Matemática II

Theoretical classes introduce concepts, properties and examples, enabling students to understand the exercises proposed and identify the mathematical tools to be used. In the remaining classes, shared, individual and/or group resolution of exercises and activities allows students to develop specific analysis and calculation skills to solve the problems proposed.

The course aims to develop theoretical and applied understanding of fundamental concepts in mathematics, particularly in the field of differential equations and differential calculus in IRn. In the theoretical classes, an expository teaching method is adopted, through which essential concepts are introduced and illustrative examples of their application are presented. In the remaining classes, an active teaching method is used, focused on solving exercises – individually and/or in groups – promoting the consolidation of content, as well as the development of analysis and problem-solving skills.

1. Introduction to the study of ordinary differential equations – Introduction and motivation. First-order differential equations: linear equations; Bernoulli equations; equations with separable variables; homogeneous equations of degree zero. Modelling and applications to engineering.
2. Differential calculus on IRn – Conics and quadric surfaces. Notions of topology on IRn. Real functions of several real variables and their derivatives: domain; contour line and graph of a function of two or more variables; limit and continuity; partial derivatives; gradient vector; differentiable functions; directional derivative; tangent plane and normal line; linear approximation; function extremes: free, constrained, Lagrange multiplier method and gradient method (or maximum descent method).

• - Tests (90%) and class questions (10%) / Exam (100%) - 100.0%

NAO