Rob J. de Boer
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There is a wise quote saying that different courses taught by the same teacher resemble each other more than the same course given by different lecturers. This is evidently true for the courses that I teach for biology students at the Utrecht University. Each of these courses has resulted into a ebook covering all the material that we teach, and providing lots of exercises with detailed answers. As confessed above these books overlap considerably. Nevertheless, they may provide a good read for self study.
My most recent book Biological Modeling of Populations is the reader of a new course for undergraduate students in biology. The course teaches students to develop ODE models for population dynamics, and study these models by phase plane analysis and numerical simulation (in R). Biologically, the course covers populations of viruses, bacteria, cells, tumors, and most of the basic material of theoretical ecology. Answers to the questions in the book are provided here. During the course we determine the stability of steady states using the eigenvalues of Jacobi matrices, and this matrial is covered in this math tutorial. Students having completed this course should be able to devise novel mathematical models in biology, and judge whether the terms used in mathematical models are realistic and/or well-defined. This book is basically a generalization of a previous reader used for students in theoretical ecology (see below).
The book Theoretical Biology comes from a course given to first year undergraduate biology students at Utrecht University. The Appendix of this book gives a short tutorial on phase plane analysis. These tools are used to study ODE models from various biological disciplines ranging from ecology, neurobiology, virology to gene regulation. Students completing this course successfully should be able to read published models critically and know how to interpret results obtained with mathematical models within their biological discipline.
The book Modeling Population Dynamics: a graphical approach originates from a course given to undergraduate students in Ecology. The book covers the basic material of Theoretical Ecology like predator prey models, competition models, and meta-population models, with a strong emphasis on model development. Models are analyzed by phase plane analysis (which is introduced shortly in the Appendix). One major aim of the book is to provide students with an approach to develop simple mechanistic ODE models. Students having completed this course should be able to define novel mathematical models by themselves. They should at least be able to judge whether the various terms used in a mathematical model are realistic and/or well-defined. The latest version of this book is the reader "Biological Modeling of Populations" presented above.
These "Population Dynamics" books assume that readers know how to linearize nonlinear ODEs, and obtain eigenvalues from the corresponding Jacobi matrix. A short reader providing an introduction into matrixes, eigenvalues and eigenvectors, linearization, and the Jacobi matrix can be found here.
The book Theoretical Physiology comes from a course given quite a while ago to undergraduate students in Biomedicine. It overlaps strongly with the Theoretical Biology book, but omits the chapters on Theoretical Ecology. A shorter variant of this book was used in several summerschools on Theoretical Immunology. After a few introductory chapters this book only discusses models in immunology. Readers of these books may also benefit from the introduction into linearization and the Jacobi matrix.
The booklet Rekenen aan de afweer contains the Dutch text of my inaugural lecture for the chair in Theoretical Immunology at Utrecht University.