Dave's Web Corner

MTH-264 Week 3 (January 21-27)

• Outline
• Assessments
• Handouts
• Videos
• Technology

Outline

1.6 Equilibria and the Phase Line

• recommended: 1, 3, 7, 8, 13, 15, 18, 19, 20, 28, 29, 30, 32, 39, 42, 44, 46
• autonomous, first-order equations \( y'=f(y) \)
• equilibrium points: sink, source, or node
• slope field and phase line
• the relationship between \( f(y) \), the phase line, and \( y(t) \)

1.7 Bifurcations

• recommended: 1, 2, 3, 4, 5, 7, 8, 12, 13, 14, 15, 18, 19, 20, 21, 22
• families of first-order equations: parameters
• families of phase lines: bifurcation diagrams
• bifurcation: the moment of fundamental change

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, January 25: 1.3 - 1.4 - 1.5 -
  • due Thursday, February 1: 1.6 - 1.7 -
  • due Thursday, February 8: 1.8 - 1.9 - 2.1 -
• 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

Videos

• Mixing Problems
  • Setting up a Mixing Problem
  • Solving a Mixing Problem
  • Graphing a Mixing Problem
• Euler's Method
  • Euler's Method in a Spreadsheet
• 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
• all MTH-264 Videos (YouTube playlist)

Technology

• Communication
  • Zoom
  • Microsoft Lens
  • Apple Notes
  • Adobe Scan
  • Joining a Zoom Webinar
  • MTH-264 Assignments folder
• GeoGebra
  • Exercise-01-06-19.ggb
  • Linear Equation.ggb
• Desmos
  • Exercise 1.6 #19
  • Exercise 1.6 #20
  • Exercise 1.8 #28 alt
  • First-Order Linear Family
  • Fox Squirrels
  • 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
  • StreamPlot[]-Coloring-Example.nb