Math 4480/5480 - Mathematical Modeling - Spring 2012
Dr. Radu C. Cascaval

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Syllabus

Homework

Exams

Lectures

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Course Info:

Time & Place: Monday & Wednesday,1:40-2:55pm, OSB B215
Office Hours: Monday & Wednesdays: 12:15-1:15pm or by appointment
My Office: ENG 271
Course Website: http://www.uccs.edu/rcascava/Math4480

Course Description:

The course material (selected sections from Chapter 1-7 in Meerschaert's book and from other sources) will cover several methods and techniques used in mathematical modeling. Matlab illustrations will be provided during the lectures. This course has an Blackboard site, for access to grades, solutions to HMW problems, handouts and other important announcements.

Textbook (required):

Mathematical Modeling, 3rd Edition, by Mark M. Meerschaert, Academic Press 2007, ISBN 978-0-12-370857-1
or, as an alternative,

The (unpublished) 4th edition is available in the UCCS bookstore as a printed PDF (spiral binded) for about $37.95. The author has agreed to share it with us for testing it in the class this Spring. It turns out that the only difference between 3rd and 4th edition are two sections added to the end of the book in the 4th edition, while the existing 3rd edition is replicated identical in the 4th edition. The additional sections will most likely not be covered due to time constraints, so it is entirely up to you whether you want to go with this 4th edition or stick with the (more expensive) 3rd edition, which the bookstore sells (new for $107.95 and used for $80.96).

Supplementary readings:

1. Mathematical Modelling: Case Studies and Projects,
by J. Caldwell and D.K.S. Ng, Kluwer Academic Publishers 2004
(FREE* download for UCCS students on Springerlink.com)

2. Mathematical Modeling for the Life Sciences,
by Jacques Istas, Springer 2005
(FREE* download for UCCS students on Springerlink.com, or you may also purchase a papercopy for $24.95 including S&H)

[*You must be on the campus network to be able to freely download individual chapters of the books.]

Computer software (MATLAB)

A majority of the problems discussed in class and those assigned for homework will require the effective use of a computer. MATLAB is the software of choice during our class; no prior experience with MATLAB is expected (This will change next year). The best way to learn how to use MATLAB is through examples; some will be given in class, others will be suggested outside class. Although mastering MATLAB is NOT one of our goals in this class, you are expected to be able to read and understand the codes I provide and modify them for your needs. If you need a more systematic introduction to MATLAB, I strongly recommend the lab course MATH 2650 below.

Access to MATLAB is available in all computer labs on campus, as well as via remote connections, thanks to a campus-wide license. Therefore, you are not required to buy a student license of MATLAB. Nevertheless, if you decide to purchase your own student copy of MATLAB, you may find it in the UCCS Bookstore or online at http://www.mathworks.com/academia/student_version/ for $99. It comes with all the toolboxes you will need in this course (Symbolic Math Toolbox, Optimization Toolbox and a few others). A MATLAB tutor will be available several hours a week (TBA) in EN 136 throughout the semester.

Recommended Lab Course

MATH 2650 - Introduction to Computational Math is a 1-credit hour lab course designed as thorough introduction to MATLAB and how it can be used effectively in solving math problems. It is highly recommended to all Math Majors, especially those takingthe Modeling courses MATH 4480 or MATH 4850. Starting Fall 2012, this will become a prerequisite course to the modeling capstone courses. While technically you are not required to take this course to complete MATH 4480 this Spring, you are still strongly recommended, especially if you have no prior experience with MATLAB.

Here is a quote from a student who took Math 2650 and Math 4480 last Spring:
"I found the MATLAB course invaluable in taking Modeling last year. There were only a few of us from the Modeling class that took the MATLAB course and we became the "go to" individuals in the Modeling class for providing help to those that did not know MATLAB. Mathematical Modeling is a challenging course and I would highly recommend that if a student does not know MATLAB, they take MATH 265."

This Spring semester MATH 2650 is offered for 10 weeks only (Fridays, 9:25-10:40am) (ends right before Spring Break!!!!)

Homework:

Bi-weekly assignments will reflect the material covered in class and will be usually due every Wednesday, unless otherwise specified. Late homework is strongly discouraged and usually only considered in VERY special circumstances, for partial credit. Additional problems and projects will be assigned for independent work. Please note that almost all HMW problems will require using a computer. You will be expected to present in your report both theoretical and computational aspects of your work.

