107 學年度數一甲微積分課程 (Calculus I, II):根據 James Stewart: Calculus, Early Transcendentals, 8th Edition 的內容製作課程影片。

第一學期

• Chapter 0 Introduction      講義請點此
• Chapter 1 Functions and Models      講義請點此
  • 1.1 Four Ways to Represent a Function
  • 1.2 Mathematical Models: A Catalog of Essential Functions
  • 1.3 New Functions from Old Functions
  • 1.4 Exponential Functions
  • 1.5 Inverse Functions and Logarithms
• Chapter 2 Limits and Derivatives      講義請點此
  • 2.1 The Tangent and Velocity Problems
  • 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
• Chapter 3 Differentiation Rules      講義請點此
  • 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
  • 3.8 Exponential Growth and Decay
  • 3.9 Related Rates
  • 3.10 Linear Approximations and Differentials
  • 3.11 Hyperbolic Functions
• Chapter 4 Applications of Differentiation      講義請點此
  • 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
  • 4.8 Newton’s Method
  • 4.9 Antiderivatives
• Chapter 5 Integrals      講義請點此
  • 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
• Chapter 6 Applications of Integration      講義請點此
  • 6.1 Areas Between Curves
  • 6.2 Volume
  • 6.3 Volumes by Cylindrical Shells
  • 6.5 Average Value of a Function
• Chapter 7 Techniques of Integration      講義請點此
  • 7.1 Integration by Parts
  • 7.2 Trigonometric Integrals
  • 7.3 Trigonometric Substitution
  • 7.4 Integration of Rational Functions by Partial Fractions
  • 7.5 Strategy for Integration
  • 7.8 Improper Integrals
• Chapter 8 Further Applications of Integration      講義請點此
  • 8.1 Arc Length
  • 8.2 Area of a Surface of Revolution
• Chapter 9 Differential Equations       9.1 講義       9.4 講義       9.4 講義       9.4 講義       9.5 講義
  • 9.1 Modeling with Differential Equations
  • 9.2 Direction Fields and Euler’s Method
  • 9.3 Separable Equations
  • 9.4 Models for Population Growth
  • 9.5 Linear Equations
• Chapter 10 Parametric Equations and Polar Coordinates      講義請點此
  • 10.1 Curves Defined by Parametric Equations
  • 10.2 Calculus with Parametric Curves
  • 10.3 Polar Coordinates
  • 10.4 Areas and Lengths in Polar Coordinates

第二學期

• Chapter 0 Introduction      講義請點此
• Chapter 11 Infinite Sequences and Series      講義請點此
  • 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
  • 11.7 Strategy for Testing Series
  • 11.8 Power Series
  • 11.9 Representations of Functions as Power Series
  • 11.10 Taylor and Maclaurin Series
  • 11.11 Applications of Taylor Polynomials
• Chapter 12 Vectors and Geometry of Space      講義請點此
  • 12.6 Cylinders and Quadric Surfaces
• Chapter 13 Vector Functions      講義請點此
  • 13.1 Vector Functions and Space Curves
  • 13.2 Derivatives and Integrals of Vector Functions
  • 13.3 Arc Length and Curvature
  • 13.4 Motion in Space: Velocity and Acceleration
• Chapter 14 Partial Derivatives      講義請點此
  • 14.1 Functions of Several Variables
  • 14.2 Limits and Continuity
  • 14.3 Partial Derivatives
  • 14.4 Tangent Planes and Linear Approximation
  • 14.5 The Chain Rule
  • 14.6 Directional Derivatives and the Gradient Vector
  • 14.7 Maximum and Minimum Values
  • 14.8 Lagrange Multipliers
• Chapter 15 Multiple Integrals      講義請點此
  • 15.1 Double Integrals over Rectangles
  • 15.2 Double Integrals over General Regions
  • 15.3 Double Integrals in Polar Coordinates
  • 15.4 Applications of Double Integrals
  • 15.5 Surface Area
  • 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
• Chapter 16 Vector Calculus      講義請點此       16.5 講義       16.6 講義       16.7 講義       16.8 講義       16.9 講義       16.10 講義
  • 16.1 Vector Fields
  • 16.2 Line Integrals
  • 16.3 The Fundamental Theorem for Line Integrals
  • 16.4 Green’s Theorem
  • 16.5 Curl and Divergence
  • 16.6 Parametric Surfaces and Their Areas
  • 16.7 Surface Integrals
  • 16.8 Stokes’ Theorem
  • 16.9 The Divergence Theorem
  • 16.10 Summary
• Chapter 17 Second-Order Differential Equations       17.1 講義       17.2 講義       17.3 講義       17.4 講義
  • 17.1 Second-Order Linear Equations
  • 17.2 Nonhomogeneous Linear Equations
  • 17.3 Applications of Second-Order Differential Equations
  • 17.4 Series Solutions
• Acknowledgements