This book introduces qualitative methods for understanding differential equations, especially when analytical solutions are not possible. Aimed at second-year undergraduate students in mathematics or science, it assumes prior knowledge of calculus, linear algebra, and curve sketching. The book focuses on phase plane methods for second-order differential equations, supported by earlier sections on analytical techniques and phase lines for first-order equations. The later chapters explore bifurcation theory and chaos. Emphasizing application over theory, the book includes diagrams, worked examples, and exercises, with minimal use of formal proofs.

Paul C. Matthews was on the faculty of the University of Nottingham for more than two decades. A specialist of dynamical systems and their numerical analysis, he is the author of the bestselling textbook Vector Calculus (Springer, 1998).