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 微積分(一) Calculus I - 103學年度

 課程進度、內容、主題 學習時數 第一章 Functions and Model 1.5 Exponential Functions 1.6 Inverse Functions and Logarithms 3小時 第二章 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 7小時 第三章 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 6小時 第四章 The Properties of Gases 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 8小時 第五章 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 6小時 第六章 Acations of Integration 6.1 Areas between Curves 6.2 Volumes 6.3 Volumes by Cylindrical Shells 6.5 Average Value of a Function 3小時 第七章 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 7小時 第八章 Further Applications of Integration 8.1 Arc Length 8.2 Area of a Surface of Revolution 8.5 Probability 3小時 第十章 Parametric Equations and Polar Coordinates 10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Curves 6小時

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