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The world abounds with introductory texts on ordinary differential equations and rightly so in view of the large number of students taking a course in this subject. However, for some time now there is a growing need for a junior-senior level book on the more advanced topics of differential equations. In fact the number of engineering and science students requiring a second course in these topics has been increasing. This book is an outgrowth of such courses taught by us in the last ten years at Worcester Polytechnic Institute. The book attempts to blend mathematical theory with nontrivial applications from varipus disciplines. It does not contain lengthy proofs of mathemati~al theorems as this would be inappropriate for its intended audience. Nevertheless, in each case we motivated these theorems and their practical use through examples and in some cases an "intuitive proof" is included. In view of this approach the book could be used also by aspiring mathematicians who wish to obtain an overview of the more advanced aspects of differential equations and an insight into some of its applications. We have included a wide range of topics in order to afford the instructor the flexibility in designing such a course according to the needs of the students. Therefore, this book contains more than enough material for a one semester course.

Introduction to Mathematical Modeling helps students master the processes used by scientists and engineers to model real-world problems, including the challenges posed by space exploration, climate change, energy sustainability, chaotic dynamical systems and random processes.Primarily intended for students with a working knowledge of calculus but minimal training in computer programming in a first course on modeling, the more advanced topics in the book are also useful for advanced undergraduate and graduate students seeking to get to grips with the analytical, numerical, and visual aspects of mathematical modeling, as well as the approximations and abstractions needed for the creation of a viable model.

This text is designed to update the Differential Geometry course by making it more relevant to today’s students. This new approach emphasizes applications and computer programs aimed at twenty-first-century audiences. It is intended for mathematics students, applied scientists, and engineers who attempt to integrate differential geometry techniques in their work or research.The course can require students to carry out a daunting amount of time-consuming hand computations like the computation of the Christoffel symbols. As a result, the scope of the applied topics and examples possible to cover might be limited. In addition, most books on this topic have only a scant number of applications.The book is meant to evolve the course by including topics that are relevant to students. To achieve this goal, this book uses numerical, symbolic computations, and graphical tools as an integral part of the topics presented. This book provides students with a set of Maple/MATLAB® programs that will enable them to explore the course topics visually and in depth. These programs facilitate topic and application integration and provide the student with visual reinforcement of the concepts, examples, and exercises of varying complexity.This unique text will empower students and users to explore in depth and visualize the topics covered, while these programs can be easily modified for other applications or other packages of numerical/symbolic languages. The programs are available to download for instructors and students using this book for coursework.

This text is designed to update the Differential Geometry course by making it more relevant to today’s students. This new approach emphasizes applications and computer programs aimed at twenty-first-century audiences. It is intended for mathematics students, applied scientists, and engineers who attempt to integrate differential geometry techniques in their work or research.The course can require students to carry out a daunting amount of time-consuming hand computations like the computation of the Christoffel symbols. As a result, the scope of the applied topics and examples possible to cover might be limited. In addition, most books on this topic have only a scant number of applications.The book is meant to evolve the course by including topics that are relevant to students. To achieve this goal, this book uses numerical, symbolic computations, and graphical tools as an integral part of the topics presented. This book provides students with a set of Maple/MATLAB® programs that will enable them to explore the course topics visually and in depth. These programs facilitate topic and application integration and provide the student with visual reinforcement of the concepts, examples, and exercises of varying complexity.This unique text will empower students and users to explore in depth and visualize the topics covered, while these programs can be easily modified for other applications or other packages of numerical/symbolic languages. The programs are available to download for instructors and students using this book for coursework.