Numerical Analysis
II (Differential Equations and Linear Algebra)
22M:171 (MATH:5810) Section AAA
The University of Iowa
The College of Liberal Arts and Sciences
Department of Mathematics This course is
cross-listed as 22C:171 (CS:5720).
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9:30–10:20am MWF; 213 MLH |
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www.math.uiowa.edu/~dstewart |
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Office location and hours: |
325 MLH; MW 10:30-11:30 & Tu 10-11 |
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david-e-stewart@uiowa.edu |
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You can see me
outside the office hours listed above provided it is mutually
convenient.
Some of the
policies relating to this course (such as the drop deadline) are
governed by its administrative home, the College of Liberal Arts
and Sciences, 120 Schaeffer Hall.
Description
of Course:
22C:171/22M:171
is the second half of a comprehensive course in numerical
analysis. Numerical analysis is what connects continuous
mathematics with computers and computing. Numerical analysis is
about how to solve equations, compute derivatives and integrals,
and solve differential equations. The difference is that computers
can only store real numbers to a finite (in fact, very limited)
number of decimal (or binary) places. Whenever a computation is
done, there is almost always some error in the result.
In this course
we will discuss methods for numerically (thus approximately)
differential equations, systems of linear equations, (linear)
least squares problems, and eigenvalue/eigenvector problems.
Note that while
22C:171/22M:171 is the “second half” of the two-semester sequence,
the two courses can be taken in either order.
Detailed
list of topics
- Numerical
solution of differential equation initial value problems
- basic
theory of ordinary differential equations
-
explicit and implicit Euler methods
-
convergence of numerical approximations
-
multistep methods (Adams–Bashforth, Adams–Moulton, and BDF
methods)
-
Runge–Kutta methods
- stiff
differential equations and stability of methods
- Matrix
computations
-
solving linear systems via LU factorization
-
perturbation theorem for linear systems
-
backward error analysis
- least
squares problems and the method of normal equations
- QR
factorization
-
eigenvalue/eigenvector calculations
-
perturbation results for eigenvalues
- power
and inverse power methods
- QR
algorithm
Objectives
and Goals of the Course:
The students
will be introduced to the derivation, implementation, and analysis
of numerical methods in the areas of numerical solution of
ordinary differential equations and matrix computations,
especially, solution of linear systems, solution of linear
least-squares problems, and computation of eigenvalues and
eigenvectors. Students are expected to become proficient in
all
aspects covered. This involves both theory (mathematial analysis)
and practice (programming and implementation). While learning a
particular programming language is not necessary, examples and
demonstrations will be given in Matlab
and students are expected to be able to read and understand code
in this language.
There will be a
more-or-less open-ended project for all students to complete which
will involve work in all three aspects (derivation,
implementation, and analysis) of numerical methods.
Texts:
Required text:
Introduction to Numerical Analysis by K. Atkinson, J.
Wiley and Sons, 2nd Edition (1989). 22C:171/22M:171 covers the
chapters six through nine. 22M:170/22C:170 covers the first five
chapters.
Grading
System and the Use of +/–:
A +/– grading
system will be used for this course. As noted on the CLAS teaching
policy page, a score of A+ is a rare grade, assigned only in the
case of exceptional work.
Assignments
and Percentage of Final Grade:
There will be
an in-class exam and a final exam (20% each), homework assignments
(30% total) which may include some programming, and a programming
assignment (30%). There may also be ungraded homework assigned
during the course. Familiarity with MATLAB will be useful during
the course.
Please remember
that final exams may only be given during finals week according to
CLAS policy. Likewise, no major exams may be given the week before
finals week.
A Word
about the Date and Time of the Final Exam:
The date and
time of every final examination is announced by the Registrar
generally by the tenth day of classes. No exams of any kind are
allowed during the last week of classes. All students should plan
on being at the UI through the final examination period. Once the
Registrar has announced the date, time, and location of each final
exam, the complete schedule will be published on the Registrar’s
web site and will be shared with instructors and students. It is
the student's responsibility to know the date, time, and place of
the final exam.
Course
Policies:
Attendance
and participation:
Students are
expected to attend all classes unless there is an important and
pressing reason otherwise. Attending students are expected to
participate in classroom discussion and be prepared to give
relevant comments on topics discussed in class in a civil and
respectful manner.
Timely
completion of assignments:
All assignments
(homework and project) are expected to be completed and handed in
on time. If you have questions about the homework or project, you
should contact the TA or instructor. Unless prior arrangements
have been made, late homework is subject to a 20% reduction in the
grade.
Student
Collaboration:
Students may
discuss the homework and project. However, all work handed in must
be the work of the student submitting the work and in their own
words. All duplicated work will be considered plagiarized and
graded as such. Any outside source of information must be cited in
a way that any third person can obtain the cited work and check
its veracity.
All exams are
purely individual and there can be no discussion between students
about the material in an exam during that exam whether in class or
take-home.
Resources for
Students:
Students may
find the Writing Center and the Speaking Center very useful for
this course:
Writing Center:
http://www.uiowa.edu/~writingc/
Speaking
Center:
http://clas.uiowa.edu/rhetoric/for-students/speaking-center
Calendar of
Course Assignments and Exams:
Homework will
be scheduled regularly, approximately every two weeks except near
the end of semester. The programming project will take place
during the last four or five weeks of semester. This will involve
a significant amount of programming and interpretation of the
results. Students should be prepared to write a substantial report
describing what they did for the project and their results and
conclusions.
The midterm
exam will be held at the regular classtime in the regular
classroom on Friday, March 7th.
Teaching
Policies & Resources
Administrative Home
The College of
Liberal Arts and Sciences is the administrative home of this
course and governs matters such as the add/drop deadlines, the
second-grade-only option, and other related issues. Different
colleges may have different policies. Questions may be addressed
to 120 Schaeffer Hall, or see the CLAS Academic Policies Handbook
at http://clas.uiowa.edu/students/handbook.
Electronic
Communication
University
policy specifies that students are responsible for all official
correspondences sent to their University of Iowa e-mail address
(@uiowa.edu). Faculty and students should use this account for
correspondences (Operations Manual, III.15.2, k.11).
Accommodations for Disabilities
A student
seeking academic accommodations should first register with Student
Disability Services and then meet privately with the course
instructor to make particular arrangements. See
www.uiowa.edu/~sds/ for more information.
Academic
Honesty
All CLAS
students or students taking classes offered by CLAS have, in
essence, agreed to the College's Code of Academic Honesty: "I
pledge to do my own academic work and to excel to the best of my
abilities, upholding the IOWA Challenge. I promise not to lie
about my academic work, to cheat, or to steal the words or ideas
of others; nor will I help fellow students to violate the Code of
Academic Honesty." Any student committing academic misconduct is
reported to the College and placed on disciplinary probation or
may be suspended or expelled (CLAS Academic Policies Handbook).
CLAS Final
Examination Policies
The final
examination schedule for each class is announced by the Registrar
generally by the tenth day of classes. Final exams are offered
only during the official final examination period. No exams of any
kind are allowed during the last week of classes. All students
should plan on being at the UI through the final examination
period. Once the Registrar has announced the date, time, and
location of each final exam, the complete schedule will be
published on the Registrar's web site and will be shared with
instructors and students. It is the student's responsibility to
know the date, time, and place of a final exam.
Making a
Suggestion or a Complaint
Students with a
suggestion or complaint should first visit with the instructor
(and the course supervisor), and then with the departmental DEO.
Complaints must be made within six months of the incident (CLAS
Academic Policies Handbook).
Understanding Sexual Harassment
Sexual
harassment subverts the mission of the University and threatens
the well-being of students, faculty, and staff. All members of the
UI community have a responsibility to uphold this mission and to
contribute to a safe environment that enhances learning. Incidents
of sexual harassment should be reported immediately. See the UI
Comprehensive Guide on Sexual Harassment for assistance,
definitions, and the full University policy.
Reacting
Safely to Severe Weather
In severe
weather, class members should seek appropriate shelter
immediately, leaving the classroom if necessary. The class will
continue if possible when the event is over. For more information
on Hawk Alert and the siren warning system, visit the Department
of Public Safety website.