Applied Differential Equations: The Primary Course (Textbooks in Mathematics)
Author: Vladimir A. Dobrushkin (Author)
Publisher finelybook 出版社: Chapman and Hall/CRC
Edition 版次: 2nd
Publication Date 出版日期: 2022-09-21
Language 语言: English
Print Length 页数: 690 pages
ISBN-10: 1138606588
ISBN-13: 9781138606586
Book Description
This book started as a collection of lecture notes for a course in differential equations taught by the Division of Applied Mathematics at Brown University. To some extent, it is a result of collective insights given by almost every instructor who taught such a course over the last 15 years. Therefore, the material and its presentation covered in this book were practically tested for many years.
This text is designed for a two-semester sophomore or junior level course in differential equations. It offers novel approaches in presentation and utilization of computer capabilities. This text intends to provide a solid background in differential equations for students majoring in a breadth of fields.
Differential equations are described in the context of applications. The author stresses differential equations constitute an essential part of modeling by showing their applications, including numerical algorithms and syntax of the four most popular software packages. Students learn how to formulate a mathematical model, how to solve differential equations (analytically or numerically), how to analyze them qualitatively, and how to interpret the results.
In writing this textbook, the author aims to assist instructors and students through:
- Showing a course in differential equations is essential for modeling real-life phenomena
- Stressing the mastery of traditional solution techniques and presenting effective methods, including reliable numerical approximations
- Providing qualitative analysis of ordinary differential equations. The reader should get an idea of how all solutions to the given problem behave, what are their validity intervals, whether there are oscillations, vertical or horizontal asymptotes, and what is their long-term behavior
- The reader will learn various methods of solving, analysis, visualization, and approximation, exploiting the capabilities of computers
- Introduces and employs Maple™, Mathematica®, MatLab®, and Maxima
- This textbook facilitates the development of the student’s skills to model real-world problems
Ordinary and partial differential equations is a classical subject that has been studied for about 300 years. The beauty and utility of differential equations and their application in mathematics, biology, chemistry, computer science, economics, engineering, geology, neuroscience, physics, the life sciences, and other fields reaffirm their inclusion in myriad curricula.
A great number of examples and exercises make this text well suited for self-study or for traditional use by a lecturer in class. Therefore, this textbook addresses the needs of two levels of audience, the beginning and the advanced.
Review
As the author states in his preface, the Ordinary Differential Equations course is taught to undergraduates since some 200 years. If however a comparison is made between the book of Coddington and Levinson or the one of Hartman – two rather standard textbooks for at least half of century – and this one, the differences may be striking. The book aims to lay down a bridge between calculus,modeling and advanced topics (resulting from application requirements). Next the book emphasizes the role and the applications of qualitative theory. Among other aspects differentiating this book from others there can be mentioned: insertion of the topics from linear algebra as pre-requisite for the study of the systems of linear differential equations; discussion of the Sturm Liouville problems in two contexts: the orthogonal expansions and the boundary value problems occurring within the method of the separationof the variables for second order partial differential equations. Summarizing, this highly original textbook can introduce a new way of teaching ordinary differential equations.
~Vladimir Rasvan (Craiova) Sept. 2018
About the Author
Vladimir A. Dobrushkin is a Professor at the Division of Applied Mathematics, Brown University. He holds a Ph.D. in Applied mathematics and Dr.Sc. in mechanical engineering. He is the author of three books for CRC Press, including Applied Differential Equations with Boundary Value Problems, and Methods in Algorithmic Analysis. He is the co-author of Handbook of Differential Equations, Fourth Edition with Daniel Zwillinger.
