Pre-Calculus (99 Academic Year)
本課程是由交通大學應用數學系、微積分教學小組提供。
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！
| Instructor(s) | 羅元勳、陳育慈 |
|---|---|
| Course Credits | 無 |
| Academic Year | 97學年度 |
| Level | 大學一年級 |
| Prior Knowledge | 高中數學、微積分 |
| Related Resources | Course Video Course Syllabus |
| Week | Course Content | Course Video |
|---|---|---|
| 11.1 Sequences 題號：簡介 | Watch Online | |
| 11.1 Sequences 題號：8 | Watch Online | |
| 11.1 Sequences 題號：12 | Watch Online | |
| 11.1 Sequences 題號：30 | Watch Online | |
| 11.1 Sequences 題號：40 | Watch Online | |
| 11.1 Sequences 題號：52 | Watch Online | |
| 11.1 Sequences 題號：57 | Watch Online | |
| 11.1 Sequences 題號：66 | Watch Online | |
| 11.1 Sequences 題號：70 | Watch Online | |
| 11.1 Sequences 題號：79 | Watch Online | |
| 11.2 Series 題號：簡介 | Watch Online | |
| 11.2 Series 題號：13 | Watch Online | |
| 11.2 Series 題號：27 | Watch Online | |
| 11.2 Series 題號：36 | Watch Online | |
| 11.2 Series 題號：50 | Watch Online | |
| 11.2 Series 題號：57 | Watch Online | |
| 11.2 Series 題號：64 | Watch Online | |
| 11.2 Series 題號：66 | Watch Online | |
| 11.2 Series 題號：70 | Watch Online | |
| 11.2 Series 題號：75 | Watch Online | |
| 11.2 Series 題號：76 | Watch Online | |
| 11.3 The Integral Test and Estimates of Sums 題號：簡介 | Watch Online | |
| 11.3 The Integral Test and Estimates of Sums 題號：7 | Watch Online | |
| 11.3 The Integral Test and Estimates of Sums 題號：26 | Watch Online | |
| 11.3 The Integral Test and Estimates of Sums 題號：30 | Watch Online | |
| 11.3 The Integral Test and Estimates of Sums 題號：35 | Watch Online | |
| 11.3 The Integral Test and Estimates of Sums 題號：39 | Watch Online | |
| 11.3 The Integral Test and Estimates of Sums 題號：41 | Watch Online | |
| 11.3 The Integral Test and Estimates of Sums 題號：42 | Watch Online | |
| 11.4 The Comparison Tests 題號：簡介 | Watch Online | |
| 11.4 The Comparison Tests 題號：9 | Watch Online | |
| 11.4 The Comparison Tests 題號：24 | Watch Online | |
| 11.4 The Comparison Tests 題號：38 | Watch Online | |
| 11.4 The Comparison Tests 題號：40 | Watch Online | |
| 11.4 The Comparison Tests 題號：40(b) | Watch Online | |
| 11.4 The Comparison Tests 題號：41 | Watch Online | |
| 11.4 The Comparison Tests 題號：43 | Watch Online | |
| 11.4 The Comparison Tests 題號：45 | Watch Online | |
| 11.5 Alternating Series 題號：簡介 | Watch Online | |
| 11.5 Alternating Series 題號：7 | Watch Online | |
| 11.5 Alternating Series 題號：17 | Watch Online | |
| 11.5 Alternating Series 題號：18 | Watch Online | |
| 11.5 Alternating Series 題號：25 | Watch Online | |
| 11.5 Alternating Series 題號：34 | Watch Online | |
| 11.5 Alternating Series 題號：35 | Watch Online | |
| 11.6 Absolute Convergence and the Ratio and Root Tests 題號：簡介 | Watch Online | |
| 11.6 Absolute Convergence and the Ratio and Root Tests 題號：3 | Watch Online | |
| 11.6 Absolute Convergence and the Ratio and Root Tests 題號：5 | Watch Online | |
| 11.6 Absolute Convergence and the Ratio and Root Tests 題號：22-28 | Watch Online | |
| 11.6 Absolute Convergence and the Ratio and Root Tests 題號：33 | Watch Online | |
| 11.6 Absolute Convergence and the Ratio and Root Tests 題號：34 | Watch Online | |
| 11.6 Absolute Convergence and the Ratio and Root Tests 題號：35 | Watch Online | |
| 11.6 Absolute Convergence and the Ratio and Root Tests 題號：38 | Watch Online | |
| 11.8 Power Series 題號：簡介 | Watch Online | |
| 11.8 Power Series 題號：4 | Watch Online | |
| 11.8 Power Series 題號：21 | Watch Online | |
| 11.8 Power Series 題號：30 | Watch Online | |
| 11.8 Power Series 題號：31 | Watch Online | |
| 11.8 Power Series 題號：33 | Watch Online | |
| 11.8 Power Series 題號：37 | Watch Online | |
