It is
well-known that the use of numerical methods for the analysis,
simulation, and design of engineering processes and industrial
systems has been increasing at a rapid rate. Therefore, this course
is intended to better prepare future engineers and computational
scientists (as well as to assist practicing engineers and
computational scientists), in understanding the fundamentals of
numerical methods, especially their application, limitations, and
potentials. This course is designed as an introductory course in
computational techniques for solving problems from science and
engineering with emphasis on applications. The course will cover the
classical fundamental topics in numerical methods such as,
solution of nonlinear algebraic systems, approximation, numerical
integration and numerical linear algebra. The viewpoint will be modern, with
connections made between each topic and a variety of applications.
By the end of the course, the student should not only be familiar,
but more confident, in effectively using numerical tools to solve
problems in their own field of interest.
Lectures: Tu Thur (3 pm - 4:30 pm)
Venue: Science and Technology I (Room 131)
INSTRUCTOR
Dr. Padmanabhan Seshaiyer
Office:MATH 222B
Office Hours: T Th (4:30 pm - 5:30 pm) and by appointment
Sufficient recall of undergraduate linear algebra, differential equations
and computer literacy including familiarity with MATLAB.
TEXTBOOK
Numerical Analysis by Timothy Sauer, Pearson Addison Wesley
(2006). Topics from the book will be
supplemented with examples in class by the
instructor.
EXPECTED LEARNING OUTCOMES
In
this course, the emphasis will be to analyze and apply well-know numerical
techniques to solve engineering problems and evaluate the results.
The objective will be to train students to understand why the
methods work, what type of errors to expect, and when an application
might lead to difficulties. In particular, the students will become
proficient in:
Understanding the theoretical and practical aspects of the use of
numerical methods
Implementing numerical methods for a variety of
multidisciplinary applications
Establishing the limitations, advantages, and disadvantages
of numerical methods
The
expected learning outcomes for the course will be assessed through:
Exams, homeworks, in-class activities and class discussions. Problem-based
learning will be an integral part of the course.
ABOUT MATLAB
The software
package MATLAB will be used for scientific computation, analysis and
presentation of data. MATLAB is an interactive programming language
for general scientific and technical computation with powerful
graphics and library functions.
MATLAB is installed in the computer labs in the Johnson Center in rooms 340, 341, and 343 and in
Innovation Hall in room 301. Check the following
website for hours of operations.
MATLAB is also installed on the Mason cluster (osf1). To use this version of MATLAB, you must
activate your account on the Mason cluster (osf1). If you haven't done this before, you must activate
your mason account.
See the web page below for instructions to activate your account and set up a
password .
One may also access the Mason cluster (and hence, MATLAB) from home
using the
Secure Shell software.
Evaluation for the course will be based on the following criteria:
Homework
40%
Computer Projects
20%
Midterm Exam
15%
Final Exam
25%
TOTAL
100%
There will be five homework assignments during the semester that will
be considered for grade, each worth 8%. There will also be computer
projects which is worth 20%. These
items
should be written up and handed in on time to receive full credit as
they add towards 60% of the total grade.
There will be one midterm exam and one comprehensive final exam
in this course.
The Final Exam will be on
Tuesday May 12, 2009 from 1:30 p.m. to 4:15 p.m. and will be
comprehensive.
Make-up exams may be possible only in the case of documented
emergencies.
COURSE OUTLINE
We plan to cover the following topics in this class. Please note that topics covered may vary slightly
from those below depending on class interest and time.
Introduction to Mathematical Modeling and
Engineering Problem Solving
Scientific Computing
Solutions of Nonlinear Equations
Numerical Linear Algebra
Linear Least Squares
Interpolation and Polynomial Approximation
Numerical Differentiation and Integration
In this course, I would like to emphasize how we can analyze and apply
numerical
techniques to solve engineering problems and evaluate
the results. Problem-based learning (both in and out of class) will be
an integral part of the course. The primary reference will be
Lecture notes provided by the instructor that will be posted on the
course website every week. The students may supplement these notes with
textbooks in numerical methods for scientists and engineers.
All
students will be expected to abide by the Honor Code: Student members of the George Mason University
community pledge not
to cheat, plagiarize, steal, or lie in matters related to academic
work .
DISABILITY ACCOMODATION
Any student who, because of a disability, may require some special
arrangements in order to meet course requirements should contact the
instructor as soon as possible to make such accommodations as may be
necessary.