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內容綱要

講授

示範

習作

其他¹

Functions and Model

1.3 New Functions

 from Old Functions

1.4 Exponential  

   Functions

1.5 Inverse Functions

and Logarithms

Limits and derivatives

2.2 The Limit of a

Function

2.3 Calculating Limits  

   Using the Limit

   Laws

2.4 The Precise

   Definition of a

   Limit

2.5 Continuity

2.6 Limits at Infinity;

Horizontal 

Asymptotes

2.7 Derivatives and

   Rates of Change

2.8 The Derivative as

   a Function

Differentiation Rules

3.1 Derivatives of

Polynomials and

Exponential

Functions

3.2 The Product and

Quotient Rules

3.3 Derivatives of

Trigonometric

Functions

3.4 The Chain Rule

3.5 Implicit

Differentiation

3.6 Derivatives of

Logarithmic

Functions

3.9 Related Rates

3.10 Linear

Approximations

and Differentials

Applications of Differentiation

4.1 Maximum and

Minimum Values

4.2 The Mean Value

Theorem

4.3 How Derivatives

Affect the Shape

of a Graph

4.4 Indeterminate

   Forms and

   L’Hospital’s Rule

4.5 Summary of Curve

   Sketching

4.7 Optimization

   Problems

4.9 Antiderivatives

Integrals

5.1 Areas and

   Distances

5.2 The Definite

   Integral

5.3 The Fundamental

Theorem of

Calculus

5.4 Indefinite Integrals

   and the Net

   Change Theorem

5.5 The Substitution

   Rule

Applications of Integration

6.1 Areas between

   Curves

6.2 Volumes

6.3 Volumes by

Cylindrical Shells

6.5 Average Value of

   a Function

Techniques of Integration

7.1 Integration by

   Parts

7.2 Trigonometric

Integrals

7.3 Trigonometric

Substitution

7.4 Integration of

   Rational Functions

   By Partial

   Fractions

7.7 Approximate

Integration

7.8 Improper Integrals

Further Applications of Integration

Parametric Equations

8.1 Arc Length

8.2 Area of a Surface

   of Revolution

Parametric Equations and Polar Coordinates

10.1 Curves Defined

    by Parametric

    Equations

10.2 Calculus with

Parametric

Curves