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: M W (8:45 pm - 10:00 pm)
Venue: Planetary Hall 206
INSTRUCTOR
Dr. Padmanabhan Seshaiyer
Office:EXP 4456 (Exploratory Hall)
Office Hours: Mon Thur (3:30 pm - 5:00 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, 2nd edition (2012).
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.
There are computer Labs in Innovations Hall, the Johnson Center, and the Field House. For hours of operation of these labs and other locations see Academic Computing Labs Page .
Connecting to MATLAB
Two options for Windows Users
Use SSH
Download Secure Shell from the mason website: https://itservices.gmu.edu/downloads
Once you have it installed, open the program.
SSH has both an FTP(Yellow Icon) and a Terminal(White Icon). Open the Terminal.
From the SSH client window, click on the 'Quick Connect' button.
In the Host Name Box type mason.gmu.edu and your user name.
Press Connect and you will be prompted to enter your password.
To begin your Matlab session, at the mason prompt type matlab and press enter.
Use Virtual Computing Lab.
After clicking on New Reservation choose from drop down menu: Matlab 2013a. Click here for PC instructions
Two options for Mac Users
Use Terminal App
In Applications/Utilities open the terminal program.
At the command prompt, type : ssh username@mason.gmu.edu
After you press enter you will be prompted to enter your password.
To begin your Matlab session, at the mason prompt type matlab and press enter.
Use Virtual Computing Lab
After clicking on New Reservation choose from drop down menu: Matlab 2013a. Click here for Mac instructions.
COURSE EVALUATION
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 (or maybe typed) 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
Monday May 14, 2018 from 7:30 p.m. to 10:15 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
Numerical Solutions to Differential Equations
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
If you are a student with a disability and you need academic
accommodations, please see me and contact the Office of Disability
Resources at 703/993-2474. All academic accommodations must be arranged
through that office.