A Course in Ordinary Differential Equations
This book serves as a guide to a basic course in ordinary differential equations for students that do not have mathematics and differential equations as their main subject. It concentrates on finding solutions to concrete equations. There is no abstract theory (existence and uniqueness); there are just theorems necessary for solving usual types of equations and for understanding the solving algorithms (without proofs). On the other hand, the book contains very detailed explanations of all solving procedures and the theory so it is intelligible for a wide range of students. Moreover, it contains codes for solving equations via Matlab, Maple or Mathematica, which may be of help to many students, professors, scientists and others. The topics dealt with are: first order equations, linear higher order equations, systems of linear equations, the Laplace transform and the power series method. Two chapters are devoted to each of the first three topics. The first of the two chapters contains abstract theory, whilst the second chapter contains algorithms for solving the equations and the codes for Matlab, Maple and Mathematica. The book also contains sections about phase diagrams and bifurcations with appendices introducing Maple, Matlab and Mathematica and some basic linear algebra. The book is self-contained; only knowledge of basic calculus is needed. Each topic is supplemented with many examples, exercises and applications to physical, chemical and biological models.