Dave's Web Corner

MTH-264 Resources

• Outline
• Assessments
• Handouts
• Videos
• Technology

Outline

• Chapter 1 First-Order Differential Equations
  • 1.1 Modeling via Differential Equations
  • 1.2 Analytic Technique: Separation of Variables
  • 1.3 Qualitative Technique: Slope Fields
  • 1.4 Numerical Technique: Euler’s Method
  • 1.5 Existence and Uniqueness of Solutions
  • 1.6 Equilibria and the Phase Line
  • 1.7 Bifurcations
  • 1.8 Linear Equations
  • 1.9 Integrating Factors for Linear Equations
• Chapter 2 First-Order Systems
  • 2.1 Modeling via Systems
  • 2.2 The Geometry of Systems
  • 2.3 The Damped Harmonic Oscillator
  • 2.4 Additional Analytic Methods for Special Systems
  • 2.5 Euler’s Method for Systems
  • 2.7 The SIR Model of an Epidemic
• Chapter 3 Linear Systems
  • 3.1 Properties of Linear Systems and the Linearity Principle
  • 3.2 Straight-Line Solutions
  • 3.3 Phase Portraits for Linear Systems with Real Eigenvalues
  • 3.4 Complex Eigenvalues
  • 3.5 Special Cases: Repeated and Zero Eigenvalues
  • 3.6 Second-Order Linear Equations
  • 3.7 The Trace-Determinant Plane
• Chapter 4 Forcing and Resonance
  • 4.1 Forced Harmonic Oscillators
  • 4.2 Sinusoidal Forcing
  • 4.3 Undamped Forcing and Resonance
  • 4.4 Amplitude and Phase of the Steady State
• Chapter 5 Nonlinear Systems
  • 5.1 Equilibrium Point Analysis
  • 5.2 Qualitative Analysis
• Chapter 6 Laplace Transforms
  • 6.1 Laplace Transforms
  • 6.2 Discontinuous Functions
  • 6.3 Second-Order Equations
  • 6.4 Delta Functions and Impulse Forcing
  • 6.5 Convolutions
• Appendices
  • Appendix B Power Series: The Ultimate Guess

Assessments

• Deadlines and File Submission
  • All assessments are due in 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 11: (none)
  • 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 -
  • 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)
  • due Thursday, February 29: 3.1 - 3.2 - 3.3 - 3.4 -
  • due Thursday, March 7: (none)
  • due Thursday, March 14: 3.5 - 3.7 -
  • due Thursday, March 21: 5.1 - 5.2 -
  • due Thursday, March 28: (none)
  • due Thursday, April 4: 3.6 - , 4.1 - , 4.2 - , 4.3 - , 4.4 -
  • due Thursday, April 11: Appendix B - , 6.1 -
  • due Thursday, April 18: 6.2 - , 6.3 - , 6.4 -
  • due Tuesday, April 23: 6.4 - , 6.5 -
• 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.
  • due Thursday, March 28: Exam 2
    • Exam 2 (solutions)
    • Exam 2 covers sections 3.1-3.5, 3.7, 5.1-5.2
    • Exam 2 will be released by 11:59pm on Thursday, March 21 and is due by 11:59pm on Thursday, March 28.
  • due Thursday, April 25: Exam 3
    • Exam 3 (solutions)
    • Exam 3 covers sections 3.6, 4.1-4.4, appendix B, and 6.1-6.5
    • Exam 3 will be released by 11:59pm on Tuesday, April 23 and will be written in class on Thursday, April 25.

Handouts

• Announcements
  • Schmidt Award
  • Math Graduate Award
  • Honors Program introduction
  • Tutoring Center services
• Lecture Notes
  • 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9
  • 2.1, 2.2, 2.3, 2.4, 2.5, 2.7
  • 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7
  • 4.1, 4.2, 4.3, 4.4
  • 5.1, 5.2
  • 6.1, 6.2, 6.3, 6.4, 6.5
  • app B
• 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
• Modeling
  • Logistic Growth Solution
• Euler's Method
  • Euler Practice (solution)
  • Euler System Practice (solution)
• First-Order Linear Equations
  • Undetermined Coefficients: Second Guess
• 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
  • Families of Two-Dimensional Linear Systems
• Series Solutions
  • Famous Power Series
  • Convergence Tests
• Laplace Transforms
  • Laplace Transform Facts
  • Laplace Transform Practice
  • Laplace Transform Solutions
  • Comparing Four Methods
  • Laplace Transform Trigonometry Derivations

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
• 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
• 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
• 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
• Linear Systems: Bifurcation Cases
  • Calculating the Almost Eigenvector
  • Sunburst and Almost Spiral Cases
  • Equilibrium Line Cases
• Nonlinear Systems: Linearization
  • The Jacobian
  • Linearization of a Nonlinear System
  • Nullclines
• Harmonic Oscillation
  • Summing Common Frequencies
  • Summing Different Frequencies
  • Three Famous Frequencies
  • Undamped Oscillation
  • Underdamped Oscillation
  • Overdamped Oscillation
  • Critically Damped Oscillation
  • Under, Over, and Critical Damped
  • Forced Damped Oscillation I
  • Forced Damped Oscillation II
  • Resonance in Action
  • Resonant Frequency in Action
• Laplace Transformations
  • Laplace Transform Definition
  • The Linearity of the Transform
  • The Transform of a Derivative
  • The Inverse Transform
  • A Basic Solution
  • Juggling Constants
  • Partial Fraction Decomposition
  • Shift and Delay
  • The First Shifting Theorem
  • The Heaviside Function
  • Heaviside Function Transformed
  • The Second Shifting Theorem
  • Shifting Theorems Applied
  • Dirac Function Transformed
• all MTH-264 Videos (YouTube playlist)

Technology

• Communication
  • Zoom
  • Microsoft Lens
  • Apple Notes
  • Adobe Scan
  • Joining a Zoom Webinar
  • MTH-264 Assignments folder
• GeoGebra
  • GeoGebra
  • Exercise-01-01-18.ggb
  • Exercise-01-06-19.ggb
  • Slope Fields.ggb
  • Autonomous and Integral Example.ggb
  • Existence and Uniqueness Example.ggb
  • Linear Equation.ggb
• Desmos
  • Exercise 1.1 #16
  • Exercise 1.2 #38 alt
  • Existence and Uniqueness
  • Exercise 1.6 #19
  • Exercise 1.6 #20
  • Exercise 1.8 #28 alt
  • First-Order Linear Family
  • Fox Squirrels
  • Retirement
  • 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
  • Basic Solution Check
• Excel
  • Euler First-Order Equation.xlsx
  • Euler Accident.xlsx
  • Exercise 01-04-01-alt-template.xlsx
  • Euler Method-01-04-20.xlsx
  • Euler First-Order System.xlsx
  • Euler Method for Systems 02-01-08.xlsx
  • Euler System Van-der-Pol-Equation.xlsx
  • Convolution.xlsx
  • piecewise-defined function
• 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
  • First Order Linear Equations.nb
  • First Order Linear Family.nb
  • Exercise-01-08-28-alt.nb
  • 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
  • First Order System Phase Portrait.nb
  • Nonlinear System Bifurcation.nb
  • Exercise-05-01-26.nb
  • Basic Solution Check.nb
  • Driving Function Awareness.nb
  • Unforced Damped Harmonic Oscillators.nb
  • Forced Damped Harmonic Oscillators.nb
  • Resonant Frequency.nb
  • Series Solution.nb
  • Dirac and Heaviside Solutions.nb
  • Discontinuous Driving Functions.nb
  • Periodic Impulse Forcing Example.nb
  • Fast 13 Concept - Defeating Speed Bumps.nb