微積分甲(一)

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高中數學

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第二周起每星期三隨堂100分鐘測驗(7月8日，15，22和29日)，共四次佔課程成績70%， 除了病假(醫院証明)，喪假或公假以外，缺考不能補考。 8月5日會考成績佔課程成績的30% 隨堂100分鐘測驗日期如果遇到颱風則會順延至星期四 註：暑修第一天上課日為7/1 (星期三)

• Functions and Models

  ◆1.3 New Functions from Old Functions 1.4 Exponential Functions 1.5 Inverse Functions and Logarithms

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  3

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• 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

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• 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 ◆3.7 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

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  8

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• 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 ◆4.8 Newtons Method 4.9 Antiderivatives

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  7

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• 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

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• Applications of Integration

  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

  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

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  7

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• 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

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  3

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• Parametric Equations and Polar Coordinates

  10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Curves

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  4

Calculus (Early Transcendentals), James Stewart, 9th Edition

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