微積分甲(一)

數學的本質是理性思考,並應用於科學與工程問題的質化與量化描述。為落實思考內容、具體化抽象概念、操作而得感知、實踐數學的應用,數學的手做計算亦是數學的重要內容。但是數學絕不是機械化的計算;要做機械化的計算,一些數學軟體(如 Maple, Mathematica, MATLAB)做的遠比人類好。本微積分課程為基礎數學課程,講授函數的基本性質、微分、積分,及其相關與應用的空間幾何。除了數學的計算之外,也重視數學概念,並強調邏輯推理及論證,以鍛鍊思考力;此教學內容對學生的數理素養與之後的用到數學理論的其他應用科學課程的學習,具有紮根的重要性

高中數學

無備註

 每學期各有一次期末會考,題型為選擇、填充、計算問答題;以鑑別基本觀念與計算能力為主。此考試成績為微積分獎給獎依據  每節將勾選習題,學生應做習題,以增進對內容之理解,建立正確觀念並練習計算及推理 (學習數學與打電動,打球或學樂器一般,需要練習)  每星期繳交作業  將使用E3教學平台:補充說明、補充教材、討論與回應將置於E3  同學應多多一起討論數學及習題;若有疑問,請主動找老師或助教討論  歡迎上課時或下課後發問討論  視需要安排習題演習課

期中考 二次 各18 % 期末考 20 % 微積分會考 30 % 作業 (隨堂交通 ) 14 %

• 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 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 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：

  7

  備註：◆ 為選教內容,不列入微積分會考考試範圍。

• 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

  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 10.3 Polar Coordinates 10.4 Areas in Polar Coordinates

  講授：

  4

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

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聯絡方式

cwshih@math.nctu.edu.tw