Calculus I - 103 Academic Year

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。

Textbook:

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

For perfect learning results, please buy textbooks!

 

Instructor(s) Department of Applied Mathematics Prof. Jonq Juang
Course Credits 4 Credits
Academic Year 103 Academic Year
Level Freshman
Prior Knowledge High School Math
Related Resources Course Video   Course Syllabus   Course Calendar    Course Handout

WeekCourse ContentCourse VideoCourse Download
莊重老師真心告白Watch OnlineMP4 Download
課程介紹Watch OnlineMP4 Download
第一章 Functions and Models
1.5 Exponential Functions
1.6 Inverse Functions and Logarithms
Watch OnlineMP4 Download
第二章 Limits and derivatives
2.2 The Limit of a Function
2.3 Calculating Limits Using the Limit Laws
Watch OnlineMP4 Download
2.4 The Precise Definition of a LimitWatch OnlineMP4 Download
2.5 ContinuityWatch OnlineMP4 Download
2.6 Limits at Infinity, Horizontal AsymptotesWatch OnlineMP4 Download
2.7 Derivatives and Rates of Change
(本影片內容有部分錯誤,詳見YouTube留言)
Watch OnlineMP4 Download
2.8 The Derivative as a FunctionWatch OnlineMP4 Download
第三章 Differentiation Rules
3.1 Derivatives of Polynomials and Exponential Functions
Watch OnlineMP4 Download
3.2 The Product and Quotient RulesWatch OnlineMP4 Download
3.3 Derivatives of Trigonometric FunctionsWatch OnlineMP4 Download
3.4 The Chain Rule
(本影片內容有部分錯誤,詳見YouTube留言)
Watch OnlineMP4 Download
3.5 Implicit DifferentiationWatch OnlineMP4 Download
3.6 Derivatives of Logarithmic FunctionsWatch OnlineMP4 Download
3.9 Related RatesWatch OnlineMP4 Download
3.10 Linear Approximations and DifferentialsWatch OnlineMP4 Download
第四章 Applications of Differentiation
4.1 Maximum and Minimum Values
Watch OnlineMP4 Download
4.2 The Mean Value TheoremWatch OnlineMP4 Download
4.3 How Derivatives Affect the Shape of a Graph
4.5 Summary of Curve Sketching
Watch OnlineMP4 Download
4.4 Indeterminate Forms and L’Hospital’s RuleWatch OnlineMP4 Download
4.7 Optimization ProblemsWatch OnlineMP4 Download
4.9 AntiderivativesWatch OnlineMP4 Download
第五章 Integrals
5.1 Areas and Distances
Watch OnlineMP4 Download
5.2 The Definite IntegralWatch OnlineMP4 Download
5.3 The Fundamental Theorem of CalculusWatch OnlineMP4 Download
5.4 Indefinite Integrals and the Net Change TheoremWatch OnlineMP4 Download
5.5 The Substitution RuleWatch OnlineMP4 Download
第六章 Applications of Integration
6.1 Areas between Curves
Watch OnlineMP4 Download
6.2 Volumes
6.3 Volumes by Cylindrical Shells
Watch OnlineMP4 Download
6.5 Average Value of a FunctionWatch OnlineMP4 Download
第七章 Techniques of Integration
7.1 Integration by Parts
Watch OnlineMP4 Download
7.2 Trigonometric IntegralsWatch OnlineMP4 Download
7.3 Trigonometric SubstitutionWatch OnlineMP4 Download
7.4 Integration of Rational Functions by Partial FractionsWatch OnlineMP4 Download
7.7 Approximate IntegrationWatch OnlineMP4 Download
7.8 Improper IntegralsWatch OnlineMP4 Download
第八章 Further Applications of Integration
8.1 Arc Length
Watch OnlineMP4 Download
8.2 Area of a Surface of RevolutionWatch OnlineMP4 Download
8.5 ProbabilityWatch OnlineMP4 Download
第十章 Parametric Equations and Polar Coordinates
10.1 Curves Defined by Parametric Equations
Watch OnlineMP4 Download
10.2 Calculus with Parametric CurvesWatch OnlineMP4 Download

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