In this book, I present the basic principles of modelling, and the bare essentials from mathematics and statistics that you need to build and apply simple models. I am writing from the perspective of TK and TKTD modelling in ecotoxicology, but these basics are applicable to many other scientific fields as well. Furthermore, I am specifically writing about models as tools to answer (applied) scientific questions. I am not so much interested in modelling for the sake of modelling. For me, models are the quantitative tools that make ideas (or theory) testable and applicable to real-world questions. Therefore, this book is not just about mathematics (though there will be equations). It contains elements from philosophy of science, and the intellectual challenge of simplifying real-world complexity into a more manageable representation. Furthermore, statistics will be treated alongside the process models, whereas these topics are usually kept well separated in textbooks and teaching. As soon as we want to compare our model to data, we inevitably have to deal with statistics, so a statistical background is essential for practical modelling.

All of these elements are treated in a somewhat cursory and selective manner. I am focussing on the essential things that you need to get started with TK and TKTD modelling, which differs substantially from what you will get from more general textbooks on mathematics, modelling or statistics. I assume that the reader only has a very limited background in applied modelling, mathematics and statistics. However, I assume that you are familiar with mathematical functions, powers and logarithms, derivatives and integration, and basic probability distributions such as the binomial and the normal.

This book will be used to support courses on dynamic modelling of toxic effects. It is under continuous development, so you can expect additions and further polishing over the next years.

Support page at debtox.info (includes a version log)

_{At this moment, this e-book is (unlike my other e-books) not available free of charge. Paying for it gives me the opportunity to continue working on this book, and it keeps Leanpub in the air. Furthermore, you will receive future updates of the book for free. Please note that you can always request a refund from Leanpub within 60 days, no questions asked, if you think the book was not worth the price. If the price is an obstacle for you, please send me a message.}