Dave's Web Corner

MTH-264 Week 3 (January 19-25)

• 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
  • Submit your assessment as a single PDF file to the Assessment Folder inside your assigned Google Drive 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 Wednesday, January 22: 1.2 - 39 alt, 1.3 - 22 alt, 1.4 - 22 alt, 1.5 - 18
  • due Wednesday, January 29: 1.6 - 18 alt, 20 alt, 1.7 - 1 alt, 8 alt, 22
  • due Wednesday, February 5: 1.8 - 11 alt, 1.9 - 24 alt, 31 alt
• Exams
  • Wednesday, February 19: Exam 1
    • Exam 1 (preview) (solutions)
    • Exam 1 covers sections 1.1-1.9, 2.1-2.3
    • A preview will be released by 10:59pm on Wednesday, February 12 and Exam 1 will be written in class from 7:00pm-9:00pm on Wednesday, February 19.

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

• First Principles
  • The Utility of Exponential Growth/Decay
• 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

Technology

• Communication
  • Zoom
  • Joining a Zoom Webinar
• 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