MATH 450

Mathematical Modeling of the Physical World

Penn State University,   Fall 2005

TR 9:45 - 11:00 AM (Schedule #550483)

Instructor: Professor Andrew Belmonte

Contact info: 322 McAllister Building, telephone: 865-2491, email:

Office hours: M 1-2, W 3-4, or by appointment.

Class location:

Prerequisites: Math 405, 411 or 412, or consent of the instructor.

Web Page:

Required Textbooks (available this fall in the bookstore):

Additional Texts and articles will be recommended or assigned in class.

Course Announcement as a PDF file.

Updated Course Information:
  Final Projects     Material Covered in-class  
(incl experiments)  
  HW # 3  

Interesting Links:

The Course:  The purpose of the course is to introduce mathematical modeling; over the semester we will explore mathematical ideas and tools used to study the natural world. Particular emphasis will be placed on the process of creating a mathematical model starting from a physical scenario. Typically this will begin with an experiment, either demonstrated in the W. G. Pritchard Lab or performed in class. Once a model has been developed, we will use a combination of analysis and experimentation to determine its properties and relevance - and to make predictions. Sometimes the first attempt is satisfactory, but more often we shall notice new features of the system that are not adequately addressed by the model, or predictions which are not borne out... and the process begins again! It is this cycle the course will emphasize.

A significant aspect of this mathematics course is its laboratory component: the students will perform experiments, and occasionally observe demonstrations. Our main focus, however, will be on creating and analyzing models - the course will try to convey some of the heuristic, intuitive, and mathematical ideas used to model observed phenomena.

Target Audience: advanced students majoring in mathematics, engineering, earth sciences, chemistry, or physics, as well as students in the biological sciences.

Modeling Topics: some of the systems include simple and compound pendulum motion, stick-slip motion, ice permeability, fluctuations and diffusion, fragmentation and fracture, fluid and granular flow, chaotic systems, and possibly some biological phenomena (heart rate variability, eye movement). Students will be encouraged to propose additional topics!

Mathematical Tools: in addition to the standards (e.g. differential equations), we will focus on some of the tools often not included in the curriculum, such as scaling laws and similarity solutions for differential equations; linear stability and normal mode analysis; stochastic differential equations; asymptotics.

Exam Schedule:

Last modified 22 December 2005, by AB