Dave's Web Corner

MTH-264 Week 4 (January 28-February 3)

• Outline
• Assessments
• Handouts
• Videos
• Technology

Outline

1.8 Linear Equations

• recommended: 1, 5, 8, 9, 10, 13, 15, 17, 20, 22, 24, 27, 30, 31
• homogeneous and nonhomogeneous linear equations
• the linearity principle
• the extended linearity principle
  • the homogeneous solution
  • the particular solution
  • the general solution
• the method of undetermined coefficients
• transient and steady-state solutions

1.9 Integrating Factors for Linear Equations

• recommended: 3, 5, 6, 7, 8, 10, 11, 12, 13, 21, 22, 24, 25, 26
• an important special case
• the product rule to the rescue
• the formula that solves first-order linear equations

2.1 Modeling via Systems

• recommended: 1, 2, 7, 8, 15, 16, 17, 19, 20, 21, 23
• phase planes and phase portraits
• converting second-order equations to first-order systems
• important examples
  • predator-prey systems
  • simple harmonic oscillators

Assessments

• Deadlines and File Submission
  • All assessments are due to our MTH-264 Assignments folder by 11:59pm on the date indicated.
  • No late assessments are accepted. If you have a conflict with a deadline, contact me before the deadline.
  • Solutions are posted under these links after the deadline.
• Homework
  • due Thursday, February 1: 1.6 - 1.7 -
  • due Thursday, February 8: 1.8 - 1.9 - 2.1 -
  • due Thursday, February 15: 2.2 - 2.3 - 2.4 - 2.5 -
• Exams
  • due Thursday, February 22: Exam 1
    • Exam 1 (solutions)
    • Exam 1 covers sections 1.1-1.9, 2.1-2.5
    • Exam 1 will be released by 11:59pm on Thursday, February 15 and is due by 11:59pm on Thursday, February 22.

Handouts

• Announcements
  • Schmidt Award
  • Math Graduate Award
  • Honors Program introduction
  • Tutoring Center services
• Technology Tips
  • Download and Install Mathematica
  • Install DETools
  • TI-89 Slope Fields
  • TI-89 Direction Fields
• Separable Equations
  • The MVPs of ODEs
  • Basic Separable Equation Examples
• First-Order Linear Equations
  • Undetermined Coefficients: Second Guess
• Euler's Method
  • Euler Practice (solution)
  • Euler System Practice (solution)

Videos

• Mixing Problems
  • Setting up a Mixing Problem
  • Solving a Mixing Problem
  • Graphing a Mixing Problem
• Phase Lines
  • From Phase Line to Slope Function
  • From Slope Function to Phase Line
• Bifurcation
  • Basic Phase Line and Bifurcation
  • Another Phase Line and Bifurcation
• Method of Undetermined Coefficients
  • Construct the Homogeneous Solution
  • Construct the Particular Solution
  • Apply Initial Conditions
• Method of the Integrating Factor
  • Construct the Integrating Factor
  • Evaluate the Integrating Formula
  • Apply the Initial Condition
• First Order System Basics
  • Converting from Second Order Equation to First Order System
  • What is a Phase Portrait
  • Direction Field of a First Order System
  • Relating Solution Graphs in the xy- tx- and ty-Planes
  • Vector Notation for a First Order System
• all MTH-264 Videos (YouTube playlist)

Technology

• Communication
  • Zoom
  • Microsoft Lens
  • Apple Notes
  • Adobe Scan
  • Joining a Zoom Webinar
  • MTH-264 Assignments folder
• GeoGebra
  • Linear Equation.ggb
• Desmos
  • Fox Squirrels
  • Exercise 1.8 #28 alt
  • First-Order Linear Family
  • Retirement
• Mathematica
  • Illustrating the DSolve Command.nb
  • Slope Fields and Direction Fields.nb
  • Slope Fields and Solutions.nb
  • First Order Linear Equations.nb
  • First Order Linear Family.nb
  • Exercise-01-08-28-alt.nb
  • First Order Linear Systems.nb
  • First Order Systems.nb
  • StreamPlot[]-Coloring-Example.nb