Differential Equations, Dynamical Systems, and Linear Algebra

This book (the original version) has all the basics to introduce the future differential equations/dynamical systems researchers into the field. Written by authorities in the field (Hirsch and Smale,) this text offers a wide variety of topics, including linear systems, local and global stability theory for non-linear systems, and applications to physics and biology. As an added treat, the inclusion of basic linear algebra and operator theory makes this a rather self-contained work. The dedicated reader will not be disappointed - the material is well organised with sufficient level of detail, illustration, and exercises.

I can see that this is not the book for you if you want to solve a particular differential equation. But in terms of understanding the field of dynamical systems, there is no rival. This book is a pleasure to read, for the first time I understood the importance and beauty of linear algebra. Academic Press says that this is their most successful mathematics text, and it is not hard to see why. I wish more texts were as clearly written and as beautiful to read.

This book is a classical in the subject. It will provide you with solid information even if you are an absolut beginner with proficiency only in undergraduate algebra, calculus.