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Calculus II - 103 Academic Year

微積分(二) - 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、微積分(一)
課程提供 課程影音   課程綱要   課程行事曆    課程講義

週次課程內容課程影音
第十章 Parametric Equations and Polar Coordinates
10.3 Polar Coordinates		線上觀看
10.4 Areas and Lengths in Polar Coordinates線上觀看
第十一章 Infinite Sequences and Series
11.1 Sequences
(本影片07:08處 a3=0為正解，a3=-1為錯誤答案)		線上觀看
11.2 Series線上觀看
11.3 The Integral Test and Estimates of Sums線上觀看
11.4 The Comparison Tests線上觀看
11.5 Alternating Series線上觀看
11.6 Absolute Convergence and the Ratio and Root Tests線上觀看
11.8 Power Series線上觀看
11.9 Representations of Functions as Power Series線上觀看
11.10 Taylor and Maclaurin Series線上觀看
11.11 Applications of Taylor Polynomials線上觀看
第十二章 Vectors and the Geometry of Space
12.2 Vectors		線上觀看
12.3 The Dot Product線上觀看
12.4 The Cross Product線上觀看
12.5 Equations of Lines and Planes線上觀看
12.6 Cylinders and Quadratic Surface線上觀看
第十三章 Vector Functions
13.1 Vector Functions and Space Curves		線上觀看
13.2 Derivatives and Integrals of Vector Functions線上觀看
13.3 Arc Length and Curvature線上觀看
14.1 Functions of Several Variables線上觀看
14.2 Limits and Continuity線上觀看
14.3 Partial Derivatives線上觀看
14.4 Tangent Planes and Linear Approximation線上觀看
14.5 The Chain Rule線上觀看
14.6 Directional Derivatives and Gradient Vector線上觀看
14.7 Maximum and Minimum Values線上觀看
14.8 Lagrange Multipliers線上觀看
15.1 Double Integrals over Rectangles線上觀看
15.2 Iterated Integrals線上觀看
15.3 Double Integrals over General Regions線上觀看
15.4 Double Integrals in Polar Coordinates線上觀看
15.5 Applications of Double Integrals線上觀看
15.6 Surface Area線上觀看
15.7 Triple Integrals線上觀看
15.8 Triple Integrals in Cylindrical Coordinates線上觀看
15.9 Triple Integrals in Spherical Coordinates線上觀看
15.10 Change of Variables in Multiple Integrals線上觀看
Chapter16 : Vector Calculus
16.0 Introduction		線上觀看
16.1 Vector Fields線上觀看
16.2 Line (Curve) Integrals線上觀看
16.3 The Fundamental Theorem for Line Integrals線上觀看
16.4 Green's Theorem
(‘二維’的微積分基本定理)		線上觀看

課程目標

本課程之目標在於學習微分積分之方法與計算，以及更重要的是基本數學觀念的理解。同時希望大家學到自律、合作與互動、獨立思考與自我學習。

課程章節

 

章節 章節內容
第十章 Parametric Equations and Polar Coordinates
第十一章 Infinite Sequences and Series
第十二章Vectors and the Geometry of Space
第十三章Vector Functions
第十四章Partial Derivatives
第十五章Multiple Integrals
第十六章Vector Calculus

 

課程書目

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

 

