|
Home
Research
Publications
Current Lectures:
238 Lectures
415 Lectures
Archived Lectures:
515 Lectures
526 Lectures
626 Lectures
614 Lectures
502 Lectures
201 Lectures
MA506
DMS
UAH
|
|
| Faculty |
Dr. Ravindran |
| Lecture Room: |
219 Shelby Center |
| Lecture Time: |
MW 2:20pm-3:40p.m. |
| Office Hours: |
MWF 3:45 - 5:00 p.m and TR 2-3:00pm. |
MA415:
Introduction to Numerical Methods
|
Numerical Analysis,
by T. Sauer,
Addison-Wesley, 2006
Additional References
Elementary Numerical Analysis
by Kendall Atkinson and Weimin Han
R.L. Burden and J.D. Faires, Introduction to Numerical Analysis,
Brooks/Cole.
Kincaid and Cheny, Numerical Analysis: Mathematics of Scientific
Computing, Brooks/Cole, 3rd Edition.
Linz and Wang, Exploring Numerical Methods,
Jones and Bartlett.
Chapra and Canale, Numerical Methods for Engineers, McGraw Hill.
Leader, Numerical Analysis and Scientific Computation, Pearson-Addison-
Wesley.
This is a standard first course in
scientific computation and numerical analysis.
We will study and derive a number of methods for approximately
solving problems that cannot otherwise be solved.
It covers the solution of large systems of simultaneous
linear equations, as well as interpolation, numerical
differentiation and methods for evaluating definite
integrals when analytical techniques cannot be applied.
The methods considered are suitable for
implementation on computers.
- Binary fractions, computer floating point format,
machine arithmetic, rounding procedures and roundoff error.
- Solution of single nonlinear equation by
Newton's iteration and secant iteration.
- Lagrange interpolation, Newton's interpolation, picewise interpolation
and cubic B-splines.
- Numerical differentiation. Numerical integration:
Trapezoidal rule, Midpoint rule, Simpson rule, Gaussian qudrature,
Richardson's extrapolation.
- Solving systems of linear equations by Gaussian elimination
with pivoting, and by the mathematically equivalent PLU-factorization.
Norms, condition numbers of matrices. Iterative methods for system
of linear equations.
MA 244,
Introduction to Linear Algebra and
MA 201,
Calculus C, and CS 121 or familiarity with computer programing
in at least MATLAB, C, Fortran or JAVA.
Hourly examinations
There will be two in-class examinations during the semester.
These are scheduled for February 27 and April 2.
Final examination
There will be a comprehensive final examination on April 28 from
3:00--5:30 p.m.
Calculators
No programmable or graphic calculators are allowed in the
tests. Only basic calculators are allowed.
If the calculator costs more than $15, you are buying the wrong calculator.
Assignments
I will give assignments nearly every week, to be turned in for grading.
This average will count 25% of
your grade. Your assignment must be neatly written with appropriate
discussions and stapled. Do not fold it or include it in
envelope. Hand-in assignments are due at the beginning of the class
period on the due date. Assignments that are not picked up in class
the day I return them will be kept in my office. Please stop by
to pick up your old assignments. I will not send assignments by email.
Student Responsibilities
Class attendance, preparation, and participation are required.
Students having difficulties
should seek assistance from the instructor. Students are encouraged to
work together on problems that will not be graded. Students are expected
to be honest and ethical at all times.
Students with disabilities needing academic accommodations should
1) register with and provide
documentation to the Student Development Services Office,
and 2) bring a letter to the instructor from SDSO indicating you need academic
accommodations. This should be done within the first week of class.
Course grading
Each student's grade will be based on the individual grades
from exams and assignments. The approximate percentage weights
are as follows:
Grade Weights
| Item |
Approx.
Weight |
| Two Mid-term Exam(s) |
40% |
| Final Exam |
30% |
| Assignments |
30% |
| Total |
100% |
Grading Scale
| A |
90.0 - 100% |
| B |
80.0 - 89.9% |
| C |
70.0 - 79.9% |
| D |
60.0 - 69.9% |
| F |
Below 60.0% |
The grades will not be curved. That is, there is no quota for the
number of A's, B's, etc. that will be given for the course.
| Week |
Sections |
Comments |
| 1 |
0.1 |
.... |
| 2 |
0.2,0.3 |
....... |
| 3 |
0.4 |
... |
| 4 |
1.1,1.2 |
......... |
| 5 |
1.3 |
.... |
| 6 |
1.4,1.5 |
..... |
| 7 |
2.1 |
........ |
| 8 |
2.2 |
| 9 |
2.3,2.4 |
.... |
| 10 |
3.1 |
.... |
11 |
3.2,3.3 |
.... |
| 12 |
3.4 |
.... |
| 13 |
4.1,4.2 |
.... |
| 14 |
5.1 |
| 16 |
5.2 |
..... |
| 17 |
Review |
Final Exam: 3:00 p.m., April 28 |
Note: This is an approximate syllabus only and because of differences in
weekly schedules, some variations are to be expected.
| Section |
Exercises |
| 0.1 |
1,2,3 |
| 0.2 |
2,4,6,8,9b),13 |
| 0.3 |
6,10 and those provided in class |
| 0.4 |
1b,3b),4,5 |
| 1.1 |
1,2,3,4,5,6,7,9,10 |
| 1.2 |
1a-d,2,3,6,9 |
| 1.3 |
1,2,3,4,5,8,9 |
| 1.4 |
1,2,3,10,11 |
| 1.5 |
1,2,3,4,5,6,7,8 |
| 2.1 |
1,2,3,4,6,7,8,24,25 |
| 2.2 |
1,2,3,4,5,7,8,14,15,16,17 |
| 2.3 |
1,2,3,4,6,7 |
| 2.4 |
1,2,3,4,5,6,7 |
| 3.1 |
1,2,3,4,5,7,9 |
| 3.2 |
1,2,3,4,5 |
| 3.3 |
1,2,3,4,5 |
| 3.4 |
1,3,4,5,7,8,9,10,11,12,13 |
| 4.1 |
1,2,3,4,5,6,7,8 |
| 4.2 |
1,2,3 |
| 5.2 |
1a,b, 3, 2a,b, 3, 7, 8, 10 |
You should read the chapter sections before class on the day indicated.
Homework will be assigned weekly in the class, but not collected.
You should consider the homework
assignments as a minimal exercise. If you don't feel confident after doing
the given homework, please
do some additional exercises in the textbook. The more exercises you do,
the better off you will be. You are encouraged to discuss homework
problems with your fellow students, especially in a group setting.
Instructions for Computer Write-ups:
Click here for a sample
computer write-up in PDF format.
The old midterm exams are available in PDF format.
A free PDF viewer is available for most computer systems from
clicking on the the icon shown below.
Midterm Exam I
Midterm Exam II
Links to access your grades etc
Student web to obtain grades etc.
Faculty web to post grades etc.
A Practical Introduction to Matlab
A visual approach to Taylor polynomial approximations
"It is the mark of an educated mind to rest satisfied with the degree of
precision which the nature of the subject admits and not to seek
exactness where only an approximation is possible".
- Aristotle
|
