Joanna Bieri

Applied Math Professor

Department of Economics

University of Redlands

Ordinary Differential Equations
Spring 2025

Office Location:
Duke Hall #209
Phone: 909-748-8630
E-Mail: joanna_bieri@redlands.edu
(Email or Teams are my preferred contact methods)

• Important Course Documents
  
  Course Syllabus
  
  Class Schedule
  
  Canvas - for submitting work and checking grades
  
  BOOK 1: Differential Equations and Boundary Value Problems: Computing and Modeling by Edwards and Penney - Fourrth Edition
  I also have extra copies of the book available in my office for loan. Practice problems are assigned from this book.
  
  BOOK 2: Elementary Differential Equations with Boundary Value Problems, William F. Trench, Trinity University
  This is a great open source differential equations book, in case you prefer a different resource.
  
• Daily Assignments - Reading - Handouts
  
  Each day I will post the homework, additional reading, in class handouts, and other information below. Click on the links below to see the information for that day.
  • Wednesday - 1/8 - Click Here
    To be successful in higher level math you need to keep practicing and often relearning the basics. Really try to work this semester to become the boss of integration, basic algebra, trigonometric functions, and graphing/answer checking!
    PRE-CLASS:

    None

    
    CLASS TIME:

    Talk about syllabus and class expectations
    Video: Introduction to Differential Equations
    
    Review of Integration
    HW1 Assigned - Click Here For this homework only - you have the rest of the semester to complete these integrals.
    Video: Review of Integration
    Website: Calculus II - Integration starts on Day 3
    
    

    
    AFTER CLASS:

    Start Prepping for Day 2

    
    
  • Friday - 1/10 - Click Here
    PRE-CLASS:

    Video: Integrals as Solutions
    Video: Direction (Slope) Fields
    Video: Software - using dfield.jar
    Link to dfield download
    Run dfield by double clicking on the .jar file. If this doesnt work try java -jar dfield.jar in a terminal window.
    Online version of Dfield - easier to use.
    HW2 Assigned
    

    
    CLASS TIME:

    Questions about Integrals as Solutions or Slope Fields
    In Class Exploration: Slope Fields
    Work on HW2 Problems
    Continue Review of Integration
    

    
    AFTER CLASS:

    Start Prepping for Day 3

  • Monday - 1/13
    PRE-CLASS:

    Video: Existence and Uniqueness
    Video: Separable Equations
    HW3 Assigned
    

    
    CLASS TIME:

    Questions about Existence, Uniqueness, or Separable Equations
    Work on HW3 Problems
    In Class Presentation Problems
    

    
    AFTER CLASS:

    Start Prepping for Day 4
    Advanced Problems 1 - Due Sunday 1/19
    

    QUIZ on FRIDAY 1/17:

    Classifying differential equations.
    Solving equations that can just be integrated.
    Might contain integrals that require substitution, or integration by parts (No Trig Subs or Algebraic Techniques).
    Understanding of how to build a slope field.
    What is a general solution?
    What is a particular solution?
    

  • Wednesday - 1/15
    PRE-CLASS:

    Video: Linear First Order Equations
    Video: More Examples
    HW4 Assigned
    

    
    CLASS TIME:

    Questions about Linear First Order Equations
    Work on HW4 Problems
    In Class Presentation Problems
    
    A Table of Integrals - for quiz
    A Table of Derivatives - for quiz
    

    
    AFTER CLASS:

    Start Prepping for Day 5
    Advanced Problems 1 - Due Sunday 1/19
    

  • Friday - 1/17 - Quiz 1
    PRE-CLASS:

    Video: Substitution Methods for ODEs
    HW5 Assigned
    

    
    CLASS TIME:

    Questions about Substitution Methods Equations
    Work on HW5 Problems
    In Class Challenge Problems
    Ouiz 1
    

    
    AFTER CLASS:

    Start Prepping for Day 6
    Advanced Problems 1 - Due Sunday 1/19
    

  • No Class - 1/20/25 - Martin Luther King Jr. Holiday
  • Wednesday - 1/22
    PRE-CLASS:

