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MA506
DMS
UAH
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| Professor: |
Dr.
S.S. Ravindran |
| Lecture Room: |
Madison Hall 330 |
| Lecture Time: |
TR 12:45 p.m - 2:05 p.m. |
| Office Hours: |
MWF 3:00 - 5:00 p.m. |
MA515:
Introduction to Numerical Analysis
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An Introduction to Numerical Methods and Analysis,
by James F. Epperson ;
John Wiley and Sons, 2002 (ISBN: 0-471-31647-4).
Errata list (doc).
Additional References
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.
J. Ortega , Numerical Analysis,
Academic Press.
K. Atkinson, An Introduction to Numerical Analysis, has a more theoretical treatment of many topics of this course.
G. Dahlquist and A. Bjorck, Numerical Methods, is a classical reference on numerical methods.
This is an introductory course in numerical analysis..
It covers analysis and development of numerical algorithms
for: the solution of differential equations, nonlinear 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 and system of nonlinear equation by
fixed point iteration, Newton's iteration and secant iteration.
Convergence of these iterative methods.
- Lagrange interpolation, Newton's interpolation, picewise interpolation
and cubic B-splines. Error estimates.
- Numerical differentiation. Numerical integration:
Trapezoidal rule, Midpoint rule, Simpson rule, Gaussian qudrature,
Richardson's extrapolation, adaptive integration and singular integrals.
- Numerical methods for solving linear and nonlinear initial value problems for differential
equations. Stability, Consistency and Convergence of the methods.
- Numerical methods for solving linear and nonlinear boundary
value problems for differential equations. Single step and
multi-step methods will be studied with attention given to stability and rate of convergence.
Differential Equations, Applied Linear Algebra and
computer programming proficiency.
At least one of the following programming languages:
Fortran, Fortran 90, C, C++, Visual Basic, Java.
Final examination
There will be a comprehensive final examination on
December 7 from 11:30- 2:00pm. You will be allowed to bring in one page
of notes to the exam.
Midterm examination
There will be two midterm examinations during the semester. These are
scheduled for 10/3 and 11/14.
Make-ups
If you miss a test due to a documented
illness, family emergency or other extreme circumstance, the weight of
your remaining grades will be adjusted to compensate provided I receive
a written excuse within a reasonable amount of time
after the missed test.
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.
Practice Assignments
Practice homework will be written on blackboard at the end of each section.
These are for practice only and will not be collected or graded.
If you have questions about them you may work with
your classmates, ask me for assistance, and/or ask some questions
during class. (We will not have time to answer all the
questions in 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% |
| Regular Assignments (Quizzes+Programming) |
30% (20%+10%) |
| Total |
100% |
Grading Scale
| A |
90.0 - 100% |
| B |
80.0 - 89% |
| C |
70.0 - 79% |
| D |
60.0 - 69% |
| F |
Below 59.0% |
| Week |
Sections |
Comments |
| 1 |
Review,2.2 |
...... |
| 2 |
2.4,2.5,2.6 |
...... |
| 3 |
2.7,3.1 |
...... |
| 4 |
3.2,3.5 |
...... |
| 5 |
3.6,3.8,3.9 |
...... |
| 6 |
4.1,4.2 |
...... |
| 7 |
4.3,4.7 |
...... |
| 8 |
4.8,4.9,4.10 |
...... |
| 9 |
5.6 |
...... |
| 10 |
6.1,6.2 |
.......... |
| 11 |
6.3,6.4 |
...... |
| 12 |
6.5,6.6 |
...... |
| 13 |
6.7,6.8 |
.......... |
| 14 |
6.10,7.8 |
.......... |
| 15 |
7.10, Review |
.......... |
Note: This is an approximate syllabus only and because of
differences in weekly schedules, some variations are to be
expected especially in summer.
| Section |
Exercises |
| 1.1 |
1,3,4,6,7,11a),12c) |
| 2.2 |
1,2a),6a),8,12,18 |
| 2.4 |
1a),2a),4,7,10,11 |
| 2.5 |
1,3,4,7,14,16a) |
| 2.6 |
1,3,5,6,8,9 |
| 2.7 |
1,3,5,7 |
| 3.1 |
1,2a),4,5,6 |
| 3.2 |
1,3,5a),7 |
| 3.5 |
1,2,3,5,6,7 |
| 3.8 |
1,3,6,7 |
| 3.9 |
1,2,4,5a),6,7 |
| 4.1 |
1,2,4,5,6,7 |
| 4.2 |
1,2,4,7,8,9,10 |
| 4.7 |
1,2,3,4,5,6 |
| 4.8 |
1,2,3,4,5,6,7,8,9,10,11 |
| 5.3 |
1,3,5,7,9,11 |
| 5.4 |
1,3,5,6,7,10 |
| 5.6 |
1,2,5,10,11,15 |
| 6.1 |
2,3,4,5 |
| 6.2 |
1,2,3,4,5 |
| 6.3 |
1,2,3,4,5,6 |
| 6.4 |
1,2,3,4,5 |
| 6.5 |
2,3,4,5 |
| 6.6 |
1,5,6,7,8,9,10 |
| 6.7 |
1,2,3,4,5,6 |
| 6.8 |
1,2,3,4,5,6 |
| 6.10 |
2,3,4,5 |
| 7.8 |
2,3,4,5 |
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
A free PDF viewer is available for most computer systems from
clicking on the the icon shown below.
FINAL EXAM
11:30-2:00pm, December 7
Class attendance, preparation, and participation are required. Learning
this course is not a spectator sport. 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.
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
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