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) 課堂上進行理論架構介紹,搭配嚴格證明與簡易操作;課後同學自行主動學習,進行微積分教學小組勾選的習題之練習。 (2) 微積分設有課程助教,在同學學習上遇到問題時,供同學諮詢。 (3) 課堂上,不實簽到、違反考試紀律者,按校規處理。 (4) 教學相關網站 http://www.math.nctu.edu.tw/~smchang/0701/C.html

(1) 作業:學生自行練習微積分教學小組勾選的習題。 (2) 考試:3次期中考、1次會考(期末全校統一微積分會考,第18週的星期三下午3:30~5:20,範圍 Ch.1~Ch.10) (3) 評量:學習表現 (0%)、期中考(70%)、會考 (30%)。

• Functions and Models

  ◆1.1 Four Ways to Represent a Function ◆1.2 Mathematical Models 1.3 New Functions from Old Functions 1.4 Exponential Functions 1.5 Inverse Functions and Logarithms

  講授：

  4

• Limits and Derivatives

  ◆2.1 The Tangent and Velocity Problems 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 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

• 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 Newtons Method 4.9 Antiderivatives

  講授：

  8

• 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：

  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

• 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

• Differential Equations

  ◆9.1 Modeling with Differential Equations ◆9.2 Direction Fields and Euler's Method ◆9.3 Separable Equations ◆9.4 Models for Population Growth ◆9.5 Linear Equations ◆9.6 Predator-Prey Systems

  講授：

  0

• Parametric Equations and Polar Coordinates

  10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Curves ◆10.3 Polar Coordinates ◆10.4 Areas and Lengths in Polar Coordinates ◆10.5 Conic Sections ◆10.6 Conic Sections in Polar Coordinates

  講授：

  3

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

地點

科學一館235室

時間

(四)12:20~13:10 欲前來晤談者,請事先用電子郵件預約。

聯絡方式

E-mail:smchang@math.nctu.edu.tw 校內分機:31216