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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

WeekCourse ContentCourse VideoCourse Download
11.1 Sequences 題號：簡介Watch OnlineMP4 Download
11.1 Sequences 題號：8Watch OnlineMP4 Download
11.1 Sequences 題號：12Watch OnlineMP4 Download
11.1 Sequences 題號：30Watch OnlineMP4 Download
11.1 Sequences 題號：40Watch OnlineMP4 Download
11.1 Sequences 題號：52Watch OnlineMP4 Download
11.1 Sequences 題號：57Watch OnlineMP4 Download
11.1 Sequences 題號：66Watch OnlineMP4 Download
11.1 Sequences 題號：70Watch OnlineMP4 Download
11.1 Sequences 題號：79Watch OnlineMP4 Download
11.2 Series 題號：簡介Watch OnlineMP4 Download
11.2 Series 題號：13Watch OnlineMP4 Download
11.2 Series 題號：27Watch OnlineMP4 Download
11.2 Series 題號：36Watch OnlineMP4 Download
11.2 Series 題號：50Watch OnlineMP4 Download
11.2 Series 題號：57Watch OnlineMP4 Download
11.2 Series 題號：64Watch OnlineMP4 Download
11.2 Series 題號：66Watch OnlineMP4 Download
11.2 Series 題號：70Watch OnlineMP4 Download
11.2 Series 題號：75Watch OnlineMP4 Download
11.2 Series 題號：76Watch OnlineMP4 Download
11.3 The Integral Test and Estimates of Sums 題號：簡介Watch OnlineMP4 Download
11.3 The Integral Test and Estimates of Sums 題號：7Watch OnlineMP4 Download
11.3 The Integral Test and Estimates of Sums 題號：26Watch OnlineMP4 Download
11.3 The Integral Test and Estimates of Sums 題號：30Watch OnlineMP4 Download
11.3 The Integral Test and Estimates of Sums 題號：35Watch OnlineMP4 Download
11.3 The Integral Test and Estimates of Sums 題號：39Watch OnlineMP4 Download
11.3 The Integral Test and Estimates of Sums 題號：41Watch OnlineMP4 Download
11.3 The Integral Test and Estimates of Sums 題號：42Watch OnlineMP4 Download
11.4 The Comparison Tests 題號：簡介Watch OnlineMP4 Download
11.4 The Comparison Tests 題號：9Watch OnlineMP4 Download
11.4 The Comparison Tests 題號：24Watch OnlineMP4 Download
11.4 The Comparison Tests 題號：38Watch OnlineMP4 Download
11.4 The Comparison Tests 題號：40Watch OnlineMP4 Download
11.4 The Comparison Tests 題號：40(b)Watch OnlineMP4 Download
11.4 The Comparison Tests 題號：41Watch OnlineMP4 Download
11.4 The Comparison Tests 題號：43Watch OnlineMP4 Download
11.4 The Comparison Tests 題號：45Watch OnlineMP4 Download
11.5 Alternating Series 題號：簡介Watch OnlineMP4 Download
11.5 Alternating Series 題號：7Watch OnlineMP4 Download
11.5 Alternating Series 題號：17Watch OnlineMP4 Download
11.5 Alternating Series 題號：18Watch OnlineMP4 Download
11.5 Alternating Series 題號：25Watch OnlineMP4 Download
11.5 Alternating Series 題號：34Watch OnlineMP4 Download
11.5 Alternating Series 題號：35Watch OnlineMP4 Download
11.6 Absolute Convergence and the Ratio and Root Tests 題號：簡介Watch OnlineMP4 Download
11.6 Absolute Convergence and the Ratio and Root Tests 題號：3Watch OnlineMP4 Download
11.6 Absolute Convergence and the Ratio and Root Tests 題號：5Watch OnlineMP4 Download
11.6 Absolute Convergence and the Ratio and Root Tests 題號：22-28Watch OnlineMP4 Download
11.6 Absolute Convergence and the Ratio and Root Tests 題號：33Watch OnlineMP4 Download
11.6 Absolute Convergence and the Ratio and Root Tests 題號：34Watch OnlineMP4 Download
11.6 Absolute Convergence and the Ratio and Root Tests 題號：35Watch OnlineMP4 Download
11.6 Absolute Convergence and the Ratio and Root Tests 題號：38Watch OnlineMP4 Download
11.8 Power Series 題號：簡介Watch OnlineMP4 Download
11.8 Power Series 題號：4Watch OnlineMP4 Download
11.8 Power Series 題號：21Watch OnlineMP4 Download
11.8 Power Series 題號：30Watch OnlineMP4 Download
11.8 Power Series 題號：31Watch OnlineMP4 Download
11.8 Power Series 題號：33Watch OnlineMP4 Download
11.8 Power Series 題號：37Watch OnlineMP4 Download
