under construction
Course Description: An introduction to partial differential equations focusing on equations in two variables. Topics include the heat and wave equation on an interval, Laplace's equation on rectangular and circular domains, separation of variables, boundary conditions and eigenfunctions, introduction to Fourier series,
Office hours: ... Please show up at least 15 minutes before the end of the office hour. I may have another office hour after the given one, or I may have to go somewhere else.
Email: hwenzl@ucsd.edu
Required Textbook: J. David Logan, Applied Partial Differential Equations, Third Edition You can access this book electronically from from uc library search by e.g. searching for the author.
Syllabus
Teaching assistant: Khoa Tran email: k2tran@ucsd.edu
Computation of grade: Your final score will be calculated by using the better score of the following two options:
Option 1: 20% homework + 20% midterm I + 20% midterm 2 + 40% Final
Option 2: 20% homework + 20% better of the two midterms + 60% Final
Dates of exams: No make-up exams!
If you miss a midterm, we will automatically use Option 2.Midterms:(tentative) October 21 and November 18
Homework assignments Homework is to be turned in via gradescope Grade Scope for HW this quarter. You will receive an email prompt some time during the second week notifying you of your gradescope enrollment and providing a link to set up your personal account.
You can watch this video which explains how to scan and submit HW online.
Due September 30: (get started now, there may be more to come!)
Due October 7:
Due October 14:
Relevant for midterm:
Due
Due
Relevant for midterm: (same rules as for first midterm; for practice midterm see bottom of this web page)
Due
Due
Syllabus and Schedule of lectures.
Below you find a tentative syllabus for the class.
In particular, the material in the later parts of the course is likely
to be subject of significant changes.
So please check back later, or compare with
the material covered in our recordings (posted on canvas).
It is important that you have a look at the material before it is covered
in the lectures.
Week
Monday
Tuesday
Wednesday
Thursday
Friday
0
Sept 23
1
Sept 26
Sept 28
Sept 30
2
Oct 3
Oct 5
Oct 7
3
Oct 10
Oct 12
Oct 14
4
Oct 17
Oct 19
Oct 21
5
Oct 24
Oct 26
Oct 28
6
Oct 31
Nov 2
Nov 4
7
Nov 7
Nov 9
8
Nov 14
Nov 16
Nov 18
9
Nov 21
Nov 23
10
Nov 28
Nov 30
Dec 2
11
Dec 7
PLEASE IGNORE LECTURE NOTES BELOW UNLESS THEY ARE SPECIFICALLY REFERRED TO. THEY ARE FROM ANOTHER COURSE WHICH USED ANOTHER BOOK
Lecture 6 October 14 Orthogonality, general outline for heat equation
Lecture 7 October 16 General outline for heat equation 2.4.2 circular ring
Lecture 8 October 19 Heat equation for a ring, Section 2.2 Linearity
Lecture 9 Laplace equation for rectangle
Lecture 10 Laplace equation for disk
Lecture 11 Section 2.5 Laplace equation: qualitative properties
Lectures Nov 6 and 9: odd/even functions, 3.4: differentiation term by term
Lecture 17 November 13 3.4 Differentiation term by term 4.2 Wave Equationy
Lecture 18 Chapter 4.2 and 4.4 Wave equation
Lecture 19 November 18 Chapter 4.4, 7.2 and Chapter 7.3 Wave equation
Lecture 20 November 20 Wave equation for rectangle
Lecture 21 Review Fourier series and wave equation
Lecture 22 Chapter 7.4, 7.7 Wave equation for disk
Lecture 23 Dec 2 Wave equation and Bessel functions
Lecture 24 Ch 7.8 Bessel functions Ch 7.7 Wave equation with circular symmetry
Lecture 25 Ch 5.3, 5.5 Orthogonality for eigenfunctions of Sturm-Liouville problems, Ch 7.7.9
Information about first midterm
CONTENT: The midterm will be a 50-minute exam, similar in nature to the practice exams, see below. You will have an additional 15 minutes to scan and upload the exam (see details below). It will cover everything up to and including HW 3: in terms of the book, this means sections 1.2, 1.3, 1.4, 1.5, 2.2, 2.3, 2.4, 2.5 (without 2.5.3). I will not ask specific questions about Fourier series covered in Section 3 yet, but you have to know about it what we did in Chapters 1 and 2.
RULES: It will be an open book exam: you will be allowed to consult the textbook, your own notes or previous homework, and the notes posted on Canvas or my webpage by me or by the TAs, but no other resources may be used. In particular, you may not use any online resources, any other printed material (such as solution manuals), or any form of calculator (all arithmetic on the exam will be easy!) and you must not communicate in any way with anyone else during the exam. You will be required to write, sign and submit with your work a statement certifying that you have followed the regulations. Breaches of the rules will be reported to the Academic Integrity office.
TECHNICAL INFORMATION: The exam will be presented through Gradescope in a form similar to a homework assignment, except that it will be timed. When you log in to Gradescope you will be able to see (and/or download) a pdf copy of the exam paper. You should write your answers on your own paper, scan and upload them to Gradescope within 65 minutes - that's 50 minutes official exam time, plus 15 minutes allowance for upload time. (Please assign the pages corresponding to the questions, just as you do for homework.)
DATE AND TIME: The exam will take place during normal class time: 2-2.50pm PT (There is a time change in the US over the weekend!) Wednesday November 4. Students who currently live in different time zones for whom the time would be very inconvenient should contact me about the possibility of taking the exam at another time by Monday, November 2. If you do so, please state where you currently live! Only students who have been approved before the exam can take it at a different time.
Practice Exam These are problems taken from another professor. There may be slightly different notations and priorities. See also the study problems posted above.
Here is a practice exam for midterm 2 from another professor. Some notations may be slightly different from this class. Ask if you are confused. See also the study problems above.
Practice midterm 2 with solutions
Here is a practice final. Please observe that it uses the Greek letter Delta for the Laplace operator, which we had denoted by nabla^2 (nabla = Delta upside down)