教    材    內    容
 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?

 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

   Lines and Planes in Space

 12.7  Cylindrical and Spherical Coordinates


 13.4  Motion in Space
 14.1  Functions of Several Variables

   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


 Double Integrals and Iterated Integrals

 15.3  Double Integral Over General Regions

   Double Integral in Polar Coordinates 

 15.7,15.8    Triple Integrals in Spherical Coordinates
     The Intersection of Cylinders