This three-part book provides a comprehensive and systematic introduction to these challenging topics such as model calibration, parameter estimation, reliability assessment, and data collection design. Part 1 covers the classical inverse problem for parameter estimation in both deterministic and statistical frameworks, Part 2 is dedicated to system identification, hyperparameter estimation, an…
This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary dif…
This textbook, now in its second edition, provides students with a firm grasp of the fundamental notions and techniques of applied mathematics as well as the software skills to implement them. The text emphasizes the computational aspects of problem solving as well as the limitations and implicit assumptions inherent in the formal methods. Readers are also given a sense of the wide variety of p…
This book developed from classes in mathematical biology taught by the authors over several years at the Technische Universität München. The main themes are modeling principles, mathematical principles for the analysis of these models and model-based analysis of data. The key topics of modern biomathematics are covered: ecology, epidemiology, biochemistry, regulatory networks, neuronal networ…
An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems …
Eine lernendenorientierte und adaptive Gestaltung von Unterricht erfordert von den Lehrkräften, dass sie vorhandene Kompetenzen und Lernprozesse der Schülerinnen und Schüler diagnostizieren. Außerdem müssen sie die Anforderungen von Aufgaben mit Blick auf deren Passung zu den Lernprozessen der Schülerinnen und Schüler analysieren können. Eine derart verstandene "diagnostische Kompetenz"…
Overview: Learning and Understanding Mathematical Concepts in the Areas of Water Distribution and Water Treatment. From College of the Canyons.