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課程資訊

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Calculus(I)

   

用書:Calculus(Early Transcendentals), James Stewart, 8th Edition

   

( 標示之章節,由老師決定是否講授,不列入微積分會考範圍)

1.

Functions and Models -- 4 hours

1.3 New Functions from Old Functions
1.4 Exponential Functions
  1.5 Inverse Functions and Logarithms
 
 
2.

Limits and Derivatives -- 8hours

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
 
 
3.

Differentiation Rules -- 8 hours

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
   
4.

Applications of Differentiation -- 8 hours

  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
   
5.

Integrals -- 6 hours

  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.

Applications of Integration -- 3 hours

  6.1 Areas between Curves
  6.2 Volumes
  6.3 Volumes by Cylindrical Shells
  6.5 Average Value of a Function
   
7.

Techniques of Integration -- 7 hours

  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
   
8.

Further Applications of Integration -- 3 hours

  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
   
10.

Parametric Equations and Polar Coordinates -- 3 hours

  10.1 Curves Defined by Parametric Equations
  10.2 Calculus with Parametric Curves
   
   
   
   

說明:

1.
第一學期課程規劃 50小時,其餘時間由任課老師運用:演習課,考試,進度調整。
2.
常微分方程因時間因素省略,在二年級由其他課程搭配。
3.
課程內之定理與性質,強調在說明與講述其內容。
4.
學期末有一次期末會考,題型為選擇題及填充題;以鑑別基本觀念與計算能力為準。
會考成績為微積分獎給獎依據。
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