Exams:

There will be 2 midterm Exams during the semester and a comprehensive Final Exam, as follows

Exam 1: Wed, Feb 29, 2012
Exam 2: Mon, Apr 9, 2011 Wed, Apr 11, 2012 (Date change announced in class!)
Final Exam: Mon, May 7, 2012 (1:40-4:10pm)

There will be no make up exams so please mark your calendars! If a student informs me well before the exam date about absolutely having to miss an upcoming exam AND provides acceptable written verification in support of the request, then the next exam score will be used to replace that particular exam. If any of the above conditions is not satisfied, the student will get a zero on the missed exam. The above procedure may only be applied once. The Final Exam cannot be missed under any circumstances.

Grading:

The course grade will be based on the cumulative score from homework (150 pts), the midterms (100 pts each) and the final (150 pts). Maximum score for Math 4480 students 500 points. 60% of 500 guarantee a passing grade. For the students enrolled in Math 5480, there will be a project (worth 100 points) due at the end of the class. Project topics will be suggested by the instructor in the first three weeks of classes. Students will need to choose a topic and present a progress report after Spring Break (more detailed timeline will follow).

Other policies:

To make the most of your class, you are required to attend every class session. Students should notify (in advance) the instructor if they need to miss more than one session. Supporting documentation may be required. Drop dates: Please seek counseling from the Dean's office before dropping any course and note the following important dates: Feb 1, 2011– last day to drop and receive a full tuition refund; March 30, 2011– last day to drop without special permission from the Dean.

Academic Dishonesty:

Academic honesty is fundamental to the activities and principles of a university. All members of the academic community must be confident that each person's work has been responsibly and honorably acquired, developed, and presented. Any effort to gain an advantage not given to all students is dishonest whether or not the effort is successful. The academic community regards academic dishonesty as an extremely serious matter, with serious consequences that range from probation to expulsion. When in doubt about plagiarism, paraphrasing, quoting, or collaboration, consult the course instructor.

Disability Services:

If you are a student with a disability and believe you will need accommodations for this class, it is your responsibility to contact and register with the Disability Services Office, and provide them with documentation of your disability, so they can determine what accommodations are appropriate for your situation. To avoid any delay in the receipt of accommodations, you should contact the Disability Services Office as soon as possible. Please note that accommodations are not retroactive, and that disability accommodations cannot provided until an accommodation letter has been given to me. Please contact Disability Services for more information about receiving accommodations at Main Hall room 105, 719-255-3354 or dservice@uccs.edu

Tentative Schedule for Spring 2012: (Website has most up-to-date version)

		Lecture 1		Wed, 1/18		Introduction. One Variable Optimization
		Lecture 2		Mon, 1/23		Sensitivity Analysis
		Lecture 3		Wed, 1/25		Multivariable Optimization
		Lecture 4		Mon 1/30		Constraint Optimization
		Lecture 5		Wed, 2/1		Computational Methods for Optimization
		Lecture 6		Mon, 2/6		Computational Methods for (Multivariable) Optimization
		Lecture 7		Wed, 2/8		Linear Programming - Simplex Method
		Lecture 8		Mon, 2/13		Linear Programming (cont)
		Lecture 9		Wed, 2/15		Dynamic Models
		Lecture 10		Mon 2/20		Continuous Time Dynamical Models
		Lecture 11		Wed, 2/22		Discrete Time Dynamical Systems
		Lecture 12		Mon, 2/24		Stability of Equilibria. Phase Portraits
				Wed, 2/29		Midterm I
		Lecture 13		Mon, 3/5		Elements of Control Theory
		Lecture 14		Wed, 3/7		Pontryagin Maximum Principle - Part I
		Lecture 15		Mon, 3/12		Pontryagin Maximum Principle - Part II
		Lecture 16		Wed, 3/14		Pontryagin Maximum Principle - Part III
		Lecture 17		Mon 3/19		Review of PMP
		Lecture 18		Mon, 3/21		Simulation of Dynamic Models.
				3/26,3/28		Spring Break
		Lecture 19		Mon, 4/2		Euler Method
		Lecture 20		Wed, 4/4		Chaotic Behavior in Nonlinear Systems
				Mon, 4/9		Midterm II
		Lecture 21		Wed, 4/11		Review of Probability
		Lecture 22		Mon, 4/16		Continuous and Discrete Probability
		Lecture 23		Wed, 4/18		Random Variables
		Lecture 24		Mon, 4/23		Central Limit Theore. Applications
		Lecture 25		Wed, 4/25		Diffusion
		Lecture 26		Mon, 4/30		Markov Chains
		Lecture 27		Wed, 5/2		Markov Chains (cont)
				Mon, 5/7		Final Exam