Ordinary Differential Equations: From Calculus to Dynamical Systems
by V. W. Noonburg
Catalog Code: FCDS
This book presents a modern treatment
of material traditionally covered in the sophomore-level course in
ordinary differential equations. While this course is usually
required for engineering students, the material is attractive to
students in any field of applied science, including those in the
biological sciences.
The standard analytic methods for
solving first and second-order differential equations are covered in
the first three chapters. Numerical and graphical methods are
considered side-by-side with the analytic methods and are then used
throughout the text. An early emphasis on the graphical treatment of
autonomous first-order equations leads easily onto a discussion of
bifurcation of solutions with respect to parameters.
The fourth chapter begins the study of
linear systems of first-order equations and includes a section
containing all of the material on matrix algebra needed in the
remainder of the text. Building on the linear analysis, the fifth
chapter brings the student to a level where two-dimensional nonlinear
systems can be analyzed graphically via the phase plane. The study of
bifurcations is extended to systems of equations using several
compelling examples, many of which are drawn from population biology.
In this chapter, the student is gently introduced to some of the more
important results in the theory of dynamical systems. A student
project involving a problem recently appearing in the mathematical
literature on dynamical systems is included at the end of chapter 5.
A full treatment of the Laplace
transform is given in Chapter 6, with several of the examples taken
from the biological sciences. An appendix contains completely
worked-out solutions to all of the odd-numbered exercises.
The book is aimed at students with a
good calculus background who want to learn more about how calculus is
used to solve real problems in today's world. It can be used as a
text for the introductory differential equations course, and is
readable enough to be used even if the class is being “flipped.”
The book is also accessible as a self-study text for anyone who has
completed two terms of calculus, including highly motivated high
school students. Graduate students preparing to take courses in
dynamical systems theory will also find this text useful.
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