Math 4250 / CS 4210, Numerical Analysis and
Differential Equations, Fall 2013
Announcements:
- Aug 25: For any enrollment questions, please see
Ms. Heather Peterson in 310 Malott Hall.
- Aug 29: The joint Math/CS Seminar on
"Scientific Computing
& Numerics" (SCAN)
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.
- Aug 29:
Lecture notes
on floating point numbers (courtesy of Prof. W. Tucker).
(Please also see the related links.)
- Sep 17:
Short intro
to Chebyshev's polynomials (courtesy of Prof. S. Fomel).
- Oct 3:
A summary
on Numerical Integration (courtesy of Prof. J. Demmel).
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/Thu 01:25 - 02:40, Location:
Malott Hall (MLT), Room 253
Staff:
-
Alex Vladimirsky,
Instructor
- Contact Info: 430 Malott Hall, 255-9871, vlad@math.cornell.edu
- Office Hours:
Wednesday 11am-12pm, Tuesday and Thursday 11:30am-12:30pm, (or by appointment).
-
Zhengdi Shen,
Teaching Assistant
- Contact Info: 657 Rhodes Hall,
zs267@cornell.edu
- Office Hours: Monday 3:00-4:00pm, Thursday 4:30-5:30pm (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
for $42-83 on-line;
the second can be bought
from SIAM for $37.80
(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 nor 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: