微積分甲(一)

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高中數學

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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/ 注意事項: 1. 如受疫情影響,無法點名、無法完成全部的實體考試,可能會更改成績計分公式(原則上:實體考試的比重 > 線上考試) 2. 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,私下 email 找我不回應。 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,逾時以棄權零分計! 極特殊理由的長假(疫檢、重病、車禍、出國比賽等)則不在此限。

學期總成績=平時考成績*65% + 會考成績*30% + 出席點名*5% 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

• 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

  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

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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

  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

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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

  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

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  4

Calculus (Early Transcendentals), James Stewart, 7/8/9th Edition

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