    Video: Exact ODEs
    Video: More Examples of Exact ODEs
    HW6 Assigned
    

    
    CLASS TIME:

    Questions about Exact Equations
    Work on HW6 Problems
    In Class Challenge Problems
    

    
    AFTER CLASS:

    Start Prepping for Day 7
    Advanced Problems 2 - Due Sunday 1/26
    

    QUIZ on FRIDAY 1/26:

    Solving Equations using separation.
    Solving Equations using Integrating Factor.
    Might contain integrals that require substitution, or integration by parts (No Trig Subs or Algebraic Techniques).
    Ability to use rules of logs and exponents.
    

  • Friday - 1/24 - Quiz 2
    PRE-CLASS:

    Video: Population Models in ODEs
    HW7 Assigned
    ZOMBIES!!!
    

    
    CLASS TIME:

    Questions about Population Models or general Modeling.
    Work on HW7 Problems
    

    
    AFTER CLASS:

    Survey: How is class going for you?
    Start Prepping for Day 8
    Advanced Problems 2 - Due Sunday 1/26
    

  • Monday - 1/27
    PRE-CLASS:

    Video: Review of First Order ODEs
    HW8 Assigned
    Survey: How is class going for you?
    

    
    CLASS TIME: (Note - Class Covered by Christopher Monge and Joey Freitas)

    Questions about First Order Equations
    Work on HW8 Problems
    In Class Challenge Problems
    

    
    AFTER CLASS:

    Start Prepping for Day 9
    Advanced Problems 3 - Due Sunday 2/2
    

    
    QUIZ on FRIDAY 1/31:

    Solving Equations using substitution or exact methods.
    Deciding what solution method to use.
    Integrals with substitution or integration by parts or partial fractions.
    

  • Wednesday - 1/29
    PRE-CLASS:

    Video: Reducible Second Order ODEs
    Video: Intro to Linear Second Order ODEs
    HW9 Assigned
    

    
    CLASS TIME: (Note - Class Covered by Christopher Monge and Joey Freitas)

    Questions about Second Order ODEs
    Do you feel comfortable with ideas like: Linear Independence, Superposition, Homogeneous, and Non-Homogeneous? IN CLASS each group present one of these ideas along with examples.
    Work on HW9 Problems
    Video: Help for HW8 problem 7
    

    
    AFTER CLASS:

    Start Prepping for Day 10
    Advanced Problems 3 - Due Sunday 2/2
    

    
    
    EXTRA:

    Review and Help:
    Edwards Algebra Review
    Algebra - Exponents and Logs
    

    
    
  • Friday - 1/31 - Quiz 3
    PRE-CLASS:

    Video: Linear Homogeneous Constant Coefficient Equations
    HW10 Assigned
    
    Code: Python Code for Solving Matrix Systems
    

    
    CLASS TIME: (Note - Class Covered by Christopher Monge and Joey Freitas)

    Questions about Linear Constant Coef Eqns with Real Distinct Roots.
    How are you feeling about the algebra here?
    Work on HW10 Problems
    

    
    AFTER CLASS:

    Start Prepping for Day 11
    Advanced Problems 3 - Due Sunday 2/2
    

    
    
  • Monday - 2/3
    PRE-CLASS:

    Video: Repeated Roots
    Video: Complex Roots
    HW11 Assigned
    

    
    CLASS TIME:

    Joanna answers quesions from last week: Second Order Equations
    Higher order equations with repeated or complex roots
    Work on HW11 Problems
    In Class Challenge Problems
    

    
    AFTER CLASS:

    Start Prepping for Day 12
    Advanced Problems 4 - Due Sunday 2/9
    

    
    QUIZ on FRIDAY 2/7:

    Higher order equations
    Linear constant coefficient homogeneous equations - real roots
    Linear independence of solutions and superposition
    

    
    EXTRA:

    Review and Help:
    Algebra of Complex Numbers
    Eulers Formula
    Algebra - Exponents and Logs
    

    
    
  • Wednesday - 2/5
    PRE-CLASS:

