Dave's Web Corner

MTH-264 Week 5 (February 4-10)

• Outline
• Assessments
• Handouts
• Videos
• Technology

Outline

2.2 The Geometry of Systems

• recommended: 5, 7, 10, 11, 12, 13, 15, 16, 17, 18, 21, 27
• vector fields and direction fields
• analogies between first-order equations and first-order systems
• equilibrium solutions
• xy-, tx-, and ty-graphs

2.3 The Damped Harmonic Oscillator

• recommended: 2, 3, 4, 6, 8, 9, 10
• damped harmonic oscillators
  • from second-order equation to first-order system
  • "guessing" solutions
  • solutions in the phase (yv-) plane
  • ty- and tv-graphs

2.4 Additional Analytic Methods for Special Systems

• recommended: 3, 5, 6, 9, 10, 11, 12, 13, 17
• checking solutions in systems
• decoupled systems
• partially decoupled systems

2.5 Euler's Method for Systems

• recommended: 3, 4, 5, 6, 8
• return to plotting and correcting a course
• more excel-ent advice
• special examples
  • the van der pol equation
  • the swaying skyscraper
    • the p-delta effect
• more comments on existence and uniqueness of solutions

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 8: 1.8 - 1.9 - 2.1 -
  • due Thursday, February 15: 2.2 - 2.3 - 2.4 - 2.5 -
  • due Thursday, February 22: (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
• Euler's Method
  • Euler Practice (solution)
  • Euler System Practice (solution)
• 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
• 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
• Excel
  • Euler First-Order Equation.xlsx
  • Euler Accident.xlsx
  • Euler First-Order System.xlsx
  • Euler Method for Systems 02-01-08.xlsx
  • Euler System Van-der-Pol-Equation.xlsx
  • Exercise 01-04-01-alt-template.xlsx
  • Euler Method-01-04-20.xlsx
• Mathematica
  • First Order Linear Systems.nb
  • First Order Systems.nb
  • Numerical Methods for Systems 02-01-08.nb
  • Exercise-02-03-03.nb
  • Partially Decoupled Phase Portrait.nb
  • A Basic Partially Decoupled System.nb
  • The Swaying Skyscraper.nb
  • The VanderPol Equation.nb
  • SIR-model.nb
  • Discrete SIR-model.nb
  • StreamPlot[]-Coloring-Example.nb