11.8 Power Series 題號：40Watch OnlineMP4 Download
11.8 Power Series 題號：41
11.9 Representations of Functions as Power Series 題號：簡介		Watch OnlineMP4 Download
11.9 Representations of Functions as Power Series 題號：4Watch OnlineMP4 Download
11.9 Representations of Functions as Power Series 題號：12Watch OnlineMP4 Download
11.9 Representations of Functions as Power Series 題號：13Watch OnlineMP4 Download
11.9 Representations of Functions as Power Series 題號：26Watch OnlineMP4 Download
11.9 Representations of Functions as Power Series 題號：32Watch OnlineMP4 Download
11.9 Representations of Functions as Power Series 題號：38Watch OnlineMP4 Download
11.9 Representations of Functions as Power Series 題號：40Watch OnlineMP4 Download
12.1 Three-Dimensional Coordinate Systems 題號：9Watch OnlineMP4 Download
12.1 Three-Dimensional Coordinate Systems 題號：12Watch OnlineMP4 Download
12.1 Three-Dimensional Coordinate Systems 題號：38Watch OnlineMP4 Download
12.1 Three-Dimensional Coordinate Systems 題號：40Watch OnlineMP4 Download
12.2 Vectors 題號：24Watch OnlineMP4 Download
12.2 Vectors 題號：31Watch OnlineMP4 Download
12.2 Vectors 題號：34Watch OnlineMP4 Download
12.2 Vectors 題號：42Watch OnlineMP4 Download
12.3 The Dot Product 題號：簡介Watch OnlineMP4 Download
12.3 The Dot Product 題號：18,24Watch OnlineMP4 Download
12.3 The Dot Product 題號：31Watch OnlineMP4 Download
12.3 The Dot Product 題號：38Watch OnlineMP4 Download
12.3 The Dot Product 題號：45Watch OnlineMP4 Download
12.3 The Dot Product 題號：52,60Watch OnlineMP4 Download
12.4 The Cross Product 題號：簡介Watch OnlineMP4 Download
12.4 The Cross Product 題號：13,18,27Watch OnlineMP4 Download
12.4 The Cross Product 題號：34-49Watch OnlineMP4 Download
12.5 Equations of Lines and Planes 題號：18Watch OnlineMP4 Download
12.5 Equations of Lines and Planes 題號：48,62Watch OnlineMP4 Download
12.5 Equations of Lines and Planes 題號：73Watch OnlineMP4 Download
12.6 Cylinders and Quadric Surface 題號：21,28Watch OnlineMP4 Download
12.6 Cylinders and Quadric Surface 題號：41Watch OnlineMP4 Download
12.6 Cylinders and Quadric Surface 題號：44Watch OnlineMP4 Download
12.6 Cylinders and Quadric Surface 題號：50Watch OnlineMP4 Download
13.1 Vector Functions and Space Curves 題號：簡介Watch OnlineMP4 Download
13.1 Vector Functions and Space Curves 題號：9Watch OnlineMP4 Download
13.1 Vector Functions and Space Curves 題號：12Watch OnlineMP4 Download
13.1 Vector Functions and Space Curves 題號：21Watch OnlineMP4 Download
13.1 Vector Functions and Space Curves 題號：23Watch OnlineMP4 Download
13.1 Vector Functions and Space Curves 題號：38Watch OnlineMP4 Download
13.1 Vector Functions and Space Curves 題號：42Watch OnlineMP4 Download
13.2 Derivatives and Integrals of Vector Functions 題號：簡介Watch OnlineMP4 Download
13.2 Derivatives and Integrals of Vector Functions 題號：7Watch OnlineMP4 Download
13.2 Derivatives and Integrals of Vector Functions 題號：12Watch OnlineMP4 Download
13.2 Derivatives and Integrals of Vector Functions 題號：21Watch OnlineMP4 Download
13.2 Derivatives and Integrals of Vector Functions 題號：26Watch OnlineMP4 Download
13.2 Derivatives and Integrals of Vector Functions 題號：32Watch OnlineMP4 Download
13.2 Derivatives and Integrals of Vector Functions 題號：40Watch OnlineMP4 Download
13.2 Derivatives and Integrals of Vector Functions 題號：48Watch OnlineMP4 Download
13.3 Arc Length And Curvature 題號：簡介Watch OnlineMP4 Download
13.3 Arc Length And Curvature 題號：3Watch OnlineMP4 Download
13.3 Arc Length And Curvature 題號：16Watch OnlineMP4 Download
13.3 Arc Length And Curvature 題號：19Watch OnlineMP4 Download
13.3 Arc Length And Curvature 題號：28,32Watch OnlineMP4 Download
13.3 Arc Length And Curvature 題號：44Watch OnlineMP4 Download
