Teaching GuideTerm Faculty