Differential Equations and Dynamical Systems
by Lawrence Perko · first published 1991
100% recommend
This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem, the use of the Poincare map in t
Affiliate links. As an Amazon Associate I earn from qualifying purchases.
Mentions per year
What Hacker News says
Related books
2008–2026Linear algebra and its applications
David C. Lay, Lay, Davic C. Lay, Steven R. Lay
Recommended by 22 · mentioned by 3022 recommend · 30 mention22 recommend · 3022 recommend
2009–2026Basic Mathematics
Serge Lang
Recommended by 22 · mentioned by 2722 recommend · 27 mention22 recommend · 2722 recommend
2010–2026Numerical linear algebra
Lloyd N. Trefethen
Recommended by 26 · mentioned by 2926 recommend · 29 mention26 recommend · 2926 recommend
2008–2026Linear Algebra Done Right
Sheldon Jay Axler
Recommended by 130 · mentioned by 179130 recommend · 179 mention130 recommend · 179130 recommend
…analysis in the past, but this book is direct and rigorous and provided a good framework to move forward into things like functional analysis in a way that I was not prepared for with other books. 2. Differential Equations and Dynamical Systems by Lawrence Perko - Solidified for me how dynamic systems behaved and were solved. Very much helped my understanding of control theory as well. 3. A Concise Introduction to the Theory of Integration…
on “Ask HN: Math books that made you significantly better at math?” ↗…ball starts rolling because of an unpredictable perturbation. Small motions are amplified according to the Lyapunov exponent, which in the unstable case is large. Hirsch and Smale and Devaney's book on differential equations and dynamical systems is a good place to learn about this. In classical mechanics we model a zero-diameter point at the top of the dome, but a real physical dome would be made of molecules vibrating randomly and that starts…
on “Scientists find an effective solution for the three-body problem” ↗I liked Hirsch and Smale's old book called something like "Linear algebra, differential equations, and dynamical systems". It is now replaced by an expanded edition with a 3rd author added and a longer title, that I expect is also good, though I haven't looked at it. I don't know if the H&S book is beginner friendly,…
on “Ask HN: Best beginner friendly linear algebra book?” ↗