Calculus I - 99 Academic Year

微積分(一) - 99學年度

本課程是由交通大學應用數學系提供。

本課程影片於99學年暑假課程錄製,配合99年上學期網路課程調整安排課程內容。

課程用書:Calculus (Early Transcendental), James Stewart, 6th EditionPublisher: Cengage Learning.

為求學習成效完美,請購買課本!

授課教師 應用數學系 白啟光老師
課程學分 4學分
授課年度 99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   Maple Worksheet

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 主題內容
第一章 Functions and Model1.5 Exponential Functions
1.6 Inverse Functions and Logarithms
第二章 Limits and derivatives2.2 The Limit of a Function
2.3 Calculating Limits Using the Limit Laws
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 Stochastic Integrals3.1 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
3.9 Related Rates
3.10 Linear Approximations and Differentials
3.11 Hyperbolic Functions 
第四章 Applications of Differentiation4.1 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
第五章 Integrals5.1 Areas and Distances
5.2 The Definite Integral
5.3 The Fundamental Theorem of Calculus
5.4 Indefinite Integrals and the Total Change Theorem
5.5 The Substitution Rule
第六章 Applications of Integration6.1 Areas between Curves
6.2 Volumes
6.3 Volumes be Cylindrical Shells
6.5 Average Value of a Function
第七章 Techniques of Integration7.1 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 Integration8.1 Further Applications of Integration
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
第十章 Parametric Equations and Polar Coordinates10.1 Curves Defined by Parametric Equations
10.2 Calculus with Parametric Curves
10.3 Polar Coordinates
10.4 Areas and Lengths in Polar Coordinates

 

課程書目

Calculus(Early Transendentals), James Stewart, 6th Edition.

 

評分標準

項目百分比
Practice Quizes5%
學習歷程檔案 & 討論區5%
小考40%
期中考20%
期末考30%

本課程行事曆提供課程進度與考試資訊參考。

學期週次
上課日期
參考課程進度
第一週 09/12-09/18
  • 1.5-2.3
第二週 09/19-09/25
  • 2.4
第三週 09/26-10/02
  • 2.5-2.6
第四週 10/03-10/09
  • 2.7-3.3(3.10)
第五週 10/10-10/16
  • 3.4
第六週 10/17-10/23
  • 3.5-3.9
第七週 10/24-10/30
  • 4.1-4.2
第八週 10/31-11/06
  • 4.3-4.7
第九週 11/07-11/13
  • 4.9
第十週 11/14-11/20
  • 5.1-5.4
第十一週 11/21-11/27
  • 5.5-6.1
第十二週 11/28-12/04
  • 6.2-7.2
第十三週 12/05-12/11
  • 7.3-7.4
第十四週 12/12-12/18
  • 7.7-8.2
第十五週 12/19-12/25
  • 10.1-10.2
第十六週 12/26-01/01
  • 10.3-10.4
第十七週 01/02-01/08
  • 總複習
第十八週 01/09-01/15
  • 期末考

請依照您電腦的版本下載 Maple Player Download Maple Player 

章節
章節內容
Maple下載
1.5Exponential Functionsworksheet
What is √2 ?worksheet
1.6Inverse Functionsworksheet
2.2Limitsworksheet
2.3Limit Lawsworksheet
2.4The Precise Definition of a Limitworksheet
2.5Couninuityworksheet
2.6Asymptotesworksheet
2.8,2.9Tangent Lines and Definition of the Derivativeworksheet
The Derivatives and Tangent Linesworksheet
3.1,3.2Continuous Functions that Fail to Be Differentiableworksheet
3.8,3.10Derivatives of Inverse Functionsworksheet
4.1Maximum and Minimum Valuesworksheet
4.2The Mean Value Theoremworksheet
4.3How Derivatives Affect the Shape of a Graph?worksheet
4.4L’Hospital’s Ruleworksheet
4.10Antiderivativesworksheet
6.2Volumes by Cross Sections?worksheet
6.3Volumes by Cylindrical Shellsworksheet
10.1Graphic Designworksheet
Bezier Curvesworksheet
10.3Polar Coordinates and Polar Curvesworksheet
10.4Area in Polar Coordinatesworksheet
 
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