MATH:6850 (22M:270)
Theoretical Numerical Analysis I, Fall 2015

Description of Course:

Textbook:

Syllabus:

• Spaces in which to do numerical analysis
  • Banach spaces and Hilbert spaces
  • $L^p(\Omega )$ spaces
  • Sobolev spaces: $H^s(\Omega )$ and $W^{k,p}(\Omega )$ spaces
  • Linear operators and functionals
  • Dual spaces and adjoint operators
  • Strong and weak (and weak*) convergence
  • Convex functions and optimization
• Approximation theory
  • Stone–Weierstrass approximation theorem
  • Interpolation in one dimension (polynomial and trigonometric)
  • Best approximation
  • Lebesgue constants
  • Jackson theorems
  • $L^2$ approximation
• Fourier analysis and wavelets
  • Trigonometric approximation
  • Gibb's phenomenon
  • Fourier transform and tempered distributions
  • The discrete Fourier transform and the FFT
  • Wavelets
• Solving equations in Banach spaces
  • Contraction mapping principle (Banach fixed point theorem)
  • Differential equations in Banach spaces
  • Calculus in Banach spaces
  • Newton's method in Banach spaces
  • Conjugate gradient method in Hilbert spaces
• Finite difference methods
  • Finite difference approximations
  • Lax equivalence theorem (stability + consistency implies convergence)

Assessment:

A Word about the Date and Time of the Final Exam:

Calendar of Course Assignments and Exams:

Objectives and Goals of the Course:

Grading System and the Use of +/–:

Course Policies:

Attendance and participation:

Timely completion of assignments:

Student Collaboration:

Notes

• Course plan: The course plan may be modified during the semester. Such modifications will be announced in advance during class periods; the student has responsibility for keeping up with such changes. You should also make a habit of reviewing the ICON web page for this course, which is accessible via: ICON http://icon.uiowa.edu/ This page will have homework details and other information posted to it as the class progresses.

• 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 http://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 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.