Contact/class information

Description

Textbook

Syllabus

• Basics of differential equations
  • Existence, uniqueness and continuous dependence of solutions on parameters/initial values
  • The smooth flow idea
  • Linear differential equations: stability & eigenvalues
  • Comparison with discrete-time systems
• Numerical methods
  • Euler's method
  • Higher accuracy: Runge–Kutta and multistep methods
  • Implicit methods and stiff differential equations
• Local analysis of nonlinear differential equations
  • Stability and equilibria
  • Stable and unstable manifolds
  • Hartman–Grobman theorem
• Bifurcations
  • saddle–node bifurcations
  • Hopf bifurcations
  • flips and other bifurcations
• Global behavior
  • periodic orbits
  • Poincaré–Bendixson theorem in two-dimensions
  • Lorenz equations and chaos in three and higher dimensions
• Advanced topics
  • fractals and dimensions
  • Lyapunov exponents
  • “mixing” and ergodic theory
  • shadowing and numerical methods

Preparation

Goals & expectations

• be able to identify equilibria, their stability, and behavior of solutions nearby;
• be able to identify different types of bifurcations and their effect on stability of solutions;
• be able to identify circumstances in which limit cycles and other periodic behavior are likely to occur;
• be able to apply numerical methods for studying differential equations, but understand their limitations.

Assessment

Notes

1. 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.
2. 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 your academic advisor, or see the CLAS Academic Policies Handbook at
   http://www.clas.uiowa.edu/students/handbook/. The Department of Mathematics offices are in 14 McLean Hall (MLH). You can contact the chair of the department through the Departmental Secretary at 14 MLH or by calling 335-0714.
3. 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).
4. 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.
5. 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).
6. 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.
7. 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).
8. 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
   http://www.uiowa.edu/~eod/policies/sexual-harassment-guide/index.html for assistance, definitions, and the full University policy.
9. 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 http://www.uiowa.edu/~pubsfty/intlinks.htm.