微積分 (Calculus):根據 James Stewart: Calculus, Early Transcendentals, 8th Edition 的內容製作課程影片。

• Chapter 1 Functions and Models
  • PDF 1.1 Four Ways to Represent a Function
  • PDF 1.2 Mathematical Models: A Catalog of Essential Functions
  • PDF 1.3 New Functions from Old Functions
  • PDF 1.4 Exponential Functions
  • PDF 1.5 Inverse Functions and Logarithms
• Chapter 2 Limits and Derivatives
  • PDF 2.1 The Tangent and Velocity Problems
  • PDF 2.2 The Limit of a Function
  • PDF 2.3 Calculating Limits Using the Limit Laws
  • PDF 2.4 The Precise Definition of a Limit
  • PDF 2.5 Continuity
  • PDF 2.6 Limits at Infinity; Horizontal Asymptotes
  • PDF 2.7 Derivatives and Rates of Change
  • PDF 2.8 The Derivative as a Function
• Chapter 3 Differentiation Rules
  • PDF 3.1 Derivatives of Polynomials and Exponential Functions
  • PDF 3.2 The Product and Quotient Rules
  • PDF 3.3 Derivatives of Trigonometric Functions
  • PDF 3.4 The Chain Rule
  • PDF 3.5 Implicit Differentiation
  • PDF 3.6 Derivatives of Logarithmic Functions
  • PDF 3.8 Exponential Growth and Decay
  • PDF 3.9 Related Rates
  • PDF 3.10 Linear Approximations and Differentials
  • PDF 3.11 Hyperbolic Functions
• Chapter 4 Applications of Differentiation
  • PDF 4.1 Maximum and Minimum Values
  • PDF 4.2 The Mean Value Theorem
  • PDF 4.3 How Derivatives Affect the Shape of a Graph
  • PDF 4.4 Indeterminate Forms and l’Hospital’s Rule
  • PDF 4.5 Summary of Curve Sketching
  • PDF 4.7 Optimization Problems
  • PDF 4.9 Antiderivatives
• Chapter 5 Integrals
  • PDF 5.1 Areas and Distances
  • PDF 5.2 The Definite Integral
  • PDF 5.3 The Fundamental Theorem of Calculus
  • PDF 5.4 Indefinite Integrals and the Net Change Theorem
  • PDF 5.5 The Substitution Rule
• Chapter 6 Applications of Integration
  • PDF 6.1 Areas Between Curves
  • PDF 6.2 Volume
  • PDF 6.3 Volumes by Cylindrical Shells
  • PDF 6.5 Average Value of a Function
• Chapter 7 Techniques of Integration
  • PDF 7.1 Integration by Parts
  • PDF 7.2 Trigonometric Integrals
  • PDF 7.3 Trigonometric Substitution
  • PDF 7.4 Integration of Rational Functions by Partial Fractions
  • PDF 7.5 Strategy for Integration
  • PDF 7.8 Improper Integrals
• Chapter 8 Further Applications of Integration
  • PDF 8.1 Arc Length
  • PDF 8.2 Area of a Surface of Revolution
  • PDF 8.3 Applications to Physics and Engineering
• Chapter 9 Differential Equations
  • PDF 9.1 Modeling with Differential Equations
  • PDF 9.3 Separable Equations
  • PDF 9.4 Models for Population Growth
  • PDF 9.5 Linear Equations
• Chapter 10 Parametric Equations and Polar Coordinates
  • PDF 10.1 Curves Defined by Parametric Equations
  • PDF 10.2 Calculus with Parametric Curves
  • PDF 10.3 Polar Coordinates
  • PDF 10.4 Areas and Lengths in Polar Coordinates
• Chapter 11 Infinite Sequences and Series
  • PDF 11.1 Sequences
  • PDF 11.2 Series
  • PDF 11.3 The Integral Test and Estimates of Sums
  • PDF 11.4 The Comparison Tests
  • PDF 11.5 Alternating Series
  • PDF 11.6 Absolute Convergence and the Ratio and Root Tests
  • PDF 11.7 Strategy for Testing Series
  • PDF 11.8 Power Series
  • PDF 11.9 Representations of Functions as Power Series
  • PDF 11.10 Taylor and Maclaurin Series
  • PDF 11.11 Applications of Taylor Polynomials
• Chapter 12 Vectors and Geometry of Space
  • PDF 12.6 Cylinders and Quadric Surfaces
• Chapter 13 Vector Functions
  • PDF 13.1 Vector Functions and Space Curves
  • PDF 13.2 Derivatives and Integrals of Vector Functions
  • PDF 13.3 Arc Length and Curvature
• Chapter 14 Partial Derivatives
  • PDF 14.1 Functions of Several Variables
  • PDF 14.2 Limits and Continuity
  • PDF 14.3 Partial Derivatives
  • PDF 14.4 Tangent Planes and Linear Approximation
  • PDF 14.5 The Chain Rule
  • PDF 14.6 Directional Derivatives and the Gradient Vector
  • PDF 14.7 Maximum and Minimum Values
  • PDF 14.8 Lagrange Multipliers
• Chapter 15 Multiple Integrals
  • PDF 15.1 Double Integrals over Rectangles
  • PDF 15.2 Double Integrals over General Regions
  • PDF 15.3 Double Integrals in Polar Coordinates
  • PDF 15.4 Applications of Double Integrals
  • PDF 15.5 Surface Area
  • PDF 15.6 Triple Integrals
  • PDF 15.7 Triple Integrals in Cylindrical Coordinates
  • PDF 15.8 Triple Integrals in Spherical Coordinates
  • PDF 15.9 Change of Variables in Multiple Integrals
• Chapter 16 Vector Calculus
  • PDF 16.1 Vector Fields
  • PDF 16.2 Line Integrals
  • PDF 16.3 The Fundamental Theorem for Line Integrals
  • PDF 16.4 Green’s Theorem
  • PDF 16.5 Curl and Divergence
  • PDF 16.6 Parametric Surfaces and Their Areas
  • PDF 16.7 Surface Integrals
  • PDF 16.8 Stokes’ Theorem
  • PDF 16.9 The Divergence Theorem
  • PDF 16.10 Summary
• Chapter 17 Second-Order Differential Equations
  • PDF 17.1 Second-Order Linear Equations
  • PDF 17.2 Nonhomogeneous Linear Equations