Syllabus for MATH 442, SECTION 930, Fall 2017

Mathematical Modeling

Instructor: Dr. Peter Howard, Blocker 625B

Email: phoward@math.tamu.edu

Office hours: TWR 1:30-2:30; also, by appointment.

Class time and place: MWF 11:30-12:20, Blocker 122.

Section web page: /~phoward/M442.html

Textbook: No textbook is required for the course. Students interested in obtaining a MATLAB reference should see the document MATLAB Releases and References on the course web site. Also, students will be expected to download a considerable amount of material from the course web site.

Prerequisites: M304 (Linear Algebra) and M308 (Differential Equations), or consent of instructor.

Catalogue Description:  The construction of mathematical models from areas such as economics, game theory, integer programming, mathematical biology, and mathematical physics.

Course Goal: The main goal of the course is to introduce students to both deterministic and probabilistic techniques useful in the mathematical description of physical events and situations. The main topics will be regression analysis, dimensional analysis, modeling with ordinary differential equations, and discrete and continuous methods of probabilistic modeling. We will also work with two software packages, MATLAB for number crunching and LYX for typesetting reports.

Homework Assignments: Individual homework assignments will be made on selected Fridays during the semester, due the following Fridays. (Once students are working on projects, little to no individual homework will be assigned.) Individual assignments will depreciate by 5 points for each class period they are late for up to one week, at which time a 0 will be assigned.

Projects: Three projects will be assigned during the semester, each of which will be roughly two to four weeks in duration. The first project will be individual, the remaining two carried out in groups of two or three students, with the groups changing after the second project.  Projects will not be accepted late.

Group Presentations: As discussed below, students taking a course with the Oral Communications (C) designation must give an oral presentation at least 5 minutes in length. During the last two or three class periods, each Project 3 group will give a presentation to the class on a topic of the group's choosing (related to mathematical modeling), and each student in the group will be responsible for at least 5 minutes of the presentation.  

Exams: There will be two exams during the semester, a midterm and a final.  The midterm exam will be an evening exam, Wednesday, October 25, 7-9 p.m. The final exam for this class will be on Wednesday, December 13, 10:30 a.m. - 12:30 p.m. Please make a note of these dates.

Grades: Final grades will be determined in the following manner: Semester Projects: Individual: 10%, Group: 15% each; Homework assignments: 10%; Group presentations: 5%; Midterm: 20%; Final: 25%. Grade ranges will be standard: 89.50-100, A; 79.50-89.49, B; 69.50-79.49, C, 59.50-69.49, D; below 59.50, F. For details about the breakdown associated with our C-course designation, see the document M442 as an Oral Communications (C) Course on our course web site.

Learning outcomes: Students will be able to: Articulate the major steps associated with using mathematics to model physical processes; Implement mathematical models in MATLAB; Write clear and accurate descriptions of modeling projects; Recognize problems for which regression is appropriate, and apply it effectively; Recognize problems for which dimensional analysis is appropriate, and apply it effectively; Model dynamical processes with ordinary differential equations; Analyze models based on ordinary differential equations in order to obtain productive information; Recognize problems for which probabilistic modeling is appropriate; Model physical processes with discrete and continuous probability methods.

C Course Designation: M442 is being offered this semester as an Oral Communications (C) Course. Additional information about this designation can be found at the web site,

http://writingcenter.tamu.edu/Students/W-and-C-Course-Facts

and in the document M442 as an Oral Communications (C) Course on our course web site. The primary requirements are given below. The course will

Make-up policy: Make-ups for exams will only be given if the student can provide a documented University-approved excuse (see University Regulations). According to University Student Rules students are required to notify an instructor by the end of the next working day after missing an exam. Otherwise the student forfeits his or her right to a make-up.

Scholastic Dishonesty: Copying work done by others, either in-class or out of class, is an act of scholastic dishonesty and will be prosecuted to the full extent allowed by University policy. "An Aggie does not lie, cheat, or steal or tolerate those who do." Please refer to the Honor Council Rules and Procedures, available at the Office of the Aggie Honor System.

Copyright policy: All printed materials disseminated in class or on the web are protected by copyright laws. One xerox copy (or download from the web) is allowed for personal use. Multiple copies or sale of any of these materials is strictly prohibited.

Students with Disabilities: The following statement was provided by the Department of Disability Services: The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact Disability Services, currently located in the Disability Services building at the Student Services at White Creek complex on west campus or call 979-845-1637. For additional information, visit http://disability.tamu.edu.

Class Schedule: Roughly speaking, we should cover the following material on the following schedule:
Week of Monday Material Covered
August  28
Introduction to MATLAB and LyX (Fri. Sept. 1 is last day for drop/add.)
September 4
Linear least squares regression
September 11
Nonlinear least squares regression
September 18
Dimensional analysis
September 25
Dimensional analysis (Project 1 assigned Fri., Sept. 29)
October 2
Modeling with ODE
October 9
Solving ODE in MATLAB (Project 1 due Fri., Oct. 13; Project 2 assigned.)
October 16
Parameter estimation for ODE
October 23
Review. Midterm Wed., Oct. 25, 7-9 p.m.
October 30
Modeling with probability: combinatorics
November 6
Modeling with probability: conditioning (Project 2 due Fri., Nov. 10; Project 3 assigned.)
November 13
Modeling with probability: random variables and expected value (Fri., Nov. 17 is last day for Q-drop.)
November 20
Modeling with probability: simulation (Thanksgiving break, Wed.-Fri., Nov. 22-24.)
November 27
Modeling with probability: simulation and limit theorems
December 4
Student presentations (Wed., Dec. 6 is last class meeting; Project 3 due.)