This project attempts to write the first draft of a mathematical modeling textbook for undergraduates. We based our information from the course we took under Professor Roger Lui in B term of 2011. The chapters in this book include: simple pendulum, escape velocity, Lotka-Volterra equations, extension on Lotka-Volterra equations, populations in competition, infectious diseases, chemostat, chemical kinetics, enzyme-substrate model, Poincare-Bendixson Theorem, and limit cycles. Emphasis of this book is on non- dimensionalization and phase plane analysis, which includes the study of the stability properties of the steady states. We also use the MATLAB program pplane8.m to help us plot the phase planes of various models.

• This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement. WPI routinely publishes these reports on its website without editorial or peer review.

Creator

• Anderson, Warren Charles
• Blake, Phillip Andrew

Publisher

• Worcester Polytechnic Institute

Identifier

• E-project-121412-123248

Advisor

• Lui, Roger Y

Year

• 2012

Date created

• 2012-12-14

Resource type

• Major Qualifying Project

Major

• Mathematical Sciences

Rights statement

• In Copyright