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微積分(一) Calculus I - 103學年度

課程行事曆

  • 微積分(一) Calculus I - 103學年度

課程行事曆  

本課程行事曆提供課程進度與考試資訊。

 

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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