Differential equations are one of the oldest subjects in modern mathematics. Not long after Newton and Leibniz invented calculus, Bernoulli, Euler, and others began considering the heat and wave equations of mathematical physics. Newton solved differential equations in the study of planetary motion and his consideration of optics.



Today, differential equations are the centrepiece of much of engineering, physics, significant parts of the life sciences, and many areas of mathematical modelling. This text describes classical ideas and provides an entree to the newer ones. The author pays careful attention to advanced topics like the Laplace transform, Sturm–Liouville theory, and boundary value problems (on the traditional side) but also pays due homage to nonlinear theory, modelling, and computing (on the modern side).



This book began as a modernization of George Simmons’ classic Differential Equations with Applications and Historical Notes. Prof. Simmons invited the author to update his book. In the third edition, this text has become the author’s unique blend of the traditional and the modern. The text describes classical ideas and provides an entree to newer ones.



Modelling brings the subject to life and makes the ideas real. Differential equations can model real-life questions, and computer calculations and graphics can provide real-life answers. Synthetic and calculational symbiosis offers a rich experience for students and prepares them for more concrete, applied work in future courses.