Instructor
Aleksandar Donev, 1016 Warren
Weaver Hall
E-mail:
donev@courant.nyu.edu
; Phone: (212) 992-7315
Office hours: Was: 2-4 pm Tuesdays until Spring Break.
New office hours during COVID-19 remote instruction: Tuesdays 2:30-3:30pm and Wednesdays 2-3pm, EST.
or by
appointment
Recitation and Grading
Two sessions: 8:00am-9:15am (CANCELLED after 3/27/2020) and also
11:00am-12:15pm, Fridays, WWH 312,
starting Feb. 7th
Teaching assistant:
Ildebrando "Brando" Magnani
Office hours: 2:30-4:30 pm Fridays, WWH 505
Grader:
Weiyi Ren
Course description
See Lectures
for details, and also outline of Recitations.
I have asked NYU ITS to record my lectures and post
them on NYUClasses (click the Panopto tool in the menu on the
left).
Many natural phenomena have been successfully formulated as partial
differential equations: common applications include Physics, Chemistry,
Biology, Economics and population dynamics. This course will be
primarily focused on the theory of linear partial differential equations
such as the heat equation, the wave equation and the Laplace equation,
including separation of variables, Fourier series and transforms,
Laplace transforms, and Green's functions. Some discussion of non-linear
conservation laws and the theory of shock waves will be given as time
permits. The use of computers to solve PDEs numerically (using Maple or
Matlab) will also be briefly covered.
Textbooks
Required textbook:
Walter
Strauss,
Partial
Differential Equations: An Introduction, John Wiley & Sons,
second edition, ISBN-13: 978-0470054567. This book has been used a number
of times in previous semesters so there should be plenty of used copies.
The main textbook is excellent but rather terse. It does not cover all of
the material I will cover, and therefore I
strongly recommend that
you supplement this book with the following two
optional but
recommended texts that are freely available
from the NYU
network in electronic (PDF) form or available for $25 as a
soft cover MyCopy (order online) via our library subscription to
SpringerLink:
- (Functional analysis focus) David F. Griffiths, John W. Dold,
David J. Silvester, Essential Partial Differential Equations:
Analytical and Computational Aspects, ISBN: 978-3-319-22569-2, available
on SpringerLink.
- (Physics/science focus) J. David Logan, Applied
Partial Differential Equations, Springer Verlag, 3rd edition,
ISBN:978-3-319-12493-3, available
on SpringerLink.
I will post a list of relevant sections to read for each class from all
three books.
Another
optional but very nice
and most complete textbook that is also freely available to you in PDF
format is
Peter J. Olver, Introduction to Partial Differential
Equations,
available
on Springer Link.
Prerequisites
Students who wish to enroll must meet the following prerequisites with
a grade of C or better or the equivalent:
- Ordinary Differential Equations
This is an advanced senior-level course that will assume
mathematical
maturity. Notably, students need to be proficient in:
ODE
including systems of equations and
linear algebra as well as the
use of
complex numbers,
vector (multivariable) calculus
including concepts such as divergence, gradient, Laplacian, Green's
identities. Many derivations will only be sketched with the assumption
that students can (and will!) fill in the rest independently.
Assignments and grading
There will be regular (approximately
weekly) assignments due
the second class of each week, a midterm and a final. No late
assignments will be accepted. The grade will be 25% based on
assignments, 25% on midterm (Thursday March 12th during class),
and 50% on the final (Thursday May 14th 10am-11:50am).
The grade scale will be based on the
percentiles:
- >92.5 = A
- 87.5-92.5 = A-
- 80.0-87.5 = B+
- 72.5-80.0 = B
- 65.0-72.5 = B-
- 57.5-65.0 = C+
- 50.0-57.5 = C
- 45.0-50.0 = C-
- <45.0 = F
Academic
integrity policies will be strictly enforced for homework
assignments. Copying homework problems from someone else is a serious
violation that can lead to expulsion from your program.
Computing
In the second half of the course we will learn how to use computers to
solve ODEs and PDEs. The Courant Institute has computer labs with Linux
workstations that have Matlab (matlab), Maple (xmaple), Mathematica
(mathematica), and other useful software installed.
Communication
There is a message and discussion board on
the course NYUCourses page that will be used for messages related to the
assignments and any scheduling changes. If you register for the class,
you automatically have access to the message board. All course materials
including lecture notes and assignments will be posted on this site as
they become available.
You should feel free to email
the instructor with any questions, concerns, or special requests
such as meeting outside of office hours, etc.