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教 材 內 容
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| 1.5 |
Exponential Functions |
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What is  |
| 1.6 |
Inverse Functions |
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| 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 |
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| 3.1,3.2 |
Continuous Functions that Fail to Be Differentiable |
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Rate of Change in Natural and Social Science? |
| 3.8,3.10 |
Derivatives of Inverse Functions |
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| 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 |
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| 6.2 |
Volumes by Cross Sections? |
| 6.3 |
Volumes by Cylindrical Shells
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| 10.1 |
Graphic Design |
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Bezier Curves |
| 10.3 |
Polar Coordinates and Polar Curves |
| 10.4 |
Area in Polar Coordinates |
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| 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 |
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| 12.2 |
Vectors and the Geometry of Space |
| 12.5 |
Lines and Planes in Space
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| 12.7 |
Cylindrical and Spherical Coordinates |
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| 13.1 |
空間曲線
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| 13.4 |
Motion in Space |
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| 14.1 |
Functions of Several Variables |
| 14.2 |
Limits of Multivariable Functions
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| 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 |
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Maximum and Minimum Values
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| 15.1,15.2 |
Double Integrals and Iterated Integrals
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| 15.3 |
Double Integral Over General Regions |
| 15.4 |
Double Integral in Polar Coordinates
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| 15.7,15.8 |
Triple Integrals in Spherical Coordinates |
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The Intersection of Cylinders |
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