲面积分.......................................................................................125
§6高斯公式......................................................................................................128
§7斯托克斯公式..............................................................................................130
第十二章无穷级数..................................................................................................133
§1常数项级数的概念及性质.........................................................................133
§2常数项级数的审敛法.................................................................................134
§3幂级数.........................................................................................................136
§4函数展开成幂级数.....................................................................................138
§5傅里叶级数.................................................................................................139
百度网盘
http://pan.baidu.com/s/1geQpDzd