Barbu V. Differential Equations

Springer International Publishing, Switzerland, 2016. — 230 p. — (Springer Undergraduate Mathematics Series) — ISBN10: 3319452606The present book is devoted to the study of differential equations. It is well known that to write a monograph or a textbook in a classical subject is a difficult enterprise requiring a rigorous selection of topics and exposition techniques. Part of mathematical analysis, the theory of differential equations is a fundamental discipline that carries a considerable weight in the professional development of mathematicians, physicists and engineers and, to a lesser extent, that of biologists and economists. Through its topics and investigative techniques, this discipline has a broad scope,
touching diverse areas such as topology, functional analysis, mechanics, mathematical and theoretical physics, and differential geometry.
Although this book is structured around the main problems and results of the theory of ordinary differential equations, it contains several more recent results which have had a significant impact on research in this area. In fact, even when studying classical problems we have opted for techniques that highlight the functional methods and which are also applicable to evolution equations in
infinite-dimensional spaces, thus smoothing the way towards a deeper understanding of the modern methods in the theory of partial differential equations.Existence and Uniqueness for the Cauchy Problem
Systems of Linear Differential Equations
Stability Theory
Prime Integrals and First-Order Partial Differential Equations