Instructor: Irene M. Gamba (gamba@math.utexas.edu) 471-7150
Office hrs: RLM 10.166, W 2:00-3:00pm,
Lecture Room: NOA 1.102, T-TH 12:30 – 2:00pm,
TA: Jose Morales-Escalante
(mescalante@math.utexas.edu),
Office hrs: RLM 9.166, Tuesdays
5-6:30pm
Required text: Numerical Analysis by Burden, Faires
and Burden(10th Edition) or Numerical Analysis by
Burden and Faires (9th edition), both by
Brooks & Cole - Cengage Learning.
Optional texts: 1- An introduction to C++ and
numerical methods, by Ortega and Grimshaw (Oxford,
1999), and/or
2- Guide to Scientific Computing in C++, by Pitt-Francis and Whiteley, Undergraduate topics in CS, Springer.
Course
webpage:
http://www.ma.utexas.edu/users/gamba/S16/S16-m348.html
This course covers a variety of topics in the theory
and application of numerical methods and provides practice in computer
programming. The main topics include computer arithmetic, nonlinear algebraic
equations, polynomial interpolation, numerical differentiation and integration,
initial-value problems for ordinary differential equations, and direct methods
for systems of linear algebraic equations. The objective is to prepare students
for advanced studies in all areas of computational science and engineering.
Emphasis will be placed on concepts and algorithms rather than proofs.
Prerequisites: M408D; M341 or M340L; CS303E or CS307
or equivalent exposure to basic programming; all with a grade of at least C-.
Homeworks: Homework sets will
be assigned weekly or biweekly throughout the semester and will contain a mix
of analytical and programming problems. It is acceptable for students to help each
other with the homework sets; however, each student must write up and submit
their own work. Both commented source code and sample output should be
submitted with programming assignments. Computers can be found in the
Undergraduate Computer Lab, RLM 7.122.
Programming:
Computer programming will be a required part of the course, and the official
language will be C++. No prior experience with C++ is necessary. Students will
be introduced to the language through various assignments from the C++ text,
sample programs, and online resources. The C++ text will be used for
self-study; it will not be discussed in class.
Exams: There will be two midterm exams and a final exam. The tentative dates
are
Midterm Exam
1
(Tuesday Feb 23),
Midterm Exam 2 ( NEW DATE Tuesday May 3),
Final Exam (Friday May
13, 9am).
Course grading policy:
In the computation
of the homework average, one homework grade (lowest) will be dropped.
Students with disabilities: The University of Texas at Austin provides upon
request appropriate academic accommodations for qualified students with
disabilities. For more information, contact the Office of the Dean of Students
at 471-6259, 471-4641 TTY.
The
following is a tentative schedule for the core topics of the course. Please be
aware that material may be reordered, added or deleted.
1. Computer
arithmetic (1 week)
·
Machine numbers
·
Round-off errors
·
Accumulation of errors
2. Equations in one variable (2 weeks)
·
Bisection method
·
Fixed-point iteration
·
Newton and related methods
3. Interpolation and polynomial approximation (2 weeks)
·
Lagrange polynomials
·
Hermite
polynomials
·
Piecewise cubic interpolation
4. Numerical differentiation and integration (3 weeks)
·
Multi-point differencing
·
Richardson extrapolation
·
Newton-Cotes quadrature
·
Gauss quadrature
·
Multi-dimensional problems
5. Initial-value problems for ordinary differential equations (3 weeks)
·
Euler and Taylor methods
·
Runge-Kutta
methods
·
Multi-step methods
·
A-Stability and Stiffness
6. Direct methods for solving linear systems (3 weeks)
·
Gaussian elimination and LU
factorization
·
Stability and condition number
·
Pivoting strategies
·
Choleski
and Crout algorithms