Math 445 Term II 2006
Mathematical Modeling
Applications in the Natural and Social Sciences
Prof. Rachel Kuske
Email: rachel@math.ubc.ca
Office: Math 217
Webpage: http://www.math.ubc.ca/˜rachel
Office hours
Monday,Friday 12:00-1:00pm
Also by appointment
Class Time and Location
MWF 2pm Math 104
Textbook: Mathematical Modeling Meerschaert, Second edition, Academic Press, 1999.
Important Dates:
January 11: Deadline for Project team sign-up
February 3: Midterm Presentation by first group of teams (optimization)
March 10: Midterm Presentation by second group of teams (dynamical systems)
March 15: Proposals Due for Final Presentation Project
April 1-7: Final Presentations by all teams
Grades based on:
Homework: 20-25%
Midterm Modeling Presentation: 20-25%
Final Modeling Presentation: 20-25%
Final Exam: 30-35%
Homework:
Homework is assigned on Friday, and due the following Friday. You may discuss the homework
together, but you must write up your homework assignment independently. No late homework will be
accepted. Solution sets will be placed on reserve on the day on which the homework sets are due.
SUGGESTION FOR HOMEWORK: The purpose of the homework is to review the material
covered in class. In general, the material related to a particular homework is covered by the time
that the homework assignment is given. Therefore it is best to start the homework AS SOON AS
POSSIBLE, since the material will be fresh in your mind, and typically the the homeworks are not
short. Usually this will make it easier to do the homework, and will help you to make the connection
with the material covered in class.
The Course:
This course emphasizes the application of math to real-world problems. The applications studied will
motivate the math that is reviewed and developed. Basic elements from calculus, differential equations, linear algebra, and probability and statistics are prerequisites for the course. Please review this
material if you do not feel comfortable with it.
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The course will follow the text, with some supplementary material from other sources. The purpose
the course is to develop skills in mathematical modeling. This includes the following:
Ability to translate real world problems into mathematical language (equations).
Ability to give a mathematical solution to a set of equations.
Ability to translate the mathematical solution back to the real world application.
Ability to assess the strengths and weaknesses of the model, and the information obtained from it.
Ability to interact with a team in developing and using a mathematical model.
The course will focus on optimization, dynamical systems, and probabilistic techniques.
Course Notes:
Course Notes are available from the course webpage.
PLEASE NOTE: THE NOTES ARE NOT A SUBSTITUTE FOR THE LECTURES. The
lectures will not follow these notes exactly, and will contain substantially more material. Students
should expect to add their own handwritten notes to these notes. They are intended as a guide for
the class, giving details and some technical calculations. Students may wish to use these notes in a
variety of ways. For example,
1. Review concepts covered in the lectures.
2. Make note-taking easier in some lectures, especially those involving a lot of technical computation.
3. Read notes before lectures as a “warm-up”.
Computer Labs:
A number of the assignments will require use of computer software, such as Mathematica, Maple, or
Matlab. Sample codes will be provided to help with the programming. These software packages are
available in many of the computational labs of the university, and Student versions of Matlab are
available from Mathworks. Students are encouraged but not obligated to use Matlab for their work.
If you do not have access to a computer lab and/or this software, please contact the professor via email.
Email/Listserve/Website:
Syllabus and course description, homework assignments, exams questions, and software will be available on the website: http://www.math.ubc.ca/˜rachel.
Email directed to the professor only can be sent to rachel@math.ubc.ca.
The Midterm and Final Presentations will test the ability to model a problem, interpret the
solution, and communicate the results effectively and efficiently. Attendance is MANDATORY for all
midterm and final presentations. The Midterm and Final Presentations depend on teamwork. Below
are guidelines for the teams and the reports.
Teams
1. Each team will consist of 4 people (3 people in special cases).
2. The teams will be decided by Wednesday, January 11, 2002.
3. Changes of the teams during the semester will not be allowed, except in extreme circumstances.
Any change must be approved by the instructor.
4. Each team member must participate in the project, but tasks can be divided up. Each presentation
will have several parts - modeling, solution, simulation, interpretation, presentation.
Midterm Presentation
1. Select a problem from a list of topics. The first set of Midterm Reports will follow optimization
techniques (Feb. 3). The second set will follow dynamical systems techniques (March 10).
2. Presentations last 10 minutes.
3. Midterm Presentations will follow the same outline as the Final Presentation.
4. Presentations will be rated by the class and the instructor.
Final Presentation
1. You must write a proposal for the topic of the Final Presentation. The topic of the Final Project
should be different from the Midterm Project; exceptions must be approved by the instructor. The
proposal for the Final Project is due on March 17.
2.Outline for the Proposal:
a. Statement of the Problem: area of application, specific questions investigated.
b. Techniques, e.g. methods studied in class, computer simulations, solution packages.
c. References about previous work on the subject.
d. New insight your study will provide.
3. Outline of Presentation
a. Statement of the Problem - Words/Pictures/minimal equations
b. Mathematical Model: Equations/Assumptions/Justifications
c. Techniques/Tools Used
d. Results of the Model: Solutions/Simulations
e. Interpretation of the Results - Relate to Statement of the Problem
f. Assessment of the Model: Strengths/Weaknesses