Calculus II（2023 ）

王姝娜

目录

  • 1 Basic Information
    • 1.1 Course Description
    • 1.2 Course Syllabus
    • 1.3 Schedule
    • 1.4 Grading
    • 1.5 Textbook and Website
  • 2 Chapter 6 Application of Definite Integral
    • 2.1 Volume Using Cross-section
      • 2.1.1 Quiz 6.1
      • 2.1.2 Supplement
    • 2.2 Volume Using Cylinder Shell
      • 2.2.1 Quiz 6.2
    • 2.3 Arc Length
      • 2.3.1 Quiz 6.3
    • 2.4 Area of Surfaces of Revolution
      • 2.4.1 Quiz 6.4
    • 2.5 Supplement:Moments and Center of Mass
    • 2.6 Test-Ch6 Application of Integral
    • 2.7 Light Your Way
  • 3 Chapter 7 Integrals and Transcendental Functions
    • 3.1 Definition of Log and Exp
      • 3.1.1 Quiz 7.1
    • 3.2 Separable Differential Equation
      • 3.2.1 Quiz 7.2
    • 3.3 Video:Hypobolic Function
      • 3.3.1 Quiz 7.3
    • 3.4 Relative Rates of Growth
      • 3.4.1 Quiz 7.4
    • 3.5 Test-Ch7 Integrals and Transcendental Functions
    • 3.6 Light your way
  • 4 Chapter 8 Techniques of Integration
    • 4.1 Integration Warm up
      • 4.1.1 Quiz 8.1
    • 4.2 Integration by Parts
      • 4.2.1 Quiz 8.2
    • 4.3 Trigonometric Integrals
      • 4.3.1 Quiz 8.3
    • 4.4 Trigonometric Substitution
      • 4.4.1 Quiz 8.4
    • 4.5 Integration of Rational Function by Partial Functions
      • 4.5.1 Quiz 8.5
    • 4.6 Numerical Integration
      • 4.6.1 Quiz 8.7
    • 4.7 Improper Integral
      • 4.7.1 Quiz 8.8
    • 4.8 Probability
    • 4.9 Test-Ch8 Techniques of Integration
    • 4.10 Light your way
  • 5 Chapter 9 First-Order Differential Equation
    • 5.1 Solution,Slope Field,and Euler’s Method
      • 5.1.1 Quiz 9.1
    • 5.2 First-Order Differential Equation
      • 5.2.1 Quiz 9.2
    • 5.3 Application
      • 5.3.1 Quiz 9.3
    • 5.4 Graphical Solutions of Autonomous Equations
      • 5.4.1 Quiz 9.4
    • 5.5 Supplement:Systems of Equations and Phase Planes
    • 5.6 Test-Ch9 First-Order Differential Equations
    • 5.7 Light your way
  • 6 Chapter 10 Infinite Sequences and Series
    • 6.1 Sequence
      • 6.1.1 Quiz 10.1
    • 6.2 Infinite Series
      • 6.2.1 Quiz 10.2
    • 6.3 The Integral Test
      • 6.3.1 Quiz 10.3
    • 6.4 Comparison Tests
      • 6.4.1 Quiz 10.4
    • 6.5 Absolute Convergence；The Ratio and Root Tests
      • 6.5.1 Quiz 10.5
    • 6.6 Alternating Series and Conditional Converge
      • 6.6.1 Quiz 10.6
    • 6.7 Power Series
      • 6.7.1 Quiz 10.7
    • 6.8 Taylor and Maclaurin Series;Application
      • 6.8.1 Quiz 10.8
    • 6.9 Test-Ch10 Infinite Sequences and Series
    • 6.10 Light your way
  • 7 问卷调查
    • 7.1 问卷调查
Graphical Solutions of Autonomous Equations
  • 1 学习目标
  • 2 学习视频
  • 3 学习视频
  • 4 练习

1. What is an autonomous differential equation? What are its equilibrium values? How do they differ from critical points? What is a stable equilibrium value? Unstable?

2. How do you construct the phase line for an autonomous differential equation? How does the phase line help you produce a graph which qualitatively depicts a solution to the differential equation?

3. Why is the exponential model unrealistic for predicting long-term population growth? How does the logistic model correct for the deficiency in the exponential model for population growth? What is the logistic differential equation? What is the form of its solution? Describe the graph of the logistic solution.