Mathematics 488/688 Homepage

Spring 2023 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
------------------------------------------------------------------------
Eric Olson  Math 488/688-1001 PDEs             4:30-5:45pm TR PE104

Course Information

Instructor:: Eric Olson
email:: Please contact me through WebCampus
Office:: DMS 238 and through Zoom by appointment
Homepage:: http://fractal.math.unr.edu/~ejolson/488/
Live Stream:: If you can't come to class due to sickness, quarantine or other reasons, please join via the Zoom link in WebCampus.
Grader:: Lauren Feldman (contact through WebCampus)
Required Texts:: Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, Fifth Edition by Richard Haberman
Other resources:: 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.

Class Handouts

Course materials specific for this section of Math 488 are available by clicking on this link. Details for how to access these files may be found on our course page in WebAssign.

Homework

HW1 problems 1.2.8, 1.3.2, 1.3.3, 1.4.1adfh, 1.4.2abc, 1.4.7a (due Feb 14) (solutions)
HW2 problems 1.5.2, 2.3.1ad, 2.3.2bd, 2.3.3ac, 2.3.8, 2.4.2 (due Mar 9) (solutions)
HW3 problems 3.2.1bdf, 3.3.1de, 3.3.7, 3.3.17abc, 3.4.5, 3.5.1abc (due Apr 6) (solutions)
HW4 problems 4.2.2, 4.4.1, 4.4.2, 4.4.5, 4.4.10, 5.3.1 (due Apr 20) (solutions)
HW5 problems 5.3.3, 5.3.4, 5.3.8, 12.2.1, 12.2.2, 12.3.4 (due May 4) (solutions)

Lecture Notes

Lecture 1: The Heat Equation
Lecture 2: Boundary Conditions
Lecture 3: Higher Dimensional Problems
Lecture 4: Separation of Variables
Lecture 5: Eigenfunctions
Lecture 6: Insulated Boundary
Lecture 7: Circular Boundary
Lecture 8: Laplace Equation
Lecture 9: Laplace on a Disk
Lecture 10: Fourier Convergence Theorem
Lecture 11: Differentiation of Fourier Series
Lecture 12: More Series Differentiation
Lecture 13: Integration and Review
Lecture 14: The Wave Equation
Lecture 15: Wave Equation Examples
Lecture 16: Sturm-Liouville Problems
Lecture 17: Self-adjoint Operators
Lecture 18: The Raleigh Quotient
Lecture 19: Sturm-Liouville Example
Lecture 20: Quiz 2 Review
Lecture 21: Method of Characteristics
Lecture 22: Characteristic Examples
Lecture 23: Traffic Flow
Lecture 24: Final Review

Announcements

[11-May-2023] Final Exam

The Final will be given Thursday, May 11, 2023 from 4:50-6:50pm in PE104. Here is a sample final to help you prepare for the exam.

[6-May-2023] Homework 5 Solutions

I have posted my solutions to Homework 5. Please let me know if you see any errors in my answers. There are also partial solutions to the starred problems in the back of the book.

[26-Apr-2023] Homework 4 Solutions

I have posted my solutions to Homework 4. Please let me know if you see any errors in my answers. There are also partial solutions to the starred problems in the back of the book.

[20-Apr-2023] Quiz 2

Quiz 2 will be given in class on April 20. Please be prepared to solve the Laplace equation as in Exercise 2.5.1 from the text and the wave equation as in Exercises 4.4.2 and 4.4.3.

[8-Apr-2023] Homework 3 Solutions

I have posted my solutions to Homework 3. Please let me know if you see any errors in my answers. There are also partial solutions to the starred problems in the back of the book.

[16-Mar-2023] Midterm

The Midterm will be given in class on March 16. Please be prepared to find equilibrium solutions of the heat equation for different boundary conditions as on the Quiz and homework 1. You will also know how to solve time-dependent heat equations using separation of variables as in homework 2. I will be posting my solutions to the homework on Monday. There are also partial solutions to the starred problems in the back of the book.

[14-Mar-2023] Sample Midterm

The Midterm will be given in class on March 16. Here is a sample midterm to help you prepare for the exam.

[13-Mar-2023] Homework 2 Solutions

I have posted my solutions to Homework 2 to help you study for the Midterm on Thursday. Please let me know if you see any errors in my answers. There are also partial solutions to the starred problems in the back of the book.

[24-Feb-2023] Quiz 1 Solutions

I'm posting my solutions for Quiz 1. Even if you received full credit for a particular problem, it may help to look at my work.

[15-Feb-2023] Homework 1 Solutions

I have posted my solutions to Homework 1 to help you study for the quiz on Thursday. Please let me know if you see any errors in my answers. There are also partial solutions to the starred problems in the back of the book.

[16-Feb-2023] Quiz 1

Quiz 1 will be given in class on February 16. Please be prepared to find equilibrium solutions of the heat equation for different boundary conditions as in the homework. I will be posting my solutions to the homework Wednesday morning. There are also partial solutions to the starred problems in the back of the book.

[21-Jan-2023] Welcome Spring 2023

I am looking forward to seeing you starting the first week of class.

Do not come to class if you are sick--even if it's something other than COVID-19. If you are subject to quarantine because of exposure to a person who is sick, please stay home.

This section of Math 488/688 is in person. However, I will live-stream our class meetings each day at a link available in WebCampus for those who are sick or unable to attend on a particular day. I will also maintain an online archive of course materials including lecture notes, assignments and other announcements.

Tentative Course Schedule

Jan 23-Jan 20   Week 1: 1.1-1.4 Heat Equation
Jan 30-Feb 03   Week 2: 1.5,2.1-2.3.2 Separation of Variables
Feb 06-Feb 10   Week 3: 2.3.2-2.3.8 Boundary Value Problems
Feb 13-Feb 17   Week 4: Quiz 1

*** President's Day Monday Feb 20

Feb 21-Feb 24   Week 5: 2.4,2.5 More Examples
Feb 27-Mar 03   Week 6: 3.1-3.3.3 Fourier Series
Mar 06-Mar 10   Week 7: 3.3.4-3.6 Differentiation and Integration

Mar 13-Mar 17   Week 8: Midterm

*** Spring Break Saturday Mar 18 to Sunday March 26

Mar 27-Mar 31   Week 9: 4.1-4.5 Wave Equation
Apr 03-Apr 07   Week 10: 5.1-5.3 Sturm-Liouville Problems
Apr 10-Apr 14   Week 11: 5.4-5.5 More Examples
Apr 17-Apr 21   Week 12: Quiz 2

Apr 24-Apr 28   Week 13: 12.1-12.3 Method of Characteristics	
May 01-May 05   Week 14: 12.4-12.5 More Examples
May 08          Week 15: Review

*** Prep Day May 10
*** Final exam Thursday, May 11 from 4:50-6:50pm in PE104

Grading

     Midterm                   50 points
     2 Quizzes                 20 points each
     5 Homework Assignments     6 points each
     Final Exam                80 points
    ------------------------------------------
                              200 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 Thursday, May 11, 2023 from 4:50-6:50pm in PE104.

Last Updated: Sat Jan 21 01:37:42 PM PST 2023