Solution by Integrating Factors

• Course Home
• Syllabus

  • Meet the TAs
• Unit I: First Order Differential Equations

  • Conventions
  • Basic DE's
  • Geometric Methods
  • Numerical Methods
  • Linear ODE's
  • Integrating Factors
  • Complex Arithmetic
  • Sinusoidal Functions
  • Constant Coefficients
  • Exponential Input
  • Autonomous Equations
  • Linear vs. Nonlinear
  • Exam 1
• Unit II: Second Order Constant Coefficient Linear Equations

  • Characteristic Equation
  • Damped Oscillators
  • Exponential Response
  • Gain and Phase Lag
  • Undetermined Coefficients
  • Linear Operators
  • Pure Resonance
  • Frequency Response
  • Applications
  • Exam 2
• Unit III: Fourier Series and Laplace Transform

  • Fourier Series: Basics
  • Operations
  • Periodic Input
  • Step and Delta
  • Impulse Response
  • Convolution
  • Laplace Transform
  • Partial Fractions
  • Solving IVP's
  • Transfer Functions
  • Poles
  • Exam 3
• Unit IV: First-order Systems

  • Linear Systems
  • Matrix Methods
  • Phase Portraits
  • Matrix Exponentials
  • Nonlinear Systems
  • Linearization
  • Limit Cycles and Chaos
• Final Exam
• Download Course Materials

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Session Overview

In this session we will learn how to solve first order linear equations. We will apply the technique to solve the DE's for several different models.

Session Activities

Read the course notes:

• Solutions by Integrating Factors: Introduction (PDF)

Watch the lecture video clip:

• Solutions to Linear First Order ODE's (00:19:37)

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  Solutions to Linear First Order ODE's (00:19:37)

  > Download from iTunes U (MP4)

  > Download from Internet Archive (MP4)

• Transcript (PDF)

Read the course notes:

• Solutions to Linear First Order ODE's (PDF)
• Example: Heat Diffusion (PDF)

Check Yourself

Take the quizzes:

• The Meaning of k (PDF)
• Choices (PDF)
• Answer (PDF)


• Units (PDF)
• Choices (PDF)
• Answer (PDF)

Session Activities

Read the course notes:

• Superposition and the Integrating Factors Solution (PDF)

Check Yourself

Take the quiz:

• Is It Particular? (PDF)
• Choices (PDF)
• Answer (PDF)

Session Activities

Watch the problem solving video:

• Solutions of First Order Linear Equations (00:08:55)

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  Solutions of First Order Linear Equations

  > Download from iTunes U (MP4)

  > Download from Internet Archive (MP4)

• Transcript (PDF)

Complete the practice problems:

• Practice Problems 5 (PDF)
• Practice Problems 5 Solutions (PDF)

Check Yourself

Complete the problem sets:

• Problem Set Part I Problems (PDF)
• Problem Set Part I Solutions (PDF)


• Problem Set Part II Problems (PDF)
• Problem Set Part II Solutions (PDF)

 

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