This book presents, in a unitary frame and from a new perspective, the main concepts and results of one of the most fascinating branches of modern mathematics, namely differential equations, and offers the reader another point of view concerning a possible way to approach the problems of existence, uniqueness, approximation, and continuation of the solutions to a Cauchy problem. In addition, it contains simple introductions to some topics which are not usually included in classical textbooks: the exponential formula, conservation laws, generalized solutions, Caratheodory solutions, differential inclusions, variational inequalities, viability, invariance, and gradient systems.
In this new edition, some typos have been corrected and two new topics have been added: Delay differential equations and differential equations subjected to nonlocal initial conditions. The bibliography has also been updated and expanded.
The Cauchy Problem
Systems of Linear Differential Equations
Elements of Stability
Extensions and Generalizations
Calculus of Variations
Delay Functional Differential Equations
Readership: Graduate or undergraduate students dealing with analysis and differential equations, Volterra equations, calculus of variations and mathematical modeling.
Targeted at both high level undergraduate and first level graduate students in mathematics, physics and engineering
Offers a unitary and modern presentation of the main concepts and results
Simple introduction to several advanced topics
Plentiful illuminating examples and applications
Contains 36 figures and 178 exercises and problems completely solved
Written in an accessible and refreshing style