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課程大綱
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課程日期
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單元主題
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內容綱要
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Functions and Model
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1.3 New Functions from Old Functions
1.4 Exponential Functions
1.5 Inverse Functions and Logarithms
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Limits and derivatives
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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
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Differentiation Rules
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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
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Applications of Differentiation
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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 Indeterminate Forms and L’Hospital’s Rule
4.5 Summary of Curve Sketching
4.7 Optimization Problems
4.9 Antiderivatives
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Integrals
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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
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Applications of Integration
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6.1 Areas between Curves
6.2 Volumes
6.3 Volumes by Cylindrical Shells
6.5 Average Value of a Function
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Techniques of Integration
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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
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Further Applications of Integration
Parametric Equations
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8.1 Arc Length
8.2 Area of a Surface of Revolution
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Parametric Equations and Polar Coordinates
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10.1 Curves Defined by Parametric Equations
10.2 Calculus with Parametric Curves
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