PREFACE

Encouraged by the positive reception to our German textbook on mathematical modeling, we were motivated to create an English version of this book. Although there is a long tradition of English textbooks on mathematical modeling to the best of our knowledge, most of them differ from the one presented here, as our book is ordered according to a hierarchy of mathematical subjects with increasing complexity. We start from simple models given by (linear) equations and end up with complex mathematical models involving nonlinear partial differential equations with free boundaries. In this way, we offer a variety of mathematically more and more inclined subjects from which both elementary undergraduate and sophisticated graduate courses can be composed. In this sense, we hope that our book fills a gap and will be of use also in the curricula for mathematical modeling in English-speaking universities. We have taken the opportunity of the translation process to correct further misprints and small inconsistencies which have come to our knowledge. This English version of this book would not have come into existence without support of the following people: Mrs. Eva Rütz, Mrs. Astrid Bigott, and Mrs. Cornelia Weber have created the TEX version on the basis of the first translation provided by the authors, as usual with enormous exactness, speediness, and dedication. This first draft has been considerably improved by Prof. Serge Kräutle and Dr. Kei Fong Lam, who worked through the whole text and removed various inconsistencies and mistakes not only in the usage of the English language but also concerning the mathematical contents. We thank Clemens Heine of SpringerVerlag for his continuous support and encouragement.