    Video: Non-Homogeneous Eqns - Method of Undetermined Coef.
    Video: MUC more Examples There is a typo in the video... A=1/5 not 1/3
    Video: MUC Tricky Duplication Examples
    HW12 Assigned
    

    
    CLASS TIME:

    Method of Undetermined Coefficients
    Work on HW12 Problems
    

    
    AFTER CLASS:

    Start Prepping for Day 13
    Advanced Problems 4 - Due Sunday 2/9
    

  • Friday - 2/7 - Quiz 4
    PRE-CLASS:

    Video: Non-Homogeneous Eqns - Variation of Parameters
    HW13 Assigned
    

    
    CLASS TIME:

    Variation of Parameters
    Work on HW13 Problems
    

    
    AFTER CLASS:

    Start Prepping for Day 14
    Advanced Problems 4 - Due Sunday 2/9
    

  • Monday - 2/10 - Pause for Understanding
    PRE-CLASS:

    Video: Python Sympy
    Link to the Code
    HW14 Assigned
    

    
    CLASS TIME:

    We will go through the lecture problems in class - Link to the Code
    Work on making Python do the tedious work for us!
    Code from in Class Today.
    
    Problem 2 from HW14 - started in Class Today.
    

    
    AFTER CLASS:

    Start Prepping for Day 15
    Advanced Problems 5 - Due Sunday 2/16
    

    
    QUIZ on FRIDAY 2/14:

    Linear Constant Coef Nonhomogeneous Equations
    Method of Undetermined Coefficients
    Variation of Parameters
    

    
    
  • Wednesday - 2/12
    PRE-CLASS:

    Video: Introduction to Eigenvalue Problems.
    Video: Eigenvalues and the Whirling String
    Video: Another Eigenvalue Example
    HW15 Assigned
    

    
    CLASS TIME:

    Experiment Whirling String
    Work on HW15 Problems
    

    
    AFTER CLASS:

    Start Prepping for Day 14
    Advanced Problems 5 - Due Sunday 2/16
    

  • Friday - 2/14 - Quiz 5
    PRE-CLASS:

    Video: Applications of ODEs - Mechanical Vibrations
    HW16 Assigned
    

    
    CLASS TIME:

    Mechanical Vibrations - and more Eigenvalue Problems
    Python - Plots of Spring Mass Solutions
    Tacoma Narrows Bridge - Video
    

    
    AFTER CLASS:

    Start Prepping for Day 17
    Advanced Problems 5 - Due Sunday 2/16
    

  • Wednesday - 2/18
    PRE-CLASS:

    Video: Intro to Laplace Transforms
    Video: Tables of Laplace Transforms and Inverses
    HW17 Assigned
    

    
    CLASS TIME:

    Practice Laplace Transforms
    

    
    AFTER CLASS:

    Start Prepping for Day 18
    Advanced Problems 6 - Due Sunday 2/23
    

    
    QUIZ on FRIDAY 2/21:

    Eigenvalue Problems
    
    

  • Friday - 2/21 - Quiz 6
    PRE-CLASS:

    Video: Introduction to Laplace Transforms of Initial Value Problems (IVPs).
    Video: Example - Laplace Transform of IVP
    HW18 Assigned
    HW solns have typos in problems 8 and 10. Problem 8 misses a -2 in the initial Laplace Transform and Problem 10 does the inverse transform of 1/s as t instead of 1, it should be 1.
    

    
    CLASS TIME:

    Laplace Transform IVPs
    

    
    AFTER CLASS:

    Advanced Problems 6 - Due Sunday 2/23
    
    Because of the sick day we are skipping Day 19 content.
    Extra Videos for Laplace Transforms Day19:
    Video: Tricks of Laplace Transforms - derivatives and translations
    Video: Tricks of Laplace Transforms - convolution and IVP example
    
    We are also skipping HW19.
    
