
教 材 內 容

1.5 
Exponential Functions 

What is 
1.6 
Inverse Functions 


2.2 
Limits 
2.3 
Limit Laws 
2.4 
The Precise Definition of a Limit 
2.5 
Couninuity 
2.6 
Asymptotes 
2.8,2.9 
Tangent Lines and Definition of the Derivative 


3.1,3.2 
Continuous Functions that Fail to Be Differentiable 

Rate of Change in Natural and Social Science? 
3.8,3.10 
Derivatives of Inverse Functions 


4.1 
Maximum and Minimum Values 
4.2 
The Mean Value Theorem 
4.3 
How Derivatives Affect the Shape of a Graph? 
4.4 
L'Hospital's Rule 
4.10 
Antiderivatives 


6.2 
Volumes by Cross Sections? 
6.3 
Volumes by Cylindrical Shells



10.1 
Graphic Design 

Bezier Curves 
10.3 
Polar Coordinates and Polar Curves 
10.4 
Area in Polar Coordinates 


11.1,11.2 
費氏數列及黃金分割 
11.5 
Alternating Series 
11.6 
Rearragement 
11.8 
Bessel Functions 
11.9 
Representations of Functions as Power series 
11.10 
Taylor Polynomial and Taylor Series 


12.2 
Vectors and the Geometry of Space 
12.5 
Lines and Planes in Space

12.7 
Cylindrical and Spherical Coordinates 


13.1 
空間曲線

13.4 
Motion in Space 


14.1 
Functions of Several Variables 
14.2 
Limits of Multivariable Functions

14.3 
Partial Derivatives 
14.4 
Tangent Planes and Linear Approximations 
14.5,14.6 
Directional Derivatives and the Gradient Vector 
14.8 
Lagrange Multipliers 

Maximum and Minimum Values



15.1,15.2 
Double Integrals and Iterated Integrals

15.3 
Double Integral Over General Regions 
15.4 
Double Integral in Polar Coordinates

15.7,15.8 
Triple Integrals in Spherical Coordinates 

The Intersection of Cylinders 

