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Teaching GuideTerm Faculty of Economics and Business |
| Grao en Administración e Dirección de Empresas |
 Subjects |
| Matemáticas II |
| Contents |
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| Identifying Data | 2016/17 | |||||||||||||
| Subject | Matemáticas II | Code | 611G02010 | |||||||||||
| Study programme |
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| Descriptors | Cycle | Period | Year | Type | Credits | |||||||||
| Graduate | 2nd four-month period |
First | FB | 6 | ||||||||||
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| 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 and convex sets. |
| 2. Functions of several variables. | Basic concepts. Graphical representation of real functions. Level sets. Limit of a function at a point. Continuity. Linear functions. Quadratic forms. Classification. Constrained quadratic forms. |
| 3. Differentiability of functions of several variables. | Partial derivatives. Differentiability. Continuously differentiable function. Theorems relative to differentiability. The chain rule. Partial derivatives of higher order. Taylor theorem. Implicit function theorem. Homogeneous functions. Euler 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. Fundamental theorems of optimization. |
| 6. Unconstrained optimization. | First-order necessary conditions. Second-order conditions. The convex case. |
| 7. Equality-constrained optimization | Formulation. First-order necessary conditions: the Lagrange theorem. Second-order conditions. The convex case. Interpretation of the multipliers. |
| 8. Linear programming. | Formulation of linear programs. Basic feasible solutions. Fundamental theorems. The simplex algorithm. Finding an initial basic feasible solution. Duality. |
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