Mathematics

Knowledge and understanding: Concerning equations and systems of ordinary differential equations (ODE) students will learn under which hypotheses solutions exist and when they can be given explicitly, how to investigate the properties of solutions and their maximal existence interval when they are not explicit. The knowledge of proofs gives students a deep understanding of the subject and of the role of hypotheses. Skills and attributes: Techniques for explicit determination of the solutions of the most common ODEs and of linear systems of differential equations with constant coefficients. Qualitative analysis of some systems of ODEs. Applying knowledge and understanding: Students will be able to study the behavior of solutions of some simple ODEs in different application fields. Communication skills: In view of the oral exam students will be able to present a rigorous mathematical proof. Learning skills: Having a complete understanding of the basic mathematical tools used in ODEs, will help students to understand their generalizations for solving more advanced problems. The proof of the existence theorem will help in studying numerical methods for solving ODEs.