    Start Prepping for Day 20
    

  • Monday - 2/24
    PRE-CLASS:

    Video: Intro to Power Series
    Video: Examples Power Series
    HW20 Assigned
    
    Calculus Book - Review of Power Series
    My Calculus II Videos - Power Series and Taylor Series on Days 30-33
    

    
    CLASS TIME:

    Practice Power Series Solutions
    Radius of Convergence
    

    
    AFTER CLASS:

    Start Prepping for Day 21
    Advanced Problems 7 - Due Sunday 3/10
    

    
    QUIZ on FRIDAY 3/8:

    Laplace Transforms to solve ODEs
    Confirming solutions with Characteristic Equations, MUC, or VOP
    
    

  • Wednesday - 2/26
    PRE-CLASS:

    Video: Power Series Solutions - Second Order Eqns and Regular Singular Points.
    Video: Example - Power Series Solutions
    HW21 Assigned
    

    
    CLASS TIME:

    More Power Series Solutions
    Regular Singular Points
    Radius of Convergence
    

    
    AFTER CLASS:

    Start Prepping for Day 22
    Advanced Problems 7 - Due Sunday 3/10
    

  • Friday - 2/28 - Quiz 7
    PRE-CLASS:

    Video: Legendre Polynomials and Legendre Equation
    Video: Python - Plot Legendre Polynomials
    Python - Plot Legendre Polynomials
    HW22 Assigned
    

    
    CLASS TIME:

    Legendre Polynomials
    

    
    AFTER CLASS:

    Start Prepping for Day 23 - after Spring Break
    Advanced Problems 7 - Due Sunday 3/9
    

  • Spring Break - 3/3-3/7
  • Monday - 3/10
    PRE-CLASS:

    Video: Intro to Frobenius Method
    Video: Examples of Frobenius Method
    Video: Problem 8.2 #17
    HW23 Assigned
    
    

    
    CLASS TIME:

    Frobenius Method Solutions
    Classify x=0 as ordinary point, regular singular point, or irregular singular point.
    

    
    AFTER CLASS:

    Start Prepping for Day 24
    Advanced Problems 8 - Due Sunday 3/16
    

    
    QUIZ on FRIDAY 3/15:

    Power Series Solutions to ODEs
    Know Power Series formulas for e^x, sin(x) and cos(x)
    
    

  • Wednesday - 3/12
    PRE-CLASS:

    Video: Another Frobenius Example.
    Video: Bessel's Equation
    HW24 Assigned
    

    
    CLASS TIME:

    More Power Series Solutions
    
    AFTER CLASS:

    No new homework for next class, review power series.
    Advanced Problems 8 - Due Sunday 3/16
    

  • Friday - 3/14 - Happy Pi Day
    PRE-CLASS:

    Review Power Series and Frobenius Method. Come to class with questions. This is a "take a breath day" - NO NEW HOMEWORK!

    
    CLASS TIME:

    NO CLASS
    

    
    AFTER CLASS:

    Start Prepping for Day 25
    Advanced Problems 8 - Due Sunday 3/16
    

  • Monday - 3/17
    PRE-CLASS:

    Video: Matrix Operations Review
    Video: Matrix Valued Functions
    HW25 Assigned
    
    Matrix Review Worksheet
    
    

    
    CLASS TIME:

    Matrix Review - Preparing for Systems of Differential Equations.
    

    
    AFTER CLASS:

    Start Prepping for Day 26
    Advanced Problems 9 - Due Sunday 3/23
    

    
    QUIZ on FRIDAY 3/28:

    Power Series Solutions to ODEs
    Know Power Series formulas for e^x, sin(x) and cos(x)
    
    

  • Wednesday - 3/19
    PRE-CLASS:

    Video: Introduction to First Order Systems.
    Video: Phase Plane to plot 2-d systems
    Video: Pplane code to plot 2-d systems
    Online version of Pplane - easier to use
    Video: More Examples First Order Systems
    HW26 Assigned
    

    
    CLASS TIME:

    First Order Systems
    Reducing higher order odes to first order systems
    
    AFTER CLASS:

    Start Prepping for Day 27
    Advanced Problems 9 - Due Sunday 3/23
    

  • Friday - 3/21 - Quiz 8
    PRE-CLASS:

