Mathematics 488/688 Homepage

Spring 2025 University of Nevada Reno

488/688 Partial Differential Equations (3+0) 3 credits

Partial differential equations; first order equations, initial and mixed boundary-value problems for the second order Laplace, heat and wave equations; finite difference approximation. Prerequisite(s): MATH 285 with a "C" or better; MATH 330 with a "C" or better.

Instructor  Course Section                     Time
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Eric Olson  Math 488/688-1001 PDEs             12:00-12:50am MWF AB634

Course Information

Instructor:: Eric Olson
email:: Please contact me through WebCampus
Office:: DMSC 238 MWF from 11am to 11:50am and through Zoom by appointment
Homepage:: https://fractal.math.unr.edu/~ejolson/488/
Required Texts:: Richard Haberman, Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, Fifth Edition, Pearson, 2018.
Other resources:: Christian Constanda, Solution Techniques for Elementary Partial Differential Equations, Fourth Edition, Chapman and Hall, 2022.; Evans, Blackledge, Yardley, Analytic Methods for Partial Differential Equations, Springer, 1999.; Farlow, Partial Differential Equations for Scientists and Engineers, Dover, 1993.

Student Learning Outcomes

Upon completion of this course, students will be able to

Use separation of variables to solve a PDE.
Work with Fourier Series.
Solve Sturm--Liouville Problems.

Homework

Lecture Notes

Lecture 1: Linear ODEs
Lecture 2: Heat Energy
Lecture 3: The Heat Equation
Lecture 4: Heat Bath Boundary
Lecture 5: Equilibrium Solutions
Lecture 6: Green's Theorem
Lecture 7: 3D Heat Equation
Lecture 8: Separation of Variables
Lecture 9: Orthogonality
Lecture 10: Time Dependent Example
Lecture 11: Computer Visualization
Lecture 12: Insulated Boundary

Announcements

[21-Feb-2025] Turn in Quiz 4

Please return your answers to take-home Quiz 4 in class.

[19-Feb-2025] Quiz 4

Quiz 4 focuses on using separation of variables and superposition to find solutions to initial-value problems involving the heat equations. It will be take home and due in class on Friday. Please look at the homework suggestions from February 12 to help prepare.

[12-Feb-2025] Homework Suggestions

The following exercises are suggested for the long weekend. They will not be turned in or graded.

Exercises 2.3.1a-f, 2.3.2a-g, 2.3.3a-e
Exercises 2.3.8, 2.4.1a-d, 2.4.3

[07-Feb-2025] Quiz 3 Practice Problems

Quiz 3 focuses on equilibrium solutions. Here are some problems to practice in preparation for the quiz on Wednesday.

Exercise 1.4.1a-h, 1.4.3, 1.4.7a-c
Exercise 1.5.12, 1.5.13

[07-Feb-2025] Turn in Quiz 2

Please return your answers to take-home Quiz 2 in class.

[05-Feb-2025] Quiz 2

Quiz 2 focuses on finding equilibrium solutions. It will be take home and due in class on Friday.

[03-Feb-2025] Quiz 2 Practice Problems

Here are some problems to practice in preparation for the quiz on Wednesday.

Exercise 1.4.1a-h.
Exercise 1.4.7a-c.

[29-Jan-2025] Quiz 1

Quiz 1 will focus on solving linear ordinary differential equations.

[26-Jan-2025] Quiz 1 Practice Problems

Here are some linear ordinary differential equations to practice in preparation for the quiz on Wednesday.

Solve xy' + 2y = x²−x+1 with initial condition y(1)=1/2.
Solve y' + 3y = 2x−1 with initial condition y(0)=3.
Solve y' + xy = 2x³ with initial condition y(1)=5.

[29-Jan-2025] Quiz 1

Quiz 1 will focus on solving linear ordinary differential equations.

[24-Jan-2025] Weekly Quizzes

After consideration of schedules the near-weekly quizzes will be given on Wednesdays. The first quiz will be January 29 in class.

[19-Jan-2025] Welcome Spring 2025

This section of Math 488/688 is in person. I am looking forward to seeing you starting the first week of class.

I will maintain an online archive of course materials including lecture notes, assignments and other announcements. Please consult the website and with me if you are sick or miss class. There will be no graded homework but instead weekly quizzes based on the lectures, textbook and selected exercises. Some of the quizzes will be in class others will be take-home quizzes.

