微積分甲(一)

在探討(人文、社會、自然、資訊)科學問題過程中,「數學」扮演關鍵的一環。希望藉由「微積分」的課程,建立基本數學觀念, 教授「極限」、「微分」與「積分」之方法與計算。期待在有基本數學觀念後,於探究科學問題時,能以這些基本數學想法作為基礎或類比。

高中數學

無備註

(1) 本課程規劃以課堂面授進行。 (2) 期中考試 補考 成績 最高70分為計算 [因 公假 而 補考 除外]。 (3) 教學相關網站 https://jupiter.math.nycu.edu.tw/~smchang/1401/C2.html

(1) 作業:學生自行練習課堂釋例、習題(9E)與微積分甲(一)會考考古題。 (2) 考試:3次小考、2次期中考、1次會考。 (3) 評量:學習表現(8%) + 小考(21%) + 期中考成績(41%) + 會考成績(30%)

• Functions and Models

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

  講授：

  3

  備註：◆ 為選教內容,不列入微積分會考考試範圍。

• 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：

  8

• 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：

  8

  備註：◆ 為選教內容,不列入微積分會考考試範圍。

• 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 Newtons Method 4.9 Antiderivatives

  講授：

  7

  備註：◆ 為選教內容,不列入微積分會考考試範圍。

• Integrals

  5.1 The Area and Distance Problems 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：

  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

• 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：

  7

  備註：◆ 為選教內容,不列入微積分會考考試範圍。

• 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

  備註：◆ 為選教內容,不列入微積分會考考試範圍。

• Parametric Equations and Polar Coordinates

  10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Curves

  講授：

  4

Calculus (Early Transcendentals), James Stewart, Metric Version 9th Edition

地點

科學一館235室

時間

(二)12:20~13:10 [by appointment only] 欲前來晤談者,請事先用電子郵件預約。

聯絡方式

E-mail:smchang@nycu.edu.tw 校內分機:31216