视频选集
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1.1 Four Ways to Represent a Function表示函数的四种方法
45:42
1.2 Mathematical Models A Catalog of Essential Functions数学模型与基本函数目录
01:00:05
1.3 New Functions from Old Functions从已知函数构造新的函数
31:02
1.4 Graphing Calculators and Computers有画图功能的计算器与计算机
13:02
1.5 Exponential Functions指数函数
38:59
1.6 Inverse Functions and Logarithms反函数与对数函数
01:24:10
2.1 The Tangent and Velocity Problems切线与速度问题
30:51
2.2 The Limit of a Function函数极限
50:38
2.3 Calculating Limits Using the Limit Laws用极限法则求极限
36:42
2.4 The Precise Definition of a Limit极限的精确定义
01:19:25
2.5 Continuity连续性
01:08:13
2.6 Limits at Infinity; Horizontal Asymptotes无穷远处的极限 水平渐近线
56:29
2.7 Derivatives and Rates of Change导数与变化率
01:09:04
2.8 The Derivative as a Function导函数
01:02:33
3.1 Derivatives of Polynomials and Exponential Functions多项式与指数函数的导数
45:42
3.2 The Product and Quotient Rules积与商的求导法
22:19
3.3 Derivatives of Trigonometric Functions三角函数的导数
27:13
3.4 The Chain Rule链式法则
41:16
3.4chain rule严格证明
12:47
3.5 Implicit Differentiation隐式微分法
02:50
3.6 Derivatives of Logarithmic Functions对数函数的导数
23:10
3.7 Rates of Change in the Natural and Social Sciences自然与社会科学中的变化率问题
28:00
3.8 Exponential Growth and Decay指数增长与衰减
21:43
3.9 Related Rates相关变化率
22:54
3.10 Linear Approximations and Differentials线性逼近与微分
22:35
3.11 Hyperbolic Functions双曲函数
15:25
4.1 Maximum and Minimum Values最大最小值
39:32
4.2 The Mean Value Theorem中值定理
24:44
4.3 How Derivatives Affect the Shape of a Graph导数对函数图形形状的影响
52:12
4.4 Indeterminate Forms and l’Hospital’s Rule不定式与洛必达法则
25:02
4.5 4.6 SUMMARY OF CURVE SKETCHING函数图形的描绘及如何用Mathematica软件作图
23:43
4.7 Optimization Problems优化问题
56:15
4.8 newton's method牛顿迭代法及其Mathematica实现
33:43
4.9 antiderivative原函数
38:43
5.1 Areas and Distances面积与距离
53:58
5.2the definite integral定积分
01:02:16
5.3补充内容 用定积分定义和微分中值定理证明牛顿莱布尼茨公式
06:06
5.3 The Fundamental Theorem of Calculus微积分基本定理
52:35
5.4 Indefinite Integrals and the Net Change Theorem不定积分与净改变量定理
36:53
5.4凑微分法
19:54
5.5 The Substitution Rule积分的变量代换
43:05
6.1 Areas Between Curves曲线所围面积
34:19
6.2volumes体积
42:11
6.3 Volumes by Cylindrical Shells柱壳法求体积
21:25
6.4 work功
20:45
6.5 Average Value of a Function函数的平均值
15:09
7.1 integration by parts分部积分法
33:30
7.2 Trigonometirc Integrals三角函数积分
17:19
7.3 Trigonometric Substitution三角代换
26:56
7.4 Integration of Rational Functions by Partial Fractions有理函数的部分分式积分法
37:25
7.5 Strategy for Integration积分策略
17:13
7.6 Integration Using Tables and Computer Algebra Systems用积分表和计算机代数系统（即数学软件）求积分
08:36
7.7定积分近似计算矩形法与梯形法
17:38
7.8 Improper Integral反常积分
53:42
8.1 Arc Length弧长
32:01
8.2 Area of a Surface of Revolution旋转体表面积
31:00
8.3 Applications to Physics and Engineering积分在物理（水压力）和工程的应用
20:51
10.3ploar coordi极坐标
33:25
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