Faculty Advisor

Lui, Roger Y


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.


Worcester Polytechnic Institute

Date Accepted

December 2012


Mathematical Sciences

Project Type

Major Qualifying Project



Advisor Department

Mathematical Sciences

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