A Modern Introduction to Differential Equations

ISBN-13: 9780128234174 / Angielski

Henry J. Ricardo

Recenzje

"...This is a student-friendly text, from which learning is easy, even if I myself would have introduced the solution of paired first-order DEs by looking for linear combinations before going into the matrix formulation. It is very well produced and I spotted no egregious errors, although the breaking of equations between lines of text is a minor nuisance. Many calculus books use quotations in what is usually no more than an attempt at whimsicality, but here I much liked the dedication, to 'the sole stable equilibrium point in my life, and for all the second derivatives' (five names following).

Instructors of many courses should certainly consider this book, despite its price, unless they are irretrievably wedded to a formal approach." --The Mathematical Gazette

"The structure of the book has not changed significantly since the first edition. The new material includes an expanded treatment of bifurcations, for first-order 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 Hartman-Grobman theorem (called the Lyapunov-Poincaré 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 worked-out examples and exercises that span application areas in biology, chemistry and economics as well as physics and engineering." --MAA Reviews

Spis treści

1. Introduction to Differential Equations2. First-Order Differential Equations3. The Numerical Approximation of Solutions4. Second- and Higher-Order Equations5. The Laplace Transform6. Systems of Linear Differential Equations7. Systems of Nonlinear Differential Equations