Explore deterministic mathematical modeling in quantitative ecology through this comprehensive lecture from the Serrapilheira/ICTP-SAIFR Training Program. Delve into topics such as simplifying assumptions, functional response, and qualitative dynamics with expert guidance from Roberto Kraenkel of IFT-Unesp. Gain insights into the locking terror system, first equations, orbits, trajectories, and orbit solutions. Apply theoretical concepts to practical examples, enhancing your understanding of mathematical modeling in ecological systems. Suitable for students and researchers seeking to deepen their knowledge in quantitative ecology and mathematical biology.