Tentative Course Schedule

Jan 22-Jan 24   Week 1: 1.1-1.4 Heat Equation
Jan 27-Jan 31   Week 2: 1.5,2.1-2.3.2 Separation of Variables
Feb 03-Feb 07   Week 3: 1.5,2.1-2.3.2 Separation of Variables (continued)
Feb 10-Feb 14   Week 4: 2.3.2-2.3.8 Boundary Value Problems

*** President's Day Monday Feb 17

Feb 19-Feb 21   Week 5: 2.4,2.5 More Examples
Feb 24-Mar 28   Week 6: 3.1-3.3.3 Fourier Series
Mar 03-Mar 07   Week 7: 3.3.4-3.6 Differentiation and Integration

Mar 10-Mar 14   Week 8: Midterm
Mar 17-Mar 21   Week 9: 4.1-4.4 Wave Equation

*** Spring Break Saturday Mar 22 to Sunday March 30

Mar 31-Apr 04   Week 10: 5.1-5.3 Sturm-Liouville Problems
Apr 07-Apr 11   Week 11: 5.1-5.3 Sturm-Liouville Problems (continued)
Apr 14-Apr 18   Week 12: 5.4-5.6 Examples and Rayleigh Quotient

Apr 21-Apr 25   Week 13: 12.1-12.3 Method of Characteristics	
Apr 28-May 02   Week 14: 12.4-12.6 More Examples
May 05          Week 15: Review and Catch Up

*** Prep Day May 07
*** Final exam Wednesday, May 14 from 12:45pm-2:45 in AB634.

Grading

     Midterm                  100 points
     10 Quizzes                10 points each
     Final Exam               100 points
    ------------------------------------------
                              300 points total

Exams and quizzes will be interpreted according to the following grading scale:

    Grade        Minimum Percentage
      A                 90 %
      B                 80 %
      C                 70 %
      D                 60 %

The instructor reserves the right to give plus or minus grades and higher grades than shown on the scale if he believes they are warranted.

Quiz and Exam Schedule

There will be two quizzes, a midterm and a final exam. In person attendance is mandatory for all exams.

Course Policies

Communications Policy

Lectures and classroom activities will held in person and live streamed through through Zoom at the scheduled meeting time listed in MyNevada for this course. Please check the canvas page for the Meeting ID and Join URL under the Zoom tab if you are unable to make it to class. If you wish to set up an appointment for office hours please send me a message through WebCampus. I am available to meet in my office or through Zoom.

Late Policy

Students must have an approved university excuse to be eligible for a make-up exam. If you know that you will miss a scheduled exam please let me know as soon as possible.

Plagiarism

Students are encouraged to work in groups and consult resources outside of the required textbook when doing the homework for this class. Please cite any sources you used to complete your work including Wikipedia, other books, online discussion groups as well as personal communications. Exams and quizzes, unless otherwise noted, will be closed book, closed notes and must reflect your own independent work. Please consult the section on academic conduct below for additional information.

Diversity

This course is designed to comply with the UNR Core Objective 10 requirement on diversity and equity. More information about the core curriculum may be found in the UNR Catalog here.

Statement on Academic Success Services

Your student fees cover usage of the University Math Center, University Tutoring Center, and University Writing and Speaking Center. These centers support your classroom learning; it is your responsibility to take advantage of their services. Keep in mind that seeking help outside of class is the sign of a responsible and successful student.

Equal Opportunity Statement

The University of Nevada Department of Mathematics and Statistics is committed to equal opportunity in education for all students, including those with documented physical disabilities or documented learning disabilities. University policy states that it is the responsibility of students with documented disabilities to speak with the Disability Resource Center during the first week of each semester to discuss appropriate accommodations to ensure equity in grading, classroom experiences and outside assignments. For assistance with accessibility, or to report an issue, please use the Accessibility Help Form. The form is set up to automatically route your request to the appropriate office that can best assist you.

Statement on Audio and Video Recording

Surreptitious or covert video-taping of class or unauthorized audio recording of class is prohibited by law and by Board of Regents policy. This class may be videotaped or audio recorded only with the written permission of the instructor. In order to accommodate students with disabilities, some students may be given permission to record class lectures and discussions. Therefore, students should understand that their comments during class may be recorded.

Academic Conduct

Bring your student identification to all exams. Work independently on all exams and quizzes. Behaviors inappropriate to test taking may disturb other students and will be considered cheating. Don't send electronic messages, talk or pass notes with other students during a quiz or exam. Homework may be discussed freely. When taking a quiz, midterm or exam don't read notes or books unless explicitly permitted. Sanctions for violations are specified in the University Academic Standards Policy. If you are unclear as to what constitutes cheating, please consult with me.

Final Exam

The final exams will be held in person at the time listed in the standard schedule of final exams for this section. Namely, the final exam is Wednesday, May 14 from 12:45pm-2:45 in AB634

Last Updated: Wed Feb 19 09:08:57 AM PST 2025