Calculus I - 103 Academic Year

微積分(一) - 103學年度

本課程是由 國立陽明交通大學應用數學系提供。

本課程除了微分積分之方法與計算之外,學習重點在於基本數學觀念的理解。例如中間值定理、平均值定理、極值定理等。這些定理不僅本身有其基本應用的價值,背後也有它們數學的涵義與想法。瞭解這些想法,一方面可以推廣這些定理,另一方面當我們面臨更複雜的問題時,解決問題初步的試探可以以這些基本數學想法做為基礎或做為類比。這是數學做為一種科學思考的價值。

課程用書:

Calculus(Early Transendentals), James Stewart, 7th Edition Publisher: Cengage Learning

為求學習成效完美,請購買課本!

 

授課教師 應用數學系 莊重老師
課程學分 4學分
授課年度 103學年度
授課對象 大學一年級學生
預備知識 高中數學
課程提供 課程影音   課程綱要   課程行事曆    課程講義

課程目標

本課程除了微分積分之方法與計算之外,學習重點在於基本數學觀念的理解。例如中間值定理、平均值定理、極值定理等。這些定理不僅本身有其基本應用的價值,背後也有它們數學的涵義與想法。瞭解這些想法,一方面可以推廣這些定理,另一方面當我們面臨更複雜的問題時,解決問題初步的試探可以以這些基本數學想法做為基礎或做為類比。這是數學做為一種科學思考的價值。

 

課程章節

 

章節 章節內容
第一章Functions and Model
第二章Limits and derivatives
第三章Differentiation Rules
第四章Applications of Differentiation
第五章Integrals
第六章Applications of Integration
第七章Techniques of Integration
第八章Further Applications of Integration
第十章Parametric Equations and Polar Coordinates

 

課程書目

Calculus(Early Transendentals), James Stewart, 7th Edition

本課程行事曆提供課程進度與考試資訊參考。

課程章節
參考課程進度

第一章 Functions and Model

  • 1.5 Exponential Functions
    1.6 Inverse Functions and Logarithms
第二章 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
第三章 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
    3.9 Related Rates
    3.10 Linear Approximations and Differentials
第四章 The Properties of Gases
  • 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
    4.9 Antiderivatives
第五章 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
第六章 Acations of Integration
  • 6.1 Areas between Curves
    6.2 Volumes
    6.3 Volumes by Cylindrical Shells
    6.5 Average Value of a Function
第七章 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
    7.7 Approximate Integration
    7.8 Improper Integrals
第八章 Further Applications of Integration
  • 8.1 Arc Length
    8.2 Area of a Surface of Revolution
    8.5 Probability
第十章 Parametric Equations and Polar Coordinates
  • 10.1 Curves Defined by Parametric Equations
    10.2 Calculus with Parametric Curves

課程講義 Course Handout

章節 下載連結
1-5 Exponential Functions
1-6 Inverse Functions and Logarithms
PDF
2-2 & 2-3 LimitPDF
2-4 Definition of the LimitPDF
2-5 ContinuityPDF
2-6 Limit at Infinity & Horizontal AsymtotesPDF
2-7 Derivatives and Rates of ChangePDF
2-8 The Derivative As a FunctionPDF
2-9 The Derivative As a FunctionPDF
3-1 Derivatives of Polynomials and Exponential FunctionsPDF
3-2 The Product and Quotient RulesPDF
3-3 Derivatives of Trigonometric FunctionsPDF
3-4 The Chain RulePDF
3-5 Implicit DifferentiationPDF
3-6 Derivatives of Logarithmic FunctionsPDF
3-9 Related RatesPDF
3-10 Linear Approximations and DifferentialsPDF
4-1 Maximum and Minimum ValuesPDF
4-2 The Mean Value TheoremPDF
4-3 & 4-5 1st and 2nd Derivatives and Curve SketchingPDF
4-4 Indeterminate Form and L'Hospital's RulePDF
4-7 OptimizationPDF
4-9 AntiderivativesPDF
5-1 Areas and DistancesPDF
5-2 The Definite IntegralPDF
5-3 The Fundamental Theorem of Calculus(TFTC)PDF
5-4 Indefinite IntegralsPDF
5-5 The Substitution RulesPDF
5-6 The Logarithm Defined as an IntegralPDF
6-1 Areas Between CurvesPDF
6-2 & 6-3 Volumes by Cylindrical ShellsPDF
6-5 Average Value of a FunctionPDF
7-1 Integration by PartsPDF
7-2 Trigonometric IntegralsPDF
7-3 Trigonometric SubstitutionPDF
7-4 Integration of Rational Function by Partial FractionPDF
7-7 Approximate IntegrationPDF
7-8 Improper IntegralsPDF
8-1 Arc LengthPDF
8-2 Area of a Surface RevolutionPDF
8-3 Applications to Physics and EngineeringPDF
8-5 ProbabilityPDF
10-1 Curves Defined by Parametric EquationPDF
10-2 Curves Defined by Parametric EquationPDF
10-3 Polar CoordinatesPDF
10-4 Area and Lengths in Polar CoordinatesPDF
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