13.3 Arc Length And Curvature 題號：49Watch OnlineMP4 Download
13.3 Arc Length And Curvature 題號：60Watch OnlineMP4 Download
14.1 Functions of Several Variables 題號：2Watch OnlineMP4 Download
14.1 Functions of Several Variables 題號：18Watch OnlineMP4 Download
14.1 Functions of Several Variables 題號：24Watch OnlineMP4 Download
14.1 Functions of Several Variables 題號：30Watch OnlineMP4 Download
14.1 Functions of Several Variables 題號：36Watch OnlineMP4 Download
14.1 Functions of Several Variables 題號：44Watch OnlineMP4 Download
14.1 Functions of Several Variables 題號：56Watch OnlineMP4 Download
14.1 Functions of Several Variables 題號：63Watch OnlineMP4 Download
14.1 Functions of Several Variables 題號：66Watch OnlineMP4 Download
14.2 Limits and Continuity 題號：簡介Watch OnlineMP4 Download
14.2 Limits and Continuity 題號：8,16Watch OnlineMP4 Download
14.2 Limits and Continuity 題號：22Watch OnlineMP4 Download
14.2 Limits and Continuity 題號：26Watch OnlineMP4 Download
14.2 Limits and Continuity 題號：32,38Watch OnlineMP4 Download
14.2 Limits and Continuity 題號：40Watch OnlineMP4 Download
14.3 Partial Derivatives 題號：簡介Watch OnlineMP4 Download
14.3 Partial Derivatives 題號：9Watch OnlineMP4 Download
14.3 Partial Derivatives 題號：37Watch OnlineMP4 Download
14.3 Partial Derivatives 題號：43Watch OnlineMP4 Download
14.3 Partial Derivatives 題號：48Watch OnlineMP4 Download
14.3 Partial Derivatives 題號：64Watch OnlineMP4 Download
14.3 Partial Derivatives 題號：76Watch OnlineMP4 Download
14.4 Tangent Plans and Differentials 題號：簡介Watch OnlineMP4 Download
14.4 Tangent Plans and Differentials 題號：5Watch OnlineMP4 Download
14.4 Tangent Plans and Differentials 題號：14Watch OnlineMP4 Download
14.4 Tangent Plans and Differentials 題號：19Watch OnlineMP4 Download
14.4 Tangent Plans and Differentials 題號：30Watch OnlineMP4 Download
14.4 Tangent Plans and Differentials 題號：36Watch OnlineMP4 Download
14.4 Tangent Plans and Differentials 題號：41Watch OnlineMP4 Download
14.4 Tangent Plans and Differentials 題號：44Watch OnlineMP4 Download
14.4 Tangent Plans and Differentials 題號：45Watch OnlineMP4 Download
14.4 Tangent Plans and Differentials 題號：46Watch OnlineMP4 Download
14.5 The Chain Rule 題號：4Watch OnlineMP4 Download
14.5 The Chain Rule 題號：14Watch OnlineMP4 Download
14.5 The Chain Rule 題號：26,33Watch OnlineMP4 Download
14.5 The Chain Rule 題號：40Watch OnlineMP4 Download
14.5 The Chain Rule 題號：45Watch OnlineMP4 Download
14.5 The Chain Rule 題號：54Watch OnlineMP4 Download
14.5 The Chain Rule 題號：55Watch OnlineMP4 Download
14.5 The Chain Rule 題號：57Watch OnlineMP4 Download
14.6 Directional Derivatives and the Gradient Vector 題號：簡介Watch OnlineMP4 Download
14.6 Directional Derivatives and the Gradient Vector 題號：14Watch OnlineMP4 Download
14.6 Directional Derivatives and the Gradient Vector 題號：31Watch OnlineMP4 Download
14.6 Directional Derivatives and the Gradient Vector 題號：38Watch OnlineMP4 Download
14.6 Directional Derivatives and the Gradient Vector 題號：42Watch OnlineMP4 Download
14.6 Directional Derivatives and the Gradient Vector 題號：58Watch OnlineMP4 Download
14.6 Directional Derivatives and the Gradient Vector 題號：61Watch OnlineMP4 Download
14.6 Directional Derivatives and the Gradient Vector 題號：64Watch OnlineMP4 Download
14.7 Maximum and Minimum Values 題號：簡介Watch OnlineMP4 Download
14.7 Maximum and Minimum Values 題號：4Watch OnlineMP4 Download
14.7 Maximum and Minimum Values 題號：19Watch OnlineMP4 Download
14.7 Maximum and Minimum Values 題號：32Watch OnlineMP4 Download
14.7 Maximum and Minimum Values 題號：47Watch OnlineMP4 Download
14.7 Maximum and Minimum Values 題號：54Watch OnlineMP4 Download
