Instructor:   Andrew Belmonte
Contact info:   322 McAllister Building, telephone: 865-2491, email: alb18@psu.edu
Office hours:   TBA, or by appointment.

Class location:                                                          Registrar Schedule Number: 713056
         104 Steidle Bldg

Prerequisites:   Math 405 or 406 or 411 or 412. For more information, please contact the instructor.

• Alternate Realities: Mathematical Models, by John L. Casti (Wiley, 1989)
  ISBN:0-471-61842-X.
• Perturbation Methods, by E. J. Hinch (Cambridge, 1991)
  ISBN: 0-521-37897-4.

The Course:  In this class you will be introduced to the fine art of mathematical modeling, a process that involves balancing the rigorous world of mathematics with the nonideal "outside world", be it mechanical, chemical, statistical, economic, or biological. Over the semester we will explore mathematical ideas and tools used to study the natural world in the various ways that we find it. Particular emphasis will be placed on the process of creating a mathematical model starting from an observed 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 the goal of this course to engage you in this cycle.

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

Modeling Topics: the systems we will study this semester may include: simple and compound pendulum motion, locomotion and sports, game theory, 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.

COURSE DESCRIPTION:   from the Penn State Blue Book