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(TM), Mathematica(R), MatLab(R), 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.
