An Introduction to Mathematical Biology

Description

For advanced undergraduate and beginning graduate courses on Modeling offered in departments of Mathematics. This text introduces a variety of mathematical models for biological systems, and presents the mathematical theory and techniques useful in analyzing those models. Material is organized according to the mathematical theory rather than the biological application. Undergraduate courses in calculus, linear algebra, and differential equations are assumed. - See more at: http://www.pearsonhighered.com/educator/product/Introduction-to-Mathematical-Biology-An/9780130352163.page#sthash.7adEVTrk.dpuf Features • Applications of mathematical theory to biological examples in each chapter. – Similar biological applications may appear in more than one chapter. For example, epidemic models and predator-prey models are formulated in terms of difference equations in Chapters 2 and 3 and as differential equations in Chapter 6. – In this way, the advantages and disadvantages of the various model formulations can be compared. – Chapters 3 and 6 are devoted primarily to biological applications. The instructor may be selective about the applications covered in these two chapters. • Focus on deterministic mathematical models, models formulated as difference equations or ordinary differential equations, with an emphasis on predicting the qualitative solution behavior over time. • Discussion of classical mathematical models from population biology – Includes the Leslie matrix model, the Nicholson-Bailey model, and the Lotka-Volterra predator-prey model. – Also discusses more recent models, such as a model for the Human Immunodeficiency Virus - HIV and a model for flour beetles. • A review of the basic theory of linear difference equations and linear differential equations (Chapters 1 and 4, respectively). – Can be covered very briefly or in more detail, depending on the students’ background. – Difference equation models are presented in Chapters 1, 2, and 3. • Coverage of ordinary differential equation models – Includes an introduction to partial differential equation models in biology. • Exercises at the end of each chapter to reinforce concepts discussed. • MATLAB and Maple programs in the appendices – Encourages students to use these programs to visualize the dynamics of various models. – Can be modified for other types of models or adapted to other programming languages. – Research topics assigned on current biological models that have appeared in the literature can be part of an individual or a group research project. • Lists of useful references for additional biological applications at the end of each chapter.