Mathematical Modeling
Syllabus
Office Hours
Monday 2-4, Friday 2-4 (no appointment necessary). Feel free to make an appointment if you cannot come to my regular office hours.
Textbook
No textbook required. Handouts with class material and practice problems will be distributed for each course topics. The textbooks used for the class preparation include the following:
D. Edwards and M. Hamson, Guide to Mathematical Modeling, Published by CRC Press, 1990.
Giordano, Weir, and Fox, First Course in Mathematical Modeling , Thomson Brooks/Cole, 2003.
Technology
Matlab will be used extensively. All students are also recommended to have a calculator.
Topics Covered
1. Basic ideas and techniques of mathematical modeling.2. Programming in Matlab. M-files.
3. Modeling with differential equations. Continuous dynamical systems.
4. Modeling with difference equations. Discrete dynamical systems.
5. Dimensional analysis.
6. Empirical (experimental) models. Effectiveness and validity.
7. Interpolation and model fitting.
8. Simulation modeling. Monte Carlo simulations.
9. Discrete and continuous optimization modeling.
10. Modeling with systems of difference and differential equations.
11. Report writing and result presentation.
Grading
| Assignment 1 | 25% |
| Assignment 2 | 25% |
| Assignment 3 | 25% |
| Project | 25% |
| TOTAL | 100% |
| A | A- | B+ | B | B- | C+ | C | C- | D+ | D | F | |
| grade | 93-100 | 90-92 | 87-89 | 83-86 | 80-82 | 77-79 | 73-76 | 70-72 | 67-69 | 60-66 | 0-59 |
Number of credits
3
Prerequisites
MA201 or the permission of instructor.
Attendance
Since the course is mostly based on material covered in class handouts and classwork, it is absolutely imperative that students attend all classes. Students are responsible for all material covered in class, even if attendance is not checked or assignments collected.Assignments, Projects
There will be three assignments plus a student project + presentation. No assignment grade will be dropped. Assignments turned in after their due date will receive an automatic reduction in grade.Response time
The assignments, projects and exams are typically graded in three days after they are turned in. Special circumstances like snow days, school closing or holidays, may occasionally delay the response time. Barring special circumstances, students’ emails are usually responded to within one working day.
More on Mathematical Modelling
- Mathematical models are used widely in the natural, health and social sciences. The course will cover a variety of topics related to mathematical modeling and modeling techniques: discrete and continuous models, dynamical systems, stability of solutions, steady states.
- Algebra, trigonometry, and calculus techniques that students have encounter in previous courses will be used for successful mathematical modeling of more complex phenomena. Because of this, the course can be considered a continuation of earlier mathematics courses and the next step in building students' problem solving skills.
- The course provides the students interested in continuing their education at a graduate level wem with mathematical techniques that certain graduate programs use.
- The course emphasizes research ideas, not just mastering various techniques or methods. These ideas of problem solving are often used in various fields and will be a useful concept for students to acquire.
Course Objectives
- identify a problem and choose an appropriate mathematical model,
- create a model that adequately describes the problem, using the appropriate technology if necessary,
- test the validity of the model,
- solve the problem using the appropriate technology if necessary,
- present the results orally, on computer and in a form of a written report.
Learning outcomes
Students will:- develop understanding of various mathematical concepts and modeling techniques required for successful application of mathematics;
- be able to model data using the language and techniques of mathematics;
- be able to understand and solve multidisciplinary application problems;
- demonstrate proficiency in using mathematical software;
- know how to use appropriate technology to solve problems applying techniques of mathematics;
- demonstrate ability to cover a topic independently and present their results in an oral presentation as well as in a written report.
Academic integrity
Saint Joseph’s University encourages the free and open pursuit of knowledge; we consider this to be a fundamental principle and strength of a democratic people. To this end, SJU expects its students, its faculty, its administrators, and its staff to uphold the highest standards of academic integrity. The University expects all members of the University community to both honor and protect one another’s individual and collective rights.Student with Disabilities Statement
Reasonable academic accommodations may be provided to students who submit appropriate documentation of their disability. If students have need of assistance or questions with this issue, they are encouraged to contact the Office of Student Disability Services (SDS) at sds@sju.edu or by phone at 610.660.1774. The Office of SDS also provides an appeal/grievance procedure for complaints regarding requested or offered reasonable accommodations. More information can be found at: www.sju.edu/sds.Health and Wellness Statement
Saint Joseph's University recognizes that physical and mental health strongly impact one's ability to do well in school and in life. As a result, there are many helpful campus resources designed to help students to care for their physical, mental, and spiritual health. Students may experience stressors that can impact both their academic experience and their personal well-being. These may include academic pressure and challenges associated with relationships, mental health, alcohol or other drugs, identities, finances, etc. All of us benefit from support during times of struggle and challenges. If you are experiencing concerns, seeking assistance sooner rather than later is a courageous thing to do for yourself and those who care about you. The resources at https://sites.sju.edu/counseling/ can help you to cope with stress and to achieve your academic and personal goals.All content copyright Lia Vas. All rights reserved.