微積分甲(一)

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高中數學

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依校方最新疫情公告,目前都不能上實體課,請登入 e3new 收看教學錄影(不是同步直播),學習上有問題請多利用「課程內容 & 解題討論區」發問。 交大微積分官網習題 exercises & 會考考古題 past exam questions: https://calculus.nctu.edu.tw/exams-index/ 莊重授課: http://ocw.nctu.edu.tw/course_detail-v.php?bgid=1&gid=1&nid=490 http://ocw.nctu.edu.tw/course_detail-v.php?bgid=1&gid=1&nid=9 白啟光授課: http://ocw.nctu.edu.tw/course_detail-v.php?bgid=1&gid=1&nid=239 符麥克授課(English): http://ocw.nctu.edu.tw/course_detail-v.php?bgid=1&gid=1&nid=17 關於考試的請假 About leave of a quiz: 考試請假非比尋常,這會影響考試的公平性、增加我的工作量,輕忽者亦會減損成績;故必須慎重! 一律使用本校的線上請假系統,不接受私下 email 給我。 事假申請必須提早一天以上,且經我同意(當場或事後申請者不准,我未回覆同意者不准),病假可以事後補請(要出具看診單,不是藥單,否則不准)。女性生理假最晚必須於考前4小時提出申請,否則不准。 合於以上條件准假者得以補考,但務必於一週內與我約定(上班時間)執行完畢,逾時棄權以零分計! 極特殊理由的長假(重病、車禍、出國比賽、疫檢等)則不在此限。

學期總成績=平時考成績*70% + 會考成績*30% 超過100以100計,no more than 100 平時考成績=(Sum of Yours grades in all Quizzes)/(Total grades of Quizzes)*100 超過100以100計,no more than 100 注意:受疫情影響,本學期的實體考試(至少有3次)可能將在週六實施(時間未定);如無特殊理由不得請假,無法接受者請勿選修本班

• Functions and Models

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

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  3

• 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

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  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

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  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

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  7

• Integrals

  5.1 The Areas 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

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  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

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  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

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• 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

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  3

• 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, 8th or 7th Edition

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