LyX Document

MATH:3800/CS:3700
Elementary Numerical Analysis (Sec 002)
Fall 2016

This course will cover basic numerical analysis and particularly issues such as roundoff error (i.e., you can't store infinitely many digits in a computer), approximating functions (you can't store

y = f (x)

for all values of

x

), how to solve equations, integrate functions (numerically), and even solve some differential equations.

Contact/class information

You can see me outside the office hours provided it is mutually convenient.

This class will use ICON: https://icon.uiowa.edu/.

Pre-requisites/Co-requisites

Pre-requisites: (MATH:2550 or MATH:2700 — Linear Algebra) and (MATH:1560 or MATH:1860 — Calculus II)

Textbook

Elementary Numerical Analysis by Weimin Han and Kendall Atkinson, 3rd edition, Wiley (2004). We plan to study chapters 1–9 (all chapters).

Syllabus

Numerical analysis is about how to design and analyze algorithms that work with real numbers. In this course you will be introduced to some surprising things about the way computers perform these kinds of computations (the computer is almost always wrong). In spite of this, it is usually not wrong by a lot. Of course, to be sure, we need to know how much error is in the answers computed. The other side of the question is how do you compute something, or solve an equation? Some algorithms are more accurate than others, and some perform faster than others. Knowing which is which is vitally important if you have to do numerical computations.

Round-off errors and machine epsilon.

How to solve a single nonlinear equation in a single unknown.

How to solve simultaneous linear equations.

How to approximate functions with polynomials & the error in the approximations.

Integration and differentiation of known functions.

Numerical solution of differential equations.

This course combines theory (mathematics) with practice (computation). So you will need to know both the mathematical theory and be able to put it into practice, which will involve programming. Programming will usually be done in Matlab

^{T M}

, which is both an interactive environment as well as a programming language, optimized for carrying out numerical computations. It is a fairly easy language to learn (especially to get started). Part of this course will help you with programming in this language, although the main focus is on the numerical computations. There will be plenty of live demonstrations to show how to use Matlab.

Students typically fall into one of two groups: students comfortable with the mathematics and worried about the programming, and students comfortable with programming and worried about the mathematics. Students in each of these groups will rise to the challenges and develop abilities where before they had worries.

Goals

The goals of this course are that the student will

understand that numerical computations inherently have errors, and understand how computations can fail;

be able to estimate the errors in various kinds of computations and approximations;

be able to implement and use numerical methods for approximating solutions of equations, approximation and interpolation of functions, approximation of definite integrals, solutions of linear systems, and solutions of differential equations;

be able to understand the sources of errors, and be able to implement methods in ways that minimize the impact of errors.

Collaboration policy

Students are encouraged to discuss homework and group work amongst the groups. However, all homework submitted must be your own work and in your own words. Group work must be the work of the group. No material in an exam can be discussed with other students while the exam is going on.

Assessment

There will be two in-class exams (20% each), a number of sets of homework (40% total), and a final exam (20%).

You will be notified of the homework sets during class; this information will be posted to ICON. You will be notified of the time and date of the final exam after the 5th week of class. The mid-semester exams will be held on Friday September 23rd and Friday October 28th. The date and time of the final exam will be announced around the 5th week of class.

Grading

+ / -

grading scheme will be used. Although the College of Liberal Arts and Sciences has some guidelines for the percentages of A's, B's, C's, etc., these are only guidelines, and the class may vary substantially from these values depending on the overall abilities of the members of the class. Note that A+ will be given only for exceptional work of unusual quality.

Additional Notes

Administrative Home
The Department of Mathematics in 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 with the course instructor privately in the instructor's office to make particular arrangements. See https://sds.studentlife.uiowa.edu/ 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 fifth week 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 (Dan Anderson, ph: 335-0714). 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.