14.7 Maximum and Minimum Values 題號：55Watch OnlineMP4 Download
14.8 Lagrange Multipliers 題號：簡介Watch OnlineMP4 Download
14.8 Lagrange Multipliers 題號：18Watch OnlineMP4 Download
14.8 Lagrange Multipliers 題號：21Watch OnlineMP4 Download
14.8 Lagrange Multipliers 題號：41Watch OnlineMP4 Download
14.8 Lagrange Multipliers 題號：46Watch OnlineMP4 Download
15.1 Double Integrals over Rectangles 題號：13Watch OnlineMP4 Download
15.2 Iterated Integrals 題號：10Watch OnlineMP4 Download
15.2 Iterated Integrals 題號：19Watch OnlineMP4 Download
15.2 Iterated Integrals 題號：23Watch OnlineMP4 Download
15.2 Iterated Integrals 題號：28Watch OnlineMP4 Download
15.2 Iterated Integrals 題號：30Watch OnlineMP4 Download
15.3 Double Integrals over General Regions 題號：21Watch OnlineMP4 Download
15.3 Double Integrals over General Regions 題號：8Watch OnlineMP4 Download
15.3 Double Integrals over General Regions 題號：27Watch OnlineMP4 Download
15.3 Double Integrals over General Regions 題號：31Watch OnlineMP4 Download
15.3 Double Integrals over General Regions 題號：43Watch OnlineMP4 Download
15.3 Double Integrals over General Regions 題號：49Watch OnlineMP4 Download
15.3 Double Integrals over General Regions 題號：51Watch OnlineMP4 Download
15.3 Double Integrals over General Regions 題號：58Watch OnlineMP4 Download
15.4 Double Integrals in Polar Coordinates 題號：9Watch OnlineMP4 Download
15.4 Double Integrals in Polar Coordinates 題號：13Watch OnlineMP4 Download
15.4 Double Integrals in Polar Coordinates 題號：17Watch OnlineMP4 Download
15.4 Double Integrals in Polar Coordinates 題號：25Watch OnlineMP4 Download
15.4 Double Integrals in Polar Coordinates 題號：35Watch OnlineMP4 Download
15.6 Triple Integrals 題號：11Watch OnlineMP4 Download
15.6 Triple Integrals 題號：16Watch OnlineMP4 Download
15.6 Triple Integrals 題號：17Watch OnlineMP4 Download
15.6 Triple Integrals 題號：20Watch OnlineMP4 Download
15.6 Triple Integrals 題號：27Watch OnlineMP4 Download
15.6 Triple Integrals 題號：31Watch OnlineMP4 Download
15.7 Triple Integrals in Cylindrical Coordinates 題號：11Watch OnlineMP4 Download
15.7 Triple Integrals in Cylindrical Coordinates 題號：18Watch OnlineMP4 Download
15.7 Triple Integrals in Cylindrical Coordinates 題號：21Watch OnlineMP4 Download
15.7 Triple Integrals in Cylindrical Coordinates 題號：28Watch OnlineMP4 Download
15.8 Triple Integrals in Spherical Coordinates 題號：4Watch OnlineMP4 Download
15.8 Triple Integrals in Spherical Coordinates 題號：8Watch OnlineMP4 Download
15.8 Triple Integrals in Spherical Coordinates 題號：10Watch OnlineMP4 Download
15.8 Triple Integrals in Spherical Coordinates 題號：12Watch OnlineMP4 Download
15.8 Triple Integrals in Spherical Coordinates 題號：17Watch OnlineMP4 Download
15.8 Triple Integrals in Spherical Coordinates 題號：21Watch OnlineMP4 Download
15.8 Triple Integrals in Spherical Coordinates 題號：25Watch OnlineMP4 Download
15.8 Triple Integrals in Spherical Coordinates 題號：29(a)Watch OnlineMP4 Download
15.8 Triple Integrals in Spherical Coordinates 題號：36Watch OnlineMP4 Download
15.8 Triple Integrals in Spherical Coordinates 題號：39Watch OnlineMP4 Download
15.9 Change of Variables in Multiple Integrals 題號：5Watch OnlineMP4 Download
15.9 Change of Variables in Multiple Integrals 題號：11Watch OnlineMP4 Download
15.9 Change of Variables in Multiple Integrals 題號：13Watch OnlineMP4 Download
15.9 Change of Variables in Multiple Integrals 題號：19Watch OnlineMP4 Download
15.9 Change of Variables in Multiple Integrals 題號：21Watch OnlineMP4 Download
15.9 Change of Variables in Multiple Integrals 題號：23Watch OnlineMP4 Download

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.

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