This refreshing, introductory textbook covers both standard techniques for solving ordinary differential equations, as well as introducing students to qualitative methods such as phase-plane analysis. The presentation is concise, informal yet rigorous; it can be used either for 1-term or 1-semester courses. Topics such as Euler's method, difference equations, the dynamics of the logistic map, and the Lorenz equations, demonstrate the vitality of the subject, and provide pointers to further study. The author also encourages a graphical approach to the equations and their solutions, and to that end the book is profusely illustrated. The files to produce the figures using MATLAB are all provided in an accompanying website. Numerous worked examples provide motivation for and illustration of key ideas and show how to make the transition from theory to practice. Exercises are also provided to test and extend understanding: solutions for these are available for teachers.

‘The presentation is sensitive to the needs of students, with careful algebraic steps included in most cases. Appendices on basic required mathematical techniques are also included.‘

Source: Mathematical Reviews

‘The book is recommended as a textbook for one-term or one-semester course.‘

Source: Zentralblatt MATH

‘… will be useful to anybody wanting to teach or learn elements of ordinary differential equations in the beginnings of their mathematical studies.‘

Source: European Mathematical Society Newsletter

‘… it is written in a friendly and informal style and covers a wide and interesting collection of topics.‘

Source: Contemporary Physics

'This is an excellent book which probably would have been most welcome to older students of differential equations had it existed and which will be of great value to those currently studying the subject.'

Source: The Mathematical Gazette