Math 4250 / CS 4210, Numerical Analysis and
Differential Equations, Fall 2009
Announcements:
- Aug 26: For any enrollment questions, please see
Ms. Heather Peterson in 310 Malott Hall.
- Aug 27:
Lecture notes
on floating point numbers (courtesy of Prof. W. Tucker).
(Please also see the related links.)
- Sep 10: The newly organized
"Scientific Computing
& Numerics" (SCAN) seminar
will cover many problems at the forefront of modern
numerical analysis. The talks will often deal
with topics related to the material covered in
this course -- please consider attending.
Other relevant local seminars can be found
here.
- Sep 15:
Short intro
to Chebyshev's polynomials (courtesy of Prof. S. Fomel).
- Sep 22:
A summary
on Numerical Integration (courtesy of Prof. J. Demmel).
- Oct 6:
A summary
on Numerical ODE solvers.
Interactive ODE Solvers for MATLAB by John Polkin.
- Oct 27:
The SOLVE key on the HP-34C.
Prof. Kahan's article about a robust Secant Method implementation.
- Nov 3:
A gentle intro
to the Method of Characteristics.
- Nov 5:
Some related classes to consider for the next semester (Spring 2010):
Math 4260 / CS 4220,
Math 4280,
CS 5220,
Math 6140,
Math 6200.
- Nov 17:
Notes on traffic flow modeling intro by Prof. Childress.
- Nov 24:
A brief intro
to epidemiological models by
Prof. J. Medlock.
From the catalog:
-
Introduction to the fundamentals of numerical analysis:
error analysis, approximation, interpolation, numerical integration.
In the second half of the course, the above are used to build
approximate solvers for ordinary and partial differential equations.
Strong emphasis is placed on understanding the advantages, disadvantages,
and limits of applicability for all the covered techniques.
Computer programming is required to test the theoretical concepts
throughout the course.
MATH 4250 (CS 4210) and MATH 4260 (CS 4220) provide a comprehensive
introduction to numerical analysis; these classes can be taken
independently from each other and in either order.
Reasons to care:
-
Most "real-world" problems are too hard (or too expensive) to solve exactly.
Hence the need for approximate methods, most often implemented
using computers. This course will be problem-driven:
computational experiments in Matlab will be used to compare and contrast
different numerical approaches for a variety of applications
(e.g., surface fitting, computation of planetary orbits,
traffic modeling, gossip propagation, diffusion of wealth,
pattern formation).
Times and Location:
- Lectures (Vladimirsky): Tue 01:25 - 02:40, Location:
Malott Hall (MLT), Room 207
- Lectures (Vladimirsky): Thu 01:25 - 02:40, Location:
Malott Hall (MLT), Room 207
Staff:
-
Alex Vladimirsky,
Instructor
- Contact Info: 430 Malott Hall, 255-9871, vlad@math.cornell.edu
- Office Hours:
Wednesday 11am-12pm, Thursday 3:00-3:55pm, (or by appointment).
-
David Blocher,
Teaching Assistant
- Contact Info: 102 Thurston Hall,
dbb74@cornell.edu
- Office Hours:
Monday 12-1pm and 4-5pm (or by appointment).
Software:
-
You will need to have access to some computer running Matlab.
A student version for your personal computer
can be purchased for $99 from
Mathworks.
Matlab is also installed on most computers in
Cornell Public Computing Labs.
-
In either case, please make sure to install the
Matlab files accompanying the second textbook.
Texts:
- Kincaid, D. and Cheney, W.,
Numerical Analysis:
Mathematics of Scientific Computing,
Third Edition, Brooks/Cole, 2001.
- Moler, C.B.,
Numerical Computing with Matlab, SIAM, 2004.
Note: the first of these can be bought
from the AMAZON
for $153.56
or
for $52-83
from other vendors;
the second can be bought
from SIAM for $32.55
(you will need a
SIAM membership,
but joining is
free for Cornell students).
An
on-line version
of Moler's book is also available free of charge.
Beware: in Moler's book some of the problem numbers are different
in the printed & on-line versions; all problem numbers in the homework
will correspond to the
on-line version.
Additional Literature:
-
As always, it is wise to consult several references to gain a broader
understanding of the subject. Below are listed a few books which may be
useful to browse through.
- A fairly rigorous & comprehensive undergraduate text:
- Atkinson, K. E., An Introduction to Numerical Analysis,
John Wiley & Sons, 2nd ed., 1989.
- Two excellent (though somewhat more advanced) introductions:
- Stoer, J. & Bulirsch, R.,
Introduction to Numerical Analysis,
3rd ed., Springer-Verlag, 2002.
- Deuflhard, P. & Hohmann, A.,
Numerical Analysis in Modern Scientific Computing,
2nd ed., Springer-Verlag, 2003.
- Two very good texts on numerical ODE solvers:
- Lambert, J.D.,
Numerical methods for ordinary differential systems :
the initial value problem,
John Wiley & Sons, 1991.
- Hairer, E. ,
Solving ordinary differential equations,
Volumes 1 and 2, Springer-Verlag, 1993.
- An extensive cookbook full of overly general statements, but with
a very good intuitive motivation for many methods
(beware - the included algorithm implementations are not
totally robust or most optimal) :
- Press, W., Flannery, B., Teukolsky, S., & Vetterling., W.,
Numerical Recipes in C , Cambridge University Press, 1988.
Tentative Schedule |
Exam schedule and Grade decomposition: