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Mathematics plays an important role in many scientific and engineering disciplines. This book deals with the numerical solution of differential equations, a very important branch of mathematics. Our aim is to give a practical and theoretical account of how to solve a large variety of differential equations, comprising ordinary differential equations, initial value problems and boundary value problems, differential algebraic equations, partial differential equations and delay differential equations. The solution of differential equations using R is the main focus of this book. It is therefore intended for the practitioner, the student and the scientist, who wants to know how to use R to solve differential equations. When writing his famous book, “A Brief History of Time”, Stephen Hawking [2] was told by his publisher that every equation he included in the book would cut its sales in half. When writing the current book, we have been mindful of this, and our main desire is to provide the reader with powerful numerical algorithms written in the R programming language for the solution of differential equations rather tha