Mathematics 488/688 Homepage

Spring 2024 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             10:00-10:50am MWF PE104

Course Information

Instructor:: Eric Olson
email:: Please contact me through WebCampus
Office:: DMS 238 MW from 11am to 1pm
Homepage:: https://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.
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.

Class Handouts

Course materials specific for this section of Math 466 are available by clicking on this link. Details for how to access these files may be found on our course page in WebCampus.

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

HW1 due Friday, Feb 2 (solutions): Turn in 1.2#8; Practice 1.3#2, 1.3#3, 1.4#1adfh
HW2 due Friday, Feb 16 (solutions): Turn in 1.4#1c; Practice 1.4#2abc, 1.5#2, 2.3#2bd
HW3 due Friday, Mar 1 (solutions): Turn in 2.3#3a; Practice 1.4#7ac, 2.3#3c, 2.4#2, 2.5#1c, 2.5#3a
HW4 due Wednesday, Mar 13 (solutions): Turn in 3.3#2c; Practice 3.2#1cdg, 3.2#2be, 3.3#1cb, 3.3#7, 3.4#1ab, 3.5#1abc
HW5 due Friday, Apr 12 (solutions): Turn in 4.4#2; Practice 4.2#2, 4.4#1, 4.4#5, 4.4#10, 5.3#1, 5.3#3
HW6 (extra) due Friday, May 3: Turn in 12.6#8eg; Practice 5.3#4, 5.3#8, 12.2.5#bd, 12.3#3, 12.6#7a, 12.6#9a

Lecture Notes

Lecture 1: The Heat Equation
Lecture 2: Conductivity and Heat Capacity
Lecture 3: Boundary Conditions
Lecture 4: Steady-state Solutions
Lecture 5: Separation of Variables
Lecture 6: Fourier Series
Snow day: no notes
Lecture 7: Superposition Principle
Lecture 8: Insulated Boundary
Lecture 9: Periodic Boundary
Lecture 10: Laplace Equation
Lecture 11: Laplace Equation Continued
President's day: no notes
Lecture 12: Polar Coordinates
Lecture 13: Laplace on a Disc
Lecture 14: Fourier Convergence Theorem
Lecture 15: Gibbs Phenomenon
Lecture 16: Differentiation in x
Lecture 17: Differentiation in t
Lecture 18: Eigenfunction Expansions
Lecture 19: Types of PDEs
Lecture 20: The Wave Equation
Lecture 21: Midterm Review
Midterm: no notes
Lecture 22: Traveling Waves
Lecture 23: Execise 4.4.3
Lecture 24: Execise 4.4.9
Lecture 25: Self Adjoint Operators
Lecture 26: Eigenvalues are Real
Lecture 27: Rayleigh Quotient
Lecture 28: Eigenfuctions are Unique
Lecture 29: Minimum Property
Lecture 30: A Nonuniform String
Lecture 31: One-way Wave Equation
Lecture 32: Wave Equation on R
Lecture 33: Characteristics
Lecture 34: Characteristic Examples
Lecture 35: Traffic Flow
Lecture 36: Propagation of Shocks
Lecture 37: Example with Shock
Lecture 38: Fan out Example
Lecture 39: Review for Final

Announcements

[10-May-2024] Final Exam

The Final will be given Friday, May 10 from 10:15am-12:15pm in PE104. Here is a sample final to help you prepare for the exam.

[19-Apr-2024] Quiz 2

There will be a quiz in class on Friday, April 19. Please be prepared to solve the Laplace equation as in Execise 2.5#1, the wave equation as in Execise 4.2#2 and show that eigenfunctions belonging to different eigenvalues are othogonal relative to the weight function σ(x) as in item 5 of the Sturm-Liouville theory.

[15-Mar-2024] Midterm

The Midterm will be given in class on March 15. Please be prepared to find equilibrium solutions of the heat equation for different boundary conditions. You will also need to know how to solve time-dependent heat equations and the Laplace equation using separation of variables. Please review the quiz and all homework problems. I will be posting my solutions to the homework 4 Thursday. There are also partial solutions to the starred problems in the back of the book. Here is a sample midterm to help you study.

[14-Mar-2024] Homework 4 Solutions

I have created solutions to help you study. Please look over my solutions and compare them to yours. If you find any errors in my work or have questions, please let me know.

[07-Mar-2024] Homework 3 Solutions

I have created solutions to help you study. Please look over my solutions and compare them to yours. If you find any errors in my work or have questions, please let me know.

[20-Feb-2024] Homework 2 Solutions

I have created solutions to help you study. Please look over my solutions and compare them to yours. If you find any errors in my work or have questions, please let me know.

[16-Feb-2024] Quiz 1

There will be a quiz in class on Friday, Feb 16 covering exercises 1.4#1abcdefgh steady state solutions to the one-dimensional heat equation.

[09-Feb-2024] Homework 1 Solutions

I have created solutions to help you study. Please look over my solutions and compare them to yours. If you find any errors in my work or have questions, please let me know.

[19-Jan-2024] Welcome Spring 2024

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 22-Jan 26   Week 1: 1.1-1.4 Heat Equation
Jan 29-Feb 02   Week 2: 1.5,2.1-2.3.2 Separation of Variables
Feb 05-Feb 09   Week 3: 2.3.2-2.3.8 Boundary Value Problems
Feb 12-Feb 16   Week 4: Quiz 1

*** President's Day Monday Feb 19

Feb 20-Feb 23   Week 5: 2.4,2.5 More Examples
Feb 26-Mar 01   Week 6: 3.1-3.3.3 Fourier Series
Mar 04-Mar 08   Week 7: 3.3.4-3.6 Differentiation and Integration

Mar 11-Mar 15   Week 8: Midterm
Mar 18-Mar 22   Week 9: 4.1-4.4 Wave Equation

*** Spring Break Saturday Mar 23 to Sunday March 31

Apr 01-Apr 05   Week 10: 5.1-5.3 Sturm-Liouville Problems
Apr 08-Apr 12   Week 11: 5.4-5.6 Examples and Rayleigh Quotient
Apr 15-Apr 19   Week 12: Quiz 2

Apr 22-Apr 26   Week 13: 12.1-12.3 Method of Characteristics	
Apr 29-May 03   Week 14: 12.4-12.6 More Examples
May 06          Week 15: Review

*** Prep Day May 08
*** Final exam Friday, May 10 from 10:15am-12:15pm 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 Friday, May 10 from 10:15am-12:15pm in PE104.

Last Updated: Fri Jan 19 09:03:00 AM PST 2024