In many respects, this book is an ideal text book for beginners. It combines a clear approach and well-rounded explanations with plenty of practice. It makes an ideal companion for those students beginning a course in applied and numerical methods, differential equations and mechanics at school, or for undergraduate courses in mathematics, engineering or physics.The study of differential equations is an extensive subject in pure and applied mathematics, physics, and engineering. All of these disciplines deal with the properties of differential equations of different types. Pure mathematics has an emphasis on the life and incomparability of solutions, while applied mathematics emphasizes the rigorous methods of approximating solutions. Differential equations are an important tool in modeling virtually every physical, technical, or biological process, from celestial motion, to bridge design, to interactions between neurons. Differential equations, such as those used to solve real-life problems, may not necessarily be directly solvable, i.e. do not have closed example solutions. Instead, solutions can be approximated using numerical methods. Many fundamental laws of physics can be formulated as differential equations. In biology and economics, differential equations are used to model complex systems. Likewise, mechanics and numerical methods are of much importance. They play an important role in mathematical problems.