About the Book
A Modern Introduction to Differential Equations, Third Edition, provides an introduction to the basic concepts of differential equations. The book begins by introducing the basic concepts of differential equations, focusing on the analytical, graphical and numerical aspects of firstorder equations, including slope fields and phase lines. The comprehensive resource then covers methods of solving secondorder homogeneous and nonhomogeneous linear equations with constant coefficients, systems of linear differential equations, the Laplace transform and its applications to the solution of differential equations and systems of differential equations, and systems of nonlinear equations.
Throughout the text, valuable pedagogical features support learning and teaching. Each chapter concludes with a summary of important concepts, and figures and tables are provided to help students visualize or summarize concepts. The book also includes examples and updated exercises drawn from biology, chemistry, and economics, as well as from traditional pure mathematics, physics, and engineering.
Readership Upper level undergraduate and graduate students from a variety of majors taking courses typically titled (Introductory) Differential Equations, (Introductory) Partial Differential Equations, Applied Mathematics, Fourier Series and Boundary Value Problems
Quotes "The structure of the book has not changed significantly since the first edition. The new material includes an expanded treatment of bifurcations, for firstorder equations and then more broadly for linear and nonlinear systems. The author has also added an optional section on limit cycles and the Hopf bifurcation. There is a particularly good application example here with the Van der Pol oscillator. This edition also includes a longer section on the HartmanGrobman theorem (called the LyapunovPoincaré theorem in the previous edition) with some good examples. As with many books at this level, a background in linear algebra is not assumed. When I have taught a course like this (usually with many engineering students who never take a linear algebra course), I found incorporating linear algebra in this context awkward and difficult to integrate smoothly. Here the author handles that relatively gracefully. One notable feature of the book is that it provides essentially no discussion of supporting software. The author assumes that students have access to a computer algebra system and possibly some specialized software for graphing and numerical approximation. Otherwise, he offers no software instruction and says that students should follow their instructor’s direction. This works, more or less, because the text shows detailed results of calculations and presents plenty of graphs of phase portraits, solution curves, and the like. This is an attractive book, designed for readability and well suited for an introductory course. It has a broad collection of workedout examples and exercises that span application areas in biology, chemistry and economics as well as physics and engineering." MAA Reviews
Content
1. Introduction to Differential Equations 2. FirstOrder Differential Equations 3. The Numerical Approximation of Solutions 4. Second and HigherOrder Equations 5. The Laplace Transform 6. Systems of Linear Differential Equations 7. Systems of Nonlinear Differential Equations
