Teaching GuideTerm
Faculty of Economics and Business
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Grao en Administración e Dirección de Empresas
  Mathematics II
Topic Sub-topic
1. The euclidean space IRn. The vector space IRn.
Inner product. Norm. Distance.
Interior, closure, isolated, limit and boundary points.
Open and closed sets.
Compact sets.
2. Functions of several variables. Basic concepts.
Graphical representation of real functions. Level sets.
Limit of a function at a point.
Linear functions.
Quadratic forms. Classification. Constrained quadratic forms.
3. Derivatives of functions of several variables. Partial derivatives.
Partial derivatives of higher order. Class one function
Chain's Rule.
Taylor's theorem.
Implicit function theorem.
4. Convexity of sets and functions. Convex sets. Properties.
Convex functions. Properties.
Characterization of twice continuously differentiable convex functions.
5. Introduction to mathematical programming. Formulation of a mathematical program.
Local and global optima.
Graphic solving.
Basic Theorems in optimization.
6. Unconstrained optimization. First-order necessary conditions.
Second-order conditions.
The convex case.
Sensitivity analysis.
7. Equality-constrained optimization Formulation.
First-order necessary conditions: the Lagrange theorem.
Second-order conditions.
The convex case.
Sensitivity analysis.
8. Linear programming. Formulation of linear programs.
Basic feasible solutions.
Fundamental theorems.
The simplex algorithm.
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