Dave's Web Corner

MTH-264 Week 7 (February 18-24)

• Outline
• Assessments
• Handouts
• Videos
• Technology

Outline

2.7 The SIR Model of an Epidemic (removed from our outline due to weather cancelation)

• recommended: 1, 3, 5, 6, 7, 9
• we assume that every member of a population is either S[usceptible], I[nfected], or R[ecovered]
• members of the population move from one group to another according to varying assumptions
• numerical analysis
• phase plane analysis
• analytic description
• this basic model can form the basis for more complicated models used in practice

3.1 Properties of Linear Systems and the Linearity Principle

• recommended: 5, 9, 10, 11, 12, 13, 14, 24, 26, 27, 28, 29
• exploiting vector and matrix notation
• equilibrium points of a linear system
• singular and nonsingular matrices, determinant
• linear independence and solutions to initial value problems

3.2 Straight-line Solutions

• recommended: 5, 7, 10, 11, 12, 13, 14, 20, 22, 23, 24
• the combination of direction and growth/decay
• the characteristic polynomial
• eigenvalues and eigenvectors, how to compute them
• the general solution of a linear first-order system

3.3 Phase Portraits for Linear Systems with Real Eigenvalues

• recommended: 3, 6, 7, 10, 11, 12, 14, 15, 16, 19, 20, 21, 22
• sink, source, and saddle
• phase planes and the dominant eigenvalue
• qualitative accuracy in tx- and ty-graphs

3.4 Complex Eigenvalues

• recommended: 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 22, 26
• spiral sink, spiral source, and center
• de moivre's theorem and euler's formula
• growth or decay and oscillation, natural frequency
• efficient calculation with complex numbers

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 22: (none)
  • due Thursday, February 29: 3.1 - 3.2 - 3.3 - 3.4 -
  • due Thursday, March 7: (none)
• 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
• Second-Order Linear Equations
  • Second Order Linear Equations
  • Forced Damped Harmonic Oscillator Graphs
• Linear Systems
  • Linear Systems Handout
  • Introduction to Linear Systems
  • Eigenvectors
  • Constructing Eigenvectors
  • Comparing Second Order Equation to First Order System
  • Sink, Source, Saddle
  • Solution Independent of Complex Eigenvalue Choice
  • Spiral Sink, Spiral Source, Center
  • Almost Spiral Sink and Source
  • Sunburst Sink and Source
  • Equilibrium Line Sink and Source
  • Classification of Linear Systems
  • The Trace Determinant Plane
  • Linear Systems Practice

Videos

• Linear Systems: Basics
  • Matrices and Vectors
  • Matrix Multiplication
  • Trace and Determinant
  • The Characteristic Equation of a Matrix
  • Quadratic Formula Shortcut
  • A Formula of Euler
  • The Adjusted Matrix
• Linear Systems: Real, Non-zero Eigenvalues
  • Linearly Independent Solutions
  • General Solutions to a Linear System
  • Specific Solutions
  • Basic Eigenvalues and Eigenvectors
  • The Hooked Exponential
  • Straight Line Solutions
  • The Dominant Eigenvalue
  • Phase Portraits - Sink, Saddle, Source
  • The Five Major Cases Completed
• Linear Systems: Complex Eigenvalues
  • Complex Eigenvalue Choice
  • Best Practices for Choosing Complex Eigenvectors
  • Decomposing a Complex Solution
  • Frequency and Angular Frequency
  • The Contests Between Frequencey and Decay
• all MTH-264 Videos (YouTube playlist)

Technology

• Communication
  • Zoom
  • Microsoft Lens
  • Apple Notes
  • Adobe Scan
  • Joining a Zoom Webinar
  • MTH-264 Assignments folder
• Desmos
  • straight-line solution example
  • sink: a parametric illustration
  • combinations of straight-line solutions
  • exercise 3.3 #22
  • graphs of spiral sink, spiral source, and centers
  • experimenting with phase shift
  • experimenting with beats
• Excel
  • Euler First-Order Equation.xlsx
  • Euler First-Order System.xlsx
• Mathematica
  • First Order Linear Systems.nb
  • First Order Systems.nb
  • Partially Decoupled Phase Portrait.nb
  • A Basic Partially Decoupled System.nb
  • The Swaying Skyscraper.nb
  • The VanderPol Equation.nb
  • SIR-model.nb
  • StreamPlot[]-Coloring-Example.nb