DESCRIPTION
The book covers the complete program of an ordinary differential equations course, which can be taught at the final undergraduate years or at the first graduate years It presents the topics in a gradual way, in a crescendo of didactic complexity, starting with the linear case.
The text contains many interesting examples and exercises, showing additional topics rarely treated in other texts, such as differential equations in probability, the Poincaré-Hopf theorem, and a brief introduction to ergodic theory. It ends with a proof of the existence and uniqueness of solutions and differentiability with respect to initial conditions and parameters. Full details and almost all prerequisites are provided to understand the proof.
ABOUT THE AUTHORS
Claus Ivo Doering
Claus Ivo Doering graduated at UFRGS and obtained his doctor degree at IMPA. He is a Full Professor at the Pure and Applied Mathematics Institute of the Federal University of Rio Grande do Sul since 1987.
Artur Oscar Lopes
Artur Oscar Lopes graduated at UFRJ and obtained his doctor degree at IMPA. He is a Full Professor at the Pure and Applied Mathematics Institute of the Federal University of Rio Grande do Sul since 1985.
His research areas are dynamical systems and ergodic theory. In 2005, he was awarded the Comenda da Ordem Nacional do Mérito Científico and, in 2007, he was elected a full member of the Brazilian Academy of Sciences.
