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Instructor: |
Dr. Peter Howard, Blocker 620D |
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Email: phoward@math.tamu.edu |
Office hours: MW 3:00-4:00; R 2:00-3:00.
Class time and place: MWF 1:50-2:40, Blocker 122.
Section web page: http://www.math.tamu.edu/~phoward/M647.html
Textbook: There is no textbook for the course, though students are expected to download a considerable amount of material from the course web site.
Prerequisites: Undergraduate linear algebra and ODE. The course catalog lists M442 (undergraduate modeling), but that's not assumed.
Catalog Description: The process and techniques of mathematical modeling; covers a variety of application areas and models such as ordinary and partial differential equations, stochastic models, discrete models and problems involving optimization.
Course Goal: The main goal of the course is to introduce students to techniques useful in the mathematical description of physical events and situations. This semester, our topics will include least squares regression and parameter estimation, dimensional analysis and non-dimensionalization, modeling with ODE, and modeling with PDE. We will carry out numerical calculations with MATLAB.
Homework
Assignments: A homework assignment will generally be posted on
the course web site each Friday, due the following Friday. Work will
be accepted up to a week late, though five points will be deducted
for each class period by which the assignment is late.A typical assignment will be worth 50 points.
Exams: There will be two exams during the semester, a midterm and a final. The midterm will be given in the evening from 7:00--9:00 p.m., Thursday, March 8. The final exam for this class will be on Tuesday May 8, 10:30 a.m.--12:30 p.m.
Grades: Final grades will be determined in the following manner: Homework assignments: 50%; Midterm: 25%; Final exam: 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.
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, in Cain Hall, Room B118, or call 845-1637. For additional information visit http://disability.tamu.edu.
Class
Schedule: Roughly speaking, we should cover the following
material on the following schedule:
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Week of Monday |
Material Covered |
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January 16 |
Introduction
to MATLAB. (Mon. Jan. 16 is Martin Luther King, Jr. Day. Classes don't meet.) |
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January 23 |
Linear least squares regression. (Mon. Jan. 23 is last day for drop-add.) |
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January 30 |
Nonlinear least squares regression. |
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February 6 |
Dimensional analysis: method and applications. |
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February 13 |
Dimensional analysis: theory. |
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February 20 |
Modeling
with ODE: compartment models; reaction kinetics; population dynamics |
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February 27 |
Modeling
with ODE: classical mechanics (Newtonian, Lagrangian, Hamiltonian) |
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March 5 |
Solving ODE in MATLAB (Midterm Thurs. Mar. 8 7:00--9:00 p.m. Class canceled Friday Mar. 9.) |
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March 12 |
Spring break |
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March 19 |
Analysis of ODE models: exact solutions; equilibrium points and stability; applications. |
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March 26 |
Modeling
with PDE in one space dimension: conserved quantities; reaction-diffusion equations; momentum equations |
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April 2 |
Solving PDE numerically in MATLAB in one space dimension. (Mon. April 2 is Q-drop deadline; All Texas A&M classes canceled Fri. April 6) |
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April 9 |
Modeling with PDE in multiple space dimensions: conserved quantities; reaction-diffusion equations |
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April 16 |
Modeling with PDE in multiple space dimensions: the Navier-Stokes momentum equations |
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April 23 |
Modeling with PDE in multiple space dimensions: energy and entropy functionals; gradient flows |
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April 30 |
Solving PDE in MATLAB in multiple space dimensions. (Tues. May 1 is the last day of classes; Fri. classes meet.) |