For the past several years the Division of Applied Mathematics at Brown University has been teaching an extremely popular sophomore level differential equations course. The immense success of this course is due primarily to two facยญ tors. First, and foremost, the material is presented in a manner which is rigorous enough for our mathematics and apยญ plied mathematics majors, but yet intuitive and practical enough for our engineering, biology, economics, physics and geology majors. Secondly, numerous case histories are given of how researchers have used differential equations to solve real life problems. This book is the outgrowth of this course. It is a rigorous treatment of differential equations and their appliยญ cations, and can be understood by anyone who has had a two semester course in Calculus. It contains all the material usually covered in a one or two semester course in differenยญ tial equations. In addition, it possesses the following unique features which distinguish it from other textbooks on differential equations
CONTENT
1. First Order Differential Equations -- 2. Second Order Linear Differential Equations -- 3. Systems of First Order Equations -- 4. Qualitative Theory of Differential Equations -- 5. Separation of Variables and Fourier Series -- Appendices -- A. Some simple facts concerning functions of several variables -- B. Sequences and series -- C. Introduction to APL
