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Instructor:
Malgorzata Peszynska
(Contact information including office hours on webpage)
Class: MWF 09:00-09:50 STAG 113. On some Fridays (dates
announced on class website) the class will meet in MLC Computer Lab
where hands-on projects close to the assigned HW will be explored.
Prerequisites: Solid undergraduate advanced calculus and
linear algebra are the prerequisites. Prior computing experience is
not required but students will be expected to grow in their
computational and theoretical abilities.
This class is the second one in a
year-long sequence MTH 654-656 but classes in this sequence can be
taken independently. (Please contact the instructor with questions.)
Course content: In the course we will cover:
- The concepts of interpolation and approximation (I/A) will be
developed from the theoretical functional analysis point of view, as
well as explored practically. We will discuss polynomial and other
bases, splines and wavelets, I/A in normed, inner product, and Sobolev
spaces; least squares and Principal Component Analysis
- Iterative methods for solution of linear and nonlinear algebraics
systems such as those arising in (1) will be studied. In particular,
we will discuss Picard's and Newton's methods.
- Applications to solving integral and (partial) differential
equations, optimization, and reduced order modeling will be developed
and used in the assignments.
Course Learning Outcomes: A successful student will be able to
- Propose an appropriate approximation method for solving
numerically selected differential and integral equations, and assess its
accuracy using theoretical and practical approaches.
- Propose and implement appropriate interpolation and approximation
schemes for univariate and multivariate data, and assess its quality.
- Implement the solution of nonlinear algebraic systems that arise
from the approximation and interpolation problems, and assess their
convergence.
Textbook: Atkinson, Han, Theoretical Numerical
Analysis. A Functional Analysis Framework, Third Edition. Springer, 2010.
We will also use other notes and materials that will be distributed in class.
Grading: Grade will be based on the total score from Homework and
Lab activities assigned after each module (Total of 6-8, with one
lowest score to be dropped). Students will be graded on their
ability to progress. There will be a possibility to select (parts of
the) assigned HW and lab projects depending on the student's track,
i.e., their background and interests.
Special arrangements for students with disabilities: please contact the instructor and Services for Students with
Disabilities prior to or during the first week of the term to discuss
accommodations. Students who believe they are eligible for
accommodations but who have not yet obtained approval through DAS
should contact DAS immediately at 737-4098.
Course drop/add information is at
http://oregonstate.edu/registrar/.
Student Conduct: All students are expected to obey to OSU's student
conduct regulations, see
OSU's Statement of Expectations for Student Conduct
at this link
http://studentlife.oregonstate.edu/sites/studentlife.oregonstate.edu/files/student_conduct_code_1.pdf,
and specifically the information about Academic or Scholarly
Dishonesty beginning on p.2. In particular, please consult the
definitions of (A) CHEATING, (C) ASSISTING, and (E) PLAGIARISM, as
well as recommended handling.
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