評分標準

項目百分比
online quizzes5%
學習歷程檔案5%
小考40%
期中考20%
期末會考30%
討論區bonus5%

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

第十章 Parametric Equations and Polar Coordinates

  • 10.3 Polar Coordinates
    10.4 Areas and Lengths in Polar Coordinates
第十一章 Infinite Sequences and Series
  • 11.1 Sequences
    11.2 Series
    11.3 The Integral Test and Estimates of Sums
    11.4 The Comparison Tests
    11.5 Alternating Series
    11.6 Absolute Convergence and the Ratio and Root Tests
    11.8 Power Series
    11.9 Representations of Functions as Power Series
    11.10 Taylor and Maclaurin Series
    11.11 Applications of Taylor Polynomials
第十二章 Vectors and the Geometry of Space (選教)
  • 12.1 Three-Dimensional Coordinate Systems
    12.2 Vectors
    12.3 The Dot Product (12.1 12.2 與 12.3 為複習課程)
    12.4 The Cross Product
    12.5 Equations of Lines and Planes
    12.6 Cylinders and Quadric Surface
第十三章 Vector Functions
  • 13.1 Vector Functions and Space Curves
    13.2 Derivatives and Integrals of Vector Functions
    13.3 Arc Length And Curvature (Curvatre 選教)
    13.4 Motion in Space: Velocity and Acceleration(本節選教)
第十四章 Partial Derivatives
  • 14.1 Functions of Several Variables
    14.2 Limits and Continuity
    14.3 Partial Derivatives
    14.4 Tangent Plans and Differentials
    14.5 The Chain Rule
    14.6 Directional Derivatives and the Gradient Vector
    14.7 Maximum and Minimum Values
    14.8 Lagrange Multipliers
第十五章 Multiple Integrals
  • 15.1 Double Integrals over Rectangles
    15.2 Iterated Integrals
    15.3 Double Integrals over General Regions
    15.4 Double Integrals in Polar Coordinates
    15.5 Application of Double Integrals
    15.6 Surface Area (選教)
    15.7 Triple Integrals
    15.8 Triple Integrals in Cylindrical Coordinates
    15.9 Triple Integrals in Spherical Coordinates
    15.10 Change of Variables in Multiple Integrals
第十六章 Vector Calculus (選教)
  • 16.1 Vector fields
    16.2 Line integrals
    16.3 The fundamental Theorem for line integrals
    16.4 Green's Theorem

課程講義 Course Handout

章節 下載連結
10.3 Polar CoordinatesPDF
10.4 Area and Lengths in Polar CoordinatesPDF
11.1 SequencesPDF
11.2 SeriesPDF
11.3 The Integral Test and Estimates of SumsPDF
11.4 The Comparison TestsPDF
11.5 Alternating SeriesPDF
11.6 Absolute Convergence and The Ratio and Root testPDF
11.8 Power SeriesPDF
11.9 Representations of Functions as Power SeriesPDF
11.10 Taylor and Maclaurin SeriesPDF
11.11 Applications of Taylor PolynomialPDF
12.2 VectorsPDF
12.3 The Dot ProductPDF
12.4 The Cross ProductPDF
12.5 Equations of Lines and PlanesPDF
12.6 Cylinders and Quadrate SurfacePDF
12.7 Cylindrical and Spherical CoordinatesPDF
13.1 Vector FunctionsPDF
13.2 Derivatives and Integrals of Vector FunctionsPDF
13.3 Arc Length and CurvaturePDF
14.1 Functions of Several VariablesPDF
14.2 Limits and ContinuityPDF
14.3 Partial DerivativesPDF
14.4 Tangent Planes and Linear ApproximationPDF
14.5 The Chain RulePDF
14.6 Directional Derivatives and Gradient VectorPDF
14.7 Maximum and Minimum ValuesPDF
14.8 Lagrange MultipliersPDF
15.1 Double Integrals over RectanglesPDF
15.2 Iterated IntegralsPDF
15.3 Double Integrals over General RegionsPDF
15.4 Double Integrals in Polar CoordinatesPDF
15.5 Applications of Double IntegralsPDF
15.6 Surface AreaPDF
15.7 Triple IntegralsPDF
15.8 Triple Integrals in Cylindrical CoordinatesPDF
15.9 Triple Integrals in Spherical CoordinatesPDF
15.10 Change of Variables in Multiple IntegralsPDF
16.0 Introduction of Vector Calculus
16.1 Vector Fields		PDF
16.2 Line (Curve) IntegralsPDF
16.3 The Fundamental Theorem for Line IntegralsPDF
16.4 Green's Theorem (‘二維’的微積分基本定理)PDF
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