    Video: Introduction to Eigenvalue Method for Systems.
    Video: Real Distinct Eigenvalues.
    Video: Complex Eigenvalues
    
    Code: Python Code for Finding Eigenvalues and Eigenvectors.
    Video: Code Walk Through
    HW27 Assigned
    

    
    CLASS TIME:

    Eigenvalues Methods for Linear Systems of ODEs
    

    
    AFTER CLASS:

    Start Prepping for Day 28
    Advanced Problems 9 - Due Sunday 3/23
    

  • Monday - 3/24
    PRE-CLASS:

    Video: Intro to Repeated Eigenvalues
    Video: Complete Case - Repeated Eigenvalues
    Video: Defective Case - Repeated Eigenvalues
    Video: Generalized Eigenvectors - Full Example
    HW28 Assigned
    
    

    
    CLASS TIME:

    Linear Systems with Repeated Eigenvalues
    

    
    AFTER CLASS:

    Start Prepping for Day 29
    Advanced Problems 10 - Due Sunday 3/30
    

    
    QUIZ on FRIDAY 3/24:

    Linear Systems
    Writing Higher Order Equations as First Order Systems
    Eigenvalue solutions to Linear Systems
    
    

  • Wednesday - 3/26
    PRE-CLASS:

    Video: Introduction to MUC for Systems.
    Video: Example of MUC for Systems
    Python: Matrix Inverse
    HW29 Assigned
    

    
    CLASS TIME:

    Nonhomogeneous Linear Systems
    
    AFTER CLASS:

    Start Prepping for Day 30
    Advanced Problems 10 - Due Sunday 3/30
    

  • Friday - 3/28 - Quiz 9
    PRE-CLASS:

    Video: Compartmental Diagrams - Modeling Lead Poisoning.
    Video: Python Code Walk-through.
    Code: Lead in Body
    
    HW30 Assigned
    

    
    CLASS TIME:

    Mathematical Models - Linear Systems
    

    
    AFTER CLASS:

    Start Prepping for Day 31
    Advanced Problems 10 - Due Sunday 3/30
    

  • Monday - 3/31
    PRE-CLASS:

    Video: Intro to Nonlinear Systems
    Worksheet - Exploration
    Online version of Pplane - easier to use
    Video: Eigenvalues and Fixed Points
    HW31 Assigned
    
    

    CLASS TIME:

    Nonlinear Systems
    Fixed Points
    Phase Plane
    

    AFTER CLASS:

    Start Prepping for Day 32
    Advanced Problems 11 - Due Sunday 4/6
    

    QUIZ on FRIDAY 4/4:

    Eigenvalue solutions to Linear Systems
    Complex, Real, or Repeated Eigenvalues
    
    

  • Wednesday - 4/2
    PRE-CLASS:

    Video: Introduction to Linearized Systems.
    Video: Jacobian Linearization Example
    Video: SIR - Example (recorded during COVID lockdown)
    Online version of Pplane - easier to use
    HW32 Assigned
    

    CLASS TIME:

    Jacobian to Linearize Nonlinear Systems
    AFTER CLASS:

    Start Prepping for Day 33
    Advanced Problems 11 - Due Sunday 4/6
    

  • Friday - 4/4 - Quiz 10
    PRE-CLASS:

    Exploration - Nonlinear Systems.
    The goal of the Exploration is to use what we learned about Fixed Points, The Jacobian, and Stability to get as much information about the nonlinear systems as possible, without formally solving the equations.
    Solutions Exploration - No Peeking! Please try the Exploration First!.
    Online version of Pplane - easier to use
    HW33 Assigned
    

    CLASS TIME:

    Mathematical Models - Nonlinear Systems
    

    AFTER CLASS:

    Start Prepping for Day 34
    Advanced Problems 11 - Due Sunday 4/6
    

  • Monday - 4/7
    PRE-CLASS:

    Video: Python for Numerical Methods
    Code: Python Workbook - homework
    HW34 Assigned
    
    Video: Using Google Colab - submitting link for homework
    

    CLASS TIME:

    Python Code for Numerical Methods
    

    AFTER CLASS:

    Start Prepping for Day 35
    Advanced Problems 12 - Due Sunday 4/12
    

    QUIZ on FRIDAY 4/10:

    Nonlinear Systems
    Jacobian and classification of Fixed Points
    
    

  • Wednesday - 4/9
    PRE-CLASS:

    Video: Intro to Euler's Method
    Spreadsheet: Euler's Method - from lecture.
    
