This book is a collection of modeling projects using rather advanced mathematical tools. It has a very good chapter on how to set up mathematical models from the description of the problem. Some of the problems in the book can be used for an advance undegraduate class at an institution with good students. The models considered cover a wide range of applications.
This book is quite useful since the author clearly outlines the modeling process and gives many examples. It requires knowledge in physics, ODEs, and probability. The drawback of this book is that it was written before personal computers were widely available and before symbolic manipulators were easily accessible.
This book is a collection of modeling projects which can be used either in an introductory modeling course or in a differential equation class where students work on team projects. See Kocak's review and the book web page for further information on the book.
This book is a collection of modeling projects using differential equations as the main mathematical tool. It has a very good chapter on how to set up a differential equation model from the description of the problem. It can be used for an advanced undegraduate class at an institution with good students. The models considered are population, traffic, mechanical, flow, and heat transfer models.
This book is a collection of case studies based on problems in some British companies. It has a good introduction and it only requires calculus. It can be used in elementary undergraduate classes.
This book outlines the modeling process and examines several examples. It requires knowledge in physics, ODEs, PDEs, probability, and statistics. See Cumberbatch's review and the book web page for further information.
This book emphasizes the educational aspect of mathematical modeling and considers various modeling projects. The student may not benefit from the book as much as the faculty who lectures.
This book would give good lecture ideas and projects if you were to teach a modeling class for a non science audience. It requires knowledge in differential equations, probability, and statistics and it is self-contained since the first half of the book is a summary of methods needed to solve the problems presented in the second half. Two chapters are discussing the modeling philosophy. This book is for advanced undergraduate students.
This book can give good ideas for lectures. It requires knowledge in physics, calculus, and ODEs.
This book considers three different types of models: discrete, continuous, and spatially distributed. It can give good ideas for lectures if you want to spend all or the majority of the time on models in biology. The book is self-contained in that only calculus is a mathematical prerequisite and all the more advanced material needed to solve the models is presented in the book. You can use part of this book for an undergraduate course in modeling if you limit yourself to discrete and rather simple continuous models. To investigate the spatially distributed models, the students in the class would have to learn some rather advanced mathematical tools. See the book web page for further information.
This book is a core book since it has sections on what modeling is about, how to write a report, and how to organize a presentation. It requires knowledge in physics, calculus, ODEs, linear algebra, probability, and statistics.
This report gathers a collection of problems on which teams of student instructors worked on for 8 days while attending the IMA Mathematical Modeling workshop held in August 1994. The problems can be used either for lectures or as projects. The audience needs to have some knowledge in physics, calculus, ODEs, and PDEs.
This report gathers a collection of problems on which teams of student instructors and graduate students worked on for 10 days while attending the IMA Mathematical Modeling workshop. The audience needs to have some knowledge in physics, ODEs, PDEs, and some computational experience. To be able to use the problems presented here in an undergraduate modeling class, the students will need quite a strong mathematical background, which is beyond the average undergraduate knowledge.
This book presents a set of projects. It requires knowledge in physics, calculus, ODEs, PDEs, linear algebra, and numerical analysis. See Cumberbatch's review and the book web page for further information.
This book is focused on the motion of projectiles. It can give good lectures or projects. It requires knowledge in physics, ODEs, and numerical analysis.
This book is more problem oriented and cannot be used as a textbook for an introductory modeling course since it is geared towards the study of particular problems. It requires knowledge in ODEs, linear algebra, probability, and statistics. It can give several examples for lectures or projects. See Milton's review and the book web page for further information on the book.
This report gathers a collection of problems on which teams of graduate students worked on for 5 days while attending the IMA Mathematical Modeling workshop held in August 1992. The problems can be used either for lectures or as projects. The audience needs to have knowledge in physics, calculus, ODEs, and PDEs.
This book considers mathematical modeling with a different perspective than most of the other books listed here: it introduces it through one or more specific techniques rather than through obtaining an insight on real-world problems with mathematical tools. It can be used for an undergraduate class if the students have had ordinary differential equations and a numerical analysis class.
This book gathers problems from various application areas and it cannot, per se, be used as the sole textbook for a modeling course. It gives several examples for lectures or projects. It requires knowledge in physics, calculus, and ODEs. See the book web page for further information.
This book gathers problems in the area of applied mathematics; it includes a few problems that can be used in a modeling course but it is not limited to that only. It gives several examples for lectures or projects. It requires knowledge in physics and applied mathematics beyond ODEs and linear algebra. The problems previously appeared in SIAM review. See the book web page for further information.
This book is an introductory modeling book and can give material for lecture and projects. It requires knowledge in physics, calculus, ODEs, linear algebra, probability, statistics, and optimization. See the author's web page for further information.
This book is a good book to have in your own library since it has many examples. It requires knowledge in physics, ODEs, linear algebra, probability, and statistics. See Cumberbatch's review and the book web page for further information.
This book covers quite a few application areas. It requires knowledge in physics, ODEs, probability, and statistics. See Sherman's review for further information on the book.
Additional unevaluated references for undergraduate classes