Joanna Bieri

Applied Math Professor

Department of Economics

University of Redlands

Partial Differential Equations - Fall 2024

Office Hours:
Click here for my schedule.
You can also email me for an appointment!

• Important Course Documents
  
  Course Syllabus
  Course Schedule
  This is our book - try to get a copy asap
  
  Canvas: Check Grades and Submit Homework
  
• Daily Assignments - Reading - Handouts
  
  Each day I will post the homework, additional reading, and additional information. Click on the links below to see the information for that day.
  • ODE REVIEW
    All content from my ODEs class - including videos!
    NOTES - Higher Order Linear Equations
    NOTES - Linear Independence, Constant Coefficient Homogeneous
    NOTES - Characteristic Equations and Constructing Solutions
    NOTES - Nonhomogeneous Equations, Method of Undetermined Coefficients
    NOTES - More Nonhomogeneous, Variation of Parameters
    
  • Tuesday 9/3- DAY 1
    Homework Day 1 - CLICK HERE You should attempt every one of these problems by the next class period and come to class with questions!
    
    Example LaTeX PDF
    Example Latex Code
    I would suggest that you create an account on overleaf.com. It is a great way to write LaTeX online and share your work with friends and collaborators.
    
    
  • Thursday 9/5 - DAY 2
    Homework Day 2
    
    Desmos Graphing Online:
    
    
    The homework for this week is due on Sunday at 11:59pm on Canvas
    What should you hand in?
    1. A scan of your homework solutions from Day 1
    2. A scan of your homework solutions from Day 2 (it's okay if the two scans are combined)
    3. A .pdf of ONE problem that you are proud of figuring out, clearly explained like you are writing a textbook or article.
    These are graded as PASS or FAIL! Here are the minimum requirements.
    
  • Tuesday 9/10 - DAY 3
    Homework Day 3
    
  • Thursday 9/12 - DAY 4
    Homework Day 4
    
    

  Tuesday 9/17 and Thursday 9/19 I am away at a conference in Boston. We will not have class! You should:
  * Get caught up on the assignments so far.
  * Make sure you REALLY understand Eigenvalue Problems, Separation of Variables and Orthogonality.
  * Watch videos from Ordinary Differential Equations and Calculus II if you need a refresher.
  * Read ahead and start the next homework assignments.
  

  • Tuesday 9/24 - DAY 5
    Homework Day 5
    
    
  • Thursday 9/26 - DAY 6
    Homework Day 6
    
    
  • Tuesday 10/1 DAY 7
    Homework Day 7
    Chapter on Laplace's Equation
    Practice Quiz 1
    
  • Thursday 10/3 - DAY 8 - Quiz 1
    Quiz 1 will take place in class (30 min).
    Then we will see an example of separation of variables on Laplace's Equation.
    Homework Day 8 - Short homework
    Next Tuesday 10/8 is Fall Break - no class.
    
    
  
  Study Days - 10/7 and 10/8(no class)
  
  • Thursday 10/9 - DAY 9
    Homework Day 9
    
    
  • Tuesday 10/15 - DAY 10
    Homework Day 10
    
    
    A nice theoretical explanation of Orthognality of Eigenfunctions with a basic proof. Notes on Sturm Liouville Theory.
    
  • Thursday 10/17 - DAY 11
    Homework Day 11
    
    
  • Tuesday 10/22 - DAY 12
    Homework Day 12
    
    Python code for Fourier Square Wave
    
  • Thursday 10/24 - Pause for Understanding
    PAUSE FOR UNDERSTANDING!
    We explored the solution to the Cauchy Equation!
    
    
    
    
  • Tuesday 10/29 - DAY 13
    Homework Day 13
    
    
    Python code for Erf and Erfc
    
    
  • Tuesday 11/5 - DAY 14 - No in person class - Joanna is sick
    
    
    Video - Lesson 15 - The Convection Term - Part 1
    Video - Lesson 15 - The Convection Term - Part 2
    
    Homework Day 14
    Practice Quiz 2
    
    Infinite Diffusion and Convection - Code
    
    
    
  • Thursday 11/7 - DAY 15 - Quiz 2 - No in person class- Joanna is sick
    Quiz 2 will take during our regular class time - you will work on this independently and hand it in on Canvas. I will be available for questions on teams chat or over email. You can work on this where ever you are comfortable!
  • Thursday 11/12 DAY 16
    Homework Day 16
    
    Traveling Wave - Code
    Traveling Wave - Initial Sine
    Traveling Wave - Cosine Velocity
    Traveling Wave - Square Wave
    
    
  • Tuesday 11/14 DAY 17
    Homework Day 17
    
    
  • Tuesday 11/19 DAY 18
    Homework Day 18
    Wire vs Beam code
    Beam Animation
    String Animation
    
    
  • Thursday 11/21 DAY 19
    Homework Day 19
    
    
  • Tuesday 12/3 DAY 20
    Homework Day 20
    
    Final exam handed out next class!
  • Last Day of PDEs - 12/5
    We are talking about Bessel's Functions and the solution to the Vibrating Drum in polar coordinates. There will be no homework this week!
    
    Use your time this week to check homework solutions, review the lecture notes, and make sure you understand all the material before I had out the final exam on Thursday. Please come to office hours if you need help!
    
    Bessel's Function First and Second Kind - code
    Good Engineering summary about Bessel's Functions - by Dr. Abdelhamid Meziani FIU
    Pattern Formation Video - Motivation
    Latex Drum Video - Motivation
    
    
• Practice Exams and Homework Solutions
  All practice exams and homework solutions are available on Canvas!
• Lecture Notes and Additional Info
  
  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:
  Notes - Introduction to PDEs
  Notes - The Heat Equation and Boundary Conditions
  Notes - Eigenvalue Problems and Separation of Variables
  Notes - Problems with Non-Homogeneous Boundary Conditions
  Notes - More Complicated Problems with Separation of Variables
  Notes - Transforming Hard Problems into Easy Ones
  Notes - Review PDEs with Separation of Variables.
  Notes -Separation of Variables and Laplace's Equation.
  Notes -Eigenfunction Expansion.
  Notes -Integral Transforms - Eigenfunctions.
  Notes -Integral Transforms - Fourier Sine and Cosine.
  Notes -Integral Transforms - Fourier Exponential.
  Notes -Integral Transforms - Laplace.
  Notes - More Laplace Transforms.
  Notes Extra - Duhamel's Principle.
  Notes - Coordinate Transformations - The Convection Diffusion Equation.
  Notes - The Wave Equation - D'Alembert Solution
  Notes - The Wave Equation - Boundary Conditions and Separation of Variables
  Notes - Fourth Order Equations
  Notes - Nondimensionalization and Canonical Forms
  Notes - More on Canonical Forms and Change of Variables
  Notes - Bessel's Equation and Method of Frobebius
  Notes - Vibrating Drum Head PDE
  
  
  EXTRA Notes - First Order Equations and Method of Characteristics
  
  
Jarvis the cat just finished finding an inverse Laplace Transform!

Photo thanks to DailyMail.com