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This book will be of interest to those in science and engineering who want to learn how to solve differential equations numerically. The examples cover a wide range of applications, including animation, fluid flow, molecular motors, etc. The emphasis is on the constructive aspects of the subject, where the methods are actually used to help understand the mathematical principles underlying how and why they work. This text skillfully demonstrates how to derive, test and analyze numerical methods for solving differential equations and discusses the computational issues that arise when this is done.