Instructor
Aleksandar Donev, 1016
Warren Weaver Hall
E-mail:
donev@courant.nyu.edu
; Phone: (212) 992-7315
Office hours: 2-4 pm Tuesdays, or by
appointment
Recitation and Grading
11:00am-12:15pm, Friday, WWH 312, starting week of Feb 1st
Teaching assistant:
Jiajun
Tong
Office hours: Wednesday 4:30-6:30pm in WWH 524, starting week of
Feb 1st
Course description
See Lectures
for details, and also the Recitation
Summary from J. Tong.
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.
You can look at the material posted online for the Fall 2015 PDE class
to get a feeling of what this course is about.
Textbooks
Required textbooks 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:
- (Primary) 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.
- (Secondary) 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 in each book for
each class.
An
optional but very nice
textbook is (check the bookstore for used copies from last
semester):
- Walter Strauss, Partial Differential Equations: An
Introduction, John Wiley & Sons, any edition, ISBN-13:
978-0470054567
- 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 30% based
on assignments, 25% on midterm (Thursday March 10th), and 45% on
the final (Thursday May 12th, 10am-11:50am, WWH 101).
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
- 42.5-50.0 = C-
- <42.5 = D or 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.