| 11.8 Power Series 題號：40 | Watch Online | |
| 11.8 Power Series 題號：41 11.9 Representations of Functions as Power Series 題號：簡介 | Watch Online | |
| 11.9 Representations of Functions as Power Series 題號：4 | Watch Online | |
| 11.9 Representations of Functions as Power Series 題號：12 | Watch Online | |
| 11.9 Representations of Functions as Power Series 題號：13 | Watch Online | |
| 11.9 Representations of Functions as Power Series 題號：26 | Watch Online | |
| 11.9 Representations of Functions as Power Series 題號：32 | Watch Online | |
| 11.9 Representations of Functions as Power Series 題號：38 | Watch Online | |
| 11.9 Representations of Functions as Power Series 題號：40 | Watch Online | |
| 12.1 Three-Dimensional Coordinate Systems 題號：9 | Watch Online | |
| 12.1 Three-Dimensional Coordinate Systems 題號：12 | Watch Online | |
| 12.1 Three-Dimensional Coordinate Systems 題號：38 | Watch Online | |
| 12.1 Three-Dimensional Coordinate Systems 題號：40 | Watch Online | |
| 12.2 Vectors 題號：24 | Watch Online | |
| 12.2 Vectors 題號：31 | Watch Online | |
| 12.2 Vectors 題號：34 | Watch Online | |
| 12.2 Vectors 題號：42 | Watch Online | |
| 12.3 The Dot Product 題號：簡介 | Watch Online | |
| 12.3 The Dot Product 題號：18,24 | Watch Online | |
| 12.3 The Dot Product 題號：31 | Watch Online | |
| 12.3 The Dot Product 題號：38 | Watch Online | |
| 12.3 The Dot Product 題號：45 | Watch Online | |
| 12.3 The Dot Product 題號：52,60 | Watch Online | |
| 12.4 The Cross Product 題號：簡介 | Watch Online | |
| 12.4 The Cross Product 題號：13,18,27 | Watch Online | |
| 12.4 The Cross Product 題號：34-49 | Watch Online | |
| 12.5 Equations of Lines and Planes 題號：18 | Watch Online | |
| 12.5 Equations of Lines and Planes 題號：48,62 | Watch Online | |
| 12.5 Equations of Lines and Planes 題號：73 | Watch Online | |
| 12.6 Cylinders and Quadric Surface 題號：21,28 | Watch Online | |
| 12.6 Cylinders and Quadric Surface 題號：41 | Watch Online | |
| 12.6 Cylinders and Quadric Surface 題號：44 | Watch Online | |
| 12.6 Cylinders and Quadric Surface 題號：50 | Watch Online | |
| 13.1 Vector Functions and Space Curves 題號：簡介 | Watch Online | |
| 13.1 Vector Functions and Space Curves 題號：9 | Watch Online | |
| 13.1 Vector Functions and Space Curves 題號：12 | Watch Online | |
| 13.1 Vector Functions and Space Curves 題號：21 | Watch Online | |
| 13.1 Vector Functions and Space Curves 題號：23 | Watch Online | |
| 13.1 Vector Functions and Space Curves 題號：38 | Watch Online | |
| 13.1 Vector Functions and Space Curves 題號：42 | Watch Online | |
| 13.2 Derivatives and Integrals of Vector Functions 題號：簡介 | Watch Online | |
| 13.2 Derivatives and Integrals of Vector Functions 題號：7 | Watch Online | |
| 13.2 Derivatives and Integrals of Vector Functions 題號：12 | Watch Online | |
| 13.2 Derivatives and Integrals of Vector Functions 題號：21 | Watch Online | |
| 13.2 Derivatives and Integrals of Vector Functions 題號：26 | Watch Online | |
| 13.2 Derivatives and Integrals of Vector Functions 題號：32 | Watch Online | |
| 13.2 Derivatives and Integrals of Vector Functions 題號：40 | Watch Online | |
| 13.2 Derivatives and Integrals of Vector Functions 題號：48 | Watch Online | |
| 13.3 Arc Length And Curvature 題號：簡介 | Watch Online | |
| 13.3 Arc Length And Curvature 題號：3 | Watch Online | |
| 13.3 Arc Length And Curvature 題號：16 | Watch Online | |
| 13.3 Arc Length And Curvature 題號：19 | Watch Online | |
| 13.3 Arc Length And Curvature 題號：28,32 | Watch Online | |
| 13.3 Arc Length And Curvature 題號：44 | Watch Online | |
| 13.3 Arc Length And Curvature 題號：49 | Watch Online | |
| 13.3 Arc Length And Curvature 題號：60 | Watch Online | |
| 14.1 Functions of Several Variables 題號：2 | Watch Online | |
| 14.1 Functions of Several Variables 題號：18 | Watch Online | |
| 14.1 Functions of Several Variables 題號：24 | Watch Online | |
| 14.1 Functions of Several Variables 題號：30 | Watch Online | |
| 14.1 Functions of Several Variables 題號：36 | Watch Online | |
| 14.1 Functions of Several Variables 題號：44 | Watch Online | |
| 14.1 Functions of Several Variables 題號：56 | Watch Online | |
| 14.1 Functions of Several Variables 題號：63 | Watch Online | |
| 14.1 Functions of Several Variables 題號：66 | Watch Online | |
| 14.2 Limits and Continuity 題號：簡介 | Watch Online | |
| 14.2 Limits and Continuity 題號：8,16 | Watch Online | |
| 14.2 Limits and Continuity 題號：22 | Watch Online | |
| 14.2 Limits and Continuity 題號：26 | Watch Online | |
| 14.2 Limits and Continuity 題號：32,38 | Watch Online | |
| 14.2 Limits and Continuity 題號：40 | Watch Online | |
| 14.3 Partial Derivatives 題號：簡介 | Watch Online | |
| 14.3 Partial Derivatives 題號：9 | Watch Online | |
| 14.3 Partial Derivatives 題號：37 | Watch Online | |
| 14.3 Partial Derivatives 題號：43 | Watch Online | |
| 14.3 Partial Derivatives 題號：48 | Watch Online | |
| 14.3 Partial Derivatives 題號：64 | Watch Online | |
| 14.3 Partial Derivatives 題號：76 | Watch Online | |
| 14.4 Tangent Plans and Differentials 題號：簡介 | Watch Online | |
| 14.4 Tangent Plans and Differentials 題號：5 | Watch Online | |
| 14.4 Tangent Plans and Differentials 題號：14 | Watch Online | |
| 14.4 Tangent Plans and Differentials 題號：19 | Watch Online | |
| 14.4 Tangent Plans and Differentials 題號：30 | Watch Online | |
| 14.4 Tangent Plans and Differentials 題號：36 | Watch Online | |
| 14.4 Tangent Plans and Differentials 題號：41 | Watch Online | |
| 14.4 Tangent Plans and Differentials 題號：44 | Watch Online | |
| 14.4 Tangent Plans and Differentials 題號：45 | Watch Online | |
| 14.4 Tangent Plans and Differentials 題號：46 | Watch Online | |
| 14.5 The Chain Rule 題號：4 | Watch Online | |
| 14.5 The Chain Rule 題號：14 | Watch Online | |
| 14.5 The Chain Rule 題號：26,33 | Watch Online | |
| 14.5 The Chain Rule 題號：40 | Watch Online | |
| 14.5 The Chain Rule 題號：45 | Watch Online | |
| 14.5 The Chain Rule 題號：54 | Watch Online | |
| 14.5 The Chain Rule 題號：55 | Watch Online | |
| 14.5 The Chain Rule 題號：57 | Watch Online | |
| 14.6 Directional Derivatives and the Gradient Vector 題號：簡介 | Watch Online | |
| 14.6 Directional Derivatives and the Gradient Vector 題號：14 | Watch Online | |
| 14.6 Directional Derivatives and the Gradient Vector 題號：31 | Watch Online | |
| 14.6 Directional Derivatives and the Gradient Vector 題號：38 | Watch Online | |
| 14.6 Directional Derivatives and the Gradient Vector 題號：42 | Watch Online | |
| 14.6 Directional Derivatives and the Gradient Vector 題號：58 | Watch Online | |
| 14.6 Directional Derivatives and the Gradient Vector 題號：61 | Watch Online | |
| 14.6 Directional Derivatives and the Gradient Vector 題號：64 | Watch Online | |
| 14.7 Maximum and Minimum Values 題號：簡介 | Watch Online | |
| 14.7 Maximum and Minimum Values 題號：4 | Watch Online | |
| 14.7 Maximum and Minimum Values 題號：19 | Watch Online | |
| 14.7 Maximum and Minimum Values 題號：32 | Watch Online | |
| 14.7 Maximum and Minimum Values 題號：47 | Watch Online | |
| 14.7 Maximum and Minimum Values 題號：54 | Watch Online | |
| 14.7 Maximum and Minimum Values 題號：55 | Watch Online | |
| 14.8 Lagrange Multipliers 題號：簡介 | Watch Online | |
| 14.8 Lagrange Multipliers 題號：18 | Watch Online | |
| 14.8 Lagrange Multipliers 題號：21 | Watch Online | |
| 14.8 Lagrange Multipliers 題號：41 | Watch Online | |
| 14.8 Lagrange Multipliers 題號：46 | Watch Online | |
| 15.1 Double Integrals over Rectangles 題號：13 | Watch Online | |
| 15.2 Iterated Integrals 題號：10 | Watch Online | |
| 15.2 Iterated Integrals 題號：19 | Watch Online | |
| 15.2 Iterated Integrals 題號：23 | Watch Online | |
| 15.2 Iterated Integrals 題號：28 | Watch Online | |
| 15.2 Iterated Integrals 題號：30 | Watch Online | |
| 15.3 Double Integrals over General Regions 題號：21 | Watch Online | |
| 15.3 Double Integrals over General Regions 題號：8 | Watch Online | |
| 15.3 Double Integrals over General Regions 題號：27 | Watch Online | |
| 15.3 Double Integrals over General Regions 題號：31 | Watch Online | |
| 15.3 Double Integrals over General Regions 題號：43 | Watch Online | |
| 15.3 Double Integrals over General Regions 題號：49 | Watch Online | |
| 15.3 Double Integrals over General Regions 題號：51 | Watch Online | |
| 15.3 Double Integrals over General Regions 題號：58 | Watch Online | |
| 15.4 Double Integrals in Polar Coordinates 題號：9 | Watch Online | |
| 15.4 Double Integrals in Polar Coordinates 題號：13 | Watch Online | |
| 15.4 Double Integrals in Polar Coordinates 題號：17 | Watch Online | |
| 15.4 Double Integrals in Polar Coordinates 題號：25 | Watch Online | |
| 15.4 Double Integrals in Polar Coordinates 題號：35 | Watch Online | |
| 15.6 Triple Integrals 題號：11 | Watch Online | |
| 15.6 Triple Integrals 題號：16 | Watch Online | |
| 15.6 Triple Integrals 題號：17 | Watch Online | |
| 15.6 Triple Integrals 題號：20 | Watch Online | |
| 15.6 Triple Integrals 題號：27 | Watch Online | |
| 15.6 Triple Integrals 題號：31 | Watch Online | |
| 15.7 Triple Integrals in Cylindrical Coordinates 題號：11 | Watch Online | |
| 15.7 Triple Integrals in Cylindrical Coordinates 題號：18 | Watch Online | |
| 15.7 Triple Integrals in Cylindrical Coordinates 題號：21 | Watch Online | |
| 15.7 Triple Integrals in Cylindrical Coordinates 題號：28 | Watch Online | |
| 15.8 Triple Integrals in Spherical Coordinates 題號：4 | Watch Online | |
| 15.8 Triple Integrals in Spherical Coordinates 題號：8 | Watch Online | |
| 15.8 Triple Integrals in Spherical Coordinates 題號：10 | Watch Online | |
| 15.8 Triple Integrals in Spherical Coordinates 題號：12 | Watch Online | |
| 15.8 Triple Integrals in Spherical Coordinates 題號：17 | Watch Online | |
| 15.8 Triple Integrals in Spherical Coordinates 題號：21 | Watch Online | |
| 15.8 Triple Integrals in Spherical Coordinates 題號：25 | Watch Online | |
| 15.8 Triple Integrals in Spherical Coordinates 題號：29(a) | Watch Online | |
| 15.8 Triple Integrals in Spherical Coordinates 題號：36 | Watch Online | |
| 15.8 Triple Integrals in Spherical Coordinates 題號：39 | Watch Online | |
| 15.9 Change of Variables in Multiple Integrals 題號：5 | Watch Online | |
| 15.9 Change of Variables in Multiple Integrals 題號：11 | Watch Online | |
| 15.9 Change of Variables in Multiple Integrals 題號：13 | Watch Online | |
| 15.9 Change of Variables in Multiple Integrals 題號：19 | Watch Online | |
| 15.9 Change of Variables in Multiple Integrals 題號：21 | Watch Online | |
| 15.9 Change of Variables in Multiple Integrals 題號：23 | Watch Online |
課程目標/概述
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/概述
| 章節 | 主題內容 |
| 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 12.1 Three-Dimensional Coordinate Systems 12.2 Vectors 12.3 The Dot Product 12.4 The Cross Product 12.5 Equations of Lines and Planes |
| 第十三章 | 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 Triple Integrals 15.7 Triple Integrals in Cylindrical Coordinates 15.8 Triple Integrals in Spherical Coordinates 15.9 Change of Variables in Multiple Integrals |
課程書目
Calculus(Early Transcendental), James Stewart, 6th Edition.
COURSE
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