Guia docente 2023_24 Facultade de Ciencias Económicas e Empresariais

Contents

Topic	Sub-topic
Preliminaries.	Mathematical symbols. Real functions of real variable. Elementary functions. Basic mathematical calculations.
Functions of a real variable.	Limits of real functions of real variable. Continuity of real functions of real variable. Theorems related to global continuity. Derivative of a function at a point. L'Hôpital's rule. Rolle and mean value theorems. Higher order derivatives and relative extremes. Concavity and convexity.
Integration.	Areas under curves. Fundamental theorem of integral calculus. Primitives.
Matrix calculus.	Matrices. Determinant of a square matrix. Systems of linear equations. Eigenvalues of a square matrix. Quadratic forms.
Derivatives of functions of several variables.	Introduction. Vectors. Partial derivatives. Differentiable functions. The chain rule. Higher order derivatives. Homogeneous functions. Euler's theorem.
Optimization.	Concave and convex functions. Unrestricted optimization. Optimization with equality constraints.