LyX Document

MATH:4610 (22M:140)
Continuous Mathematical Models
Fall 2015

This course will be on mathematical models for a wide range of phenomena. The models will mainly be based on differential equations (ordinary and partial), but will also include random processes. Phenomena that will be modeled will include basic mechanics, traffic flow, population dynamics, solid and fluid mechanics, epidemics, and may include other topics such as optimization, statistical mechanics, and quantum mechanics.

Contact/class information

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

This course will use ICON; go to http://icon.uiowa.edu/ and log in with your HawkID and password.

Textbook

The main textbook will be Introduction to the Foundations of Applied Mathematics by Mark H. Holmes (published by Springer, 2009; ISBN 978-0387877495 for $47.03 from Amazon.com). This book is available from the library, and also online via the University's electronic access; see Infohawk.

Syllabus

Below is a list of topics I expect to cover (not necessarily in this order):

Conserved quantities

Densities and fluxes

Physical units and non-dimensionalization

Randomness and Markov chains (e.g., for radioactive decay); mass action principles

Basic mechanics (Newton's laws & applications)

Rigid body mechanics

Angular momentum

Eulerian (fixed in space) and Lagrangian (fixed in body) coordinates

Convection and diffusion processes

“Stirred tanks” and compartment models

Reactions and populations

Stress and strain

Equations of elasticity

Equations of fluids (liquids and gases)

Other topics may be covered if time permits.

Preparation

You will need to review multivariate calculus and linear algebra. However, you will not need any background in mechanics; that will be taught as needed.

Goals & expectations

Students taking this course should at the end of this course

have learned some important mathematical models of physical, chemical and other systems;

be able to develop new mathematical models;

be able to articulate the assumptions behind the models created;

be able to critique models in terms of the relation of mathematics to the system(s) being modeled.

Students are naturally expected to attend class and be diligent in completing homework assignments in a timely manner. Submitted student work will be original except as noted and original source(s) cited clearly in an appropriate way. Students will also make all reasonable efforts to understand and master the material of the course, seeking help when appropriate, and participating in classroom discussions.

The instructor will also seek to communicate the material of this course in a manner that is clear and understandable, and seek to bring all students to a mastery of the material.

Assessment

There will be two exams, one midterm and one final (25% each), homework (40%), and a presentation (10%).

You will be notified of the homework sets during class; this information will be posted to ICON. You will be notified about the date of the final exam after the tenth day of classes. The midterm exam will be held on Friday, October 16th (Friday of week 8) at the usual class time in the usual classroom.

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:

All exams must be your own work. Some consultation between students regarding homework is permitted, but every homework must present each student's solutions in their own words. Copying materials without understanding or copying anything verbatim other than direct quotes (cited appropriately) is a waste of time and will be graded as such. Presentations are the work of small group (often two students); consultation with the instructor(s) and TA(s) are permitted. All members of such a group are expected to contribute roughly equal effort but possibly in different ways.

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.

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.