Dave's Web Corner

MTH-264 Week 2 (January 14-20)

• Outline
• Assessments
• Handouts
• Videos
• Technology

Outline

1.3 Qualitative Technique: Slope Fields

• recommended: 1, 3, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 22
• the flow of the equation
• the geometry of a first-order equation
• integral and autonomous equations and their slope fields

1.4 Numerical Technique: Euler's Method

• recommended: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20
• plotting and correcting a course
• how to excel at euler's method
• ordinary machines make extraordinary errors

1.5 Existence and Uniqueness

• recommended: 3, 7, 9, 11, 12, 13, 14, 15, 16, 18
• how do we know if an initial value problem even has a solution?
• worse, how do we know that it doesn't have more than one?
• conditions that guarantee useful results
• "if two solutions are ever in the same place at the same time, then they are the same solution"
• related to exercise 18:
  • How Raindrops Form, American Physical Society

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 18: 1.1 - 1.2 -
  • due Thursday, January 25: 1.3 - 1.4 - 1.5 -
  • due Thursday, February 1: 1.6 - 1.7 -
• 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 Direction Fields
• Separable Equations
  • The MVPs of ODEs
  • Basic Separable Equation Examples
• Modeling
  • Logistic Growth Solution
• Euler's Method
  • Euler Practice (solution)

Videos

• First Principles
  • The MVP of ODEs
  • Integrating Linear Factors
  • Verifying Implicit Solutions
  • Domain of a Solution
  • 1.2 - 13 alt
  • 1.2 - 35
  • Extracting Explicit from Implicit
  • Equilibrium Solutions
  • 1.3 - 15
• Mixing Problems
  • Setting up a Mixing Problem
  • Solving a Mixing Problem
  • Graphing a Mixing Problem
• Euler's Method
  • Euler's Method in a Spreadsheet
• all MTH-264 Videos (YouTube playlist)

Technology

• Communication
  • Zoom
  • Microsoft Lens
  • Apple Notes
  • Adobe Scan
  • Joining a Zoom Webinar
  • MTH-264 Assignments folder
• GeoGebra
  • Autonomous and Integral Example.ggb
  • Existence and Uniqueness Example.ggb
  • Existence and Uniqueness Example.ggb
• Desmos
  • Existence and Uniqueness
• Excel
  • Euler First-Order Equation.xlsx
  • Euler Method-01-04-20.xlsx
  • Euler Accident.xlsx
  • Exercise 01-04-01-alt-template.xlsx
• Mathematica
  • Illustrating the DSolve Command.nb
  • Slope Fields and Direction Fields.nb
  • Slope Fields and Solutions.nb
  • 264-mathematica-01-03-10-alt.nb
  • Logistic Growth with Harvesting.nb
  • Autonomous and Integral Equations.nb
  • Existence and Uniqueness.nb