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。 In concepts, extending from rigorous definition of limit, to the continuity of functions, the existence of derivatives, and the deduction of differential and integral formulas. In skills, training the ability of differentiation and integration, and getting acquianted with the usage of the important tool of scientific research -- Calculus.

高中數學。 Senior high school mathematics.

僅講授不進行測驗 其他為隨堂測驗與講解時間總計 其他為隨堂測驗與講解時間總計 其他為隨堂測驗與講解時間總計 其他為隨堂測驗與講解時間總計 其他為隨堂測驗與講解時間總計 其他為隨堂測驗與講解時間總計 其他為隨堂測驗與講解時間總計 僅講授不進行測驗

相關事項將公佈於 E3(https://e3p.nycu.edu.tw/)，並於 E3 提供授課講義與作業參考解答供課前預習與課後複習。 安排助教 office hour 解答學生問題，助教名單與其值班時間將公佈於 E3。 Announcement on E3(https://e3p.nycu.edu.tw/), lecture notes and homework answers will be provided on E3 for pre-class and post-class review. The teaching assistants (TAs) office hour is arranged to answer students' questions. The list of TA assistants and their duty time will be announced on E3.

1. 隨堂考(Quiz) 10%. 2. 期中考(Midterm) 30%. 3. 期末考(Finalterm) 30%. 4. 大會考(Joint Exam) 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 and Inverse Trigonometric 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 What Derivatives Tell Us about 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：

  1.5

  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：

  2

  其他：

  0

  備註：僅講授不進行測驗

Calculus(Early Transendentals), James Stewart, 9th Edition.

地點

科一館231。 SA231.

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。 Before, in, and after class, or making an appointment.

聯絡方式

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