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(◆為選教內容)
Ch1. Functions and Models
◆ 1.3 New Functions from Old Functions
1.4 Exponential Functions
1.5 Inverse Functions and Logarithms
Ch2. 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
Ch3. 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 and Inverse Trigonometric Functions
◆ 3.7 Rates of Change in the Natural and Social Sciences
◆ 3.8 Exponential Growth and Decay
◆ 3.9 Related Rates
3.10 Linear Approximations and Differentials
◆ 3.11 Hyperbolic Functions
Ch4. Applications of Differentiation
4.1 Maximum and Minimum Values
4.2 The Mean Value Theorem
4.3 What Derivatives Tell Us about the Shape of a Graph
4.4 Indeterminate Forms and L’Hospital’s Rule
4.5 Summary of Curve Sketching
4.7 Optimization Problems
◆ 4.8 Newtons Method
4.9 Antiderivatives
Ch5. 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
Ch6. Applications of Integration
6.1 Areas Between Curves
6.2 Volumes
6.3 Volumes by Cylindrical Shells
6.5 Average Value of a Function
Ch7. 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
◆ 7.5 Strategy for Integration
◆ 7.7 Approximate Integration
7.8 Improper Integrals
Ch8. Further Applications of Integration
8.1 Arc Length
8.2 Area of a Surface of Revolution
◆ 8.3 Applications to Physics and Engineering
◆ 8.4 Applications to Economics and Biology
◆ 8.5 Probability
Ch10. Parametric Equations and Polar Coordinates
10.1 Curves Defined by Parametric Equations
10.2 Calculus with Parametric Curves
10.3 Polar Coordinates
10.4 Calculus in Polar Coordinates
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