微積分甲(一)

概念上以嚴謹定義的極限,延伸至函數的連續、 導數的存在、以及微分與積分的公式推導。技巧上訓練微分與積分的計算能力,熟悉科學研究之重要工具 -- 微積分的使用。

高中數學

無備註

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1. 隨堂考 10%. 2. 期中考 30%. 3. 期末考 30%. 4. 大會考 30%.

• 1 Functions and Model

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

  講授：

  4

  其他：

  0

  備註：僅講授不進行測驗

• 2 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

  講授：

  10.5

  其他：

  1.5

  備註：其他為隨堂測驗與講解時間總計

• 3 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

  講授：

  6.5

  其他：

  1.5

  備註：其他為隨堂測驗與講解時間總計

• 4 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 Newton's Method 4.9 Antiderivatives

  講授：

  9

  其他：

  1

  備註：其他為隨堂測驗與講解時間總計

• 5 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

  講授：

  5

  其他：

  1

  備註：其他為隨堂測驗與講解時間總計

• 6 Applications of Integration

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

  講授：

  3.5

  其他：

  .5

  備註：其他為隨堂測驗與講解時間總計

• 7 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

  講授：

  11

  其他：

  1

  備註：其他為隨堂測驗與講解時間總計

• 8 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

  講授：

  3.5

  其他：

  .5

  備註：其他為隨堂測驗與講解時間總計

• 10 Parametric Equations and Polar Coordinates

  10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Curves

  講授：

  3.5

  其他：

  .5

  備註：其他為隨堂測驗與講解時間總計

Calculus(Early Transendentals), James Stewart, 8th Edition

地點

科一館231.

時間

Catch me if you can. 上課前後或中間下課等課餘時間, 或可另約時間找我.

聯絡方式

E-mail: wuhsiunglin@nctu.edu.tw 校內分機: 03-5712121 #56438