    Introduction to Numerical Methods Worksheet
    
    Code: Euler's Method - first problem on worksheet
    HW35 Assigned
    
    

    CLASS TIME:

    Euler's Method
    

    AFTER CLASS:

    Start Prepping for Day 36
    Advanced Problems 12 - Due Sunday 4/13
    

    
    
  • Friday - 4/11 - Quiz 11
    PRE-CLASS:

    Video: Intro to Euler's Method
    Introduction to Numerical Methods Worksheet
    
    Video: Code Walk Through - Error Euler's Method
    Code: Error in Euler's Method - first problem on worksheet
    HW36 Assigned
    
    

    CLASS TIME:

    Error in Euler's Method
    

    AFTER CLASS:

    Start Prepping for Day 37
    Advanced Problems 12 - Due Sunday 4/13
    

    
    
  • Monday - 4/14
    PRE-CLASS:

    Video: Intro to Improved Euler's Method
    Improved Euler Methods Worksheet
    
    Video: Code Walk Through - Improved Euler's Method
    Code: Improved Euler's Method - first problem on worksheet
    HW37 Assigned
    
    

    CLASS TIME:

    Improved Euler's Method
    

    AFTER CLASS:

    Optional Advanced Problems - class review - Due Friday 4/18
    

    
    
  • Wednesday 4/16
    If you have Quizzes to make up this is your last chance. Our class period will be the time to retak any quizzes that you still have left to do.
    
  ------------------------------------------------
  • Python and CoCalc Code
    
    Over the course of the semester we will be doing some programming to help us solve hard programs. I will try to collect all programs here for your reference.
    
    Code: Python Code for Solving Matrix Systems
    Sympy Intro Code
    Python - Plots of Spring Mass Solutions
    Python - Plot Legendre Polynomials
    Python: Matrix Inverse - again
    Code: Lead in Body
    
    Code: Python for Numerical Methods
    Code: Euler's Method
    Code: Error in Euler's Method
    
    
    
• Lecture Notes
  USE AT YOUR OWN RISK - There could be typos that are corrected in class, so please use common sense and your own notes to compare to what you see here:
  
  Review of Integration
  Solution by Integration and Slope Fields
  Existence and Uniqueness - Separation
  Linear First Order Eqna - Integrating Factor
  Substitution Methods
  Exact Equations and Reduction of Order Substitutions
  Population Models
  More Applications
  Linear Higher Order Equations
  Linear Higher Order Equations - Characteristic Equations
  Linear Higher Order Equations - Repeated and Complex Roots
  Nonhomogeneous Equations - Undetermined Coefficients
  Nonhomogeneous Equations - Variation of Parameters
  Boundary Value Problems
  Applications of Second Order Equations
  Laplace Transforms
  Laplace Transforms of ODEs
  Laplace Transform Tricks and Practice
  Introduction to Power Series
  Introduction to Power Series - continued
  Lagendre Polynomials
  Frobenius Method
  Frobenius Method - continued - Bessel order zero
  Introduction to Linear Systems
  Review of Matrix Operations
  Eigenvalue Method for Systems
  Eigenvalue Method for Systems
  Nonhomogeneous Linear Systems
  Compartmental Diagrams - Applications of Linear Systems
  Introduction to Nonlinear Systems
  Nonlinear Systems
  Nonlinear Systems - Applications (In-class Activity)
  Numerical Methods - Euler's Method
  Numerical Methods - More Euler's Method
  Numerical Methods - Improved Euler's Method
  
  
Dancing Kitten is taking Differential Equationss!!

"I iz da algebra boss!
"I eats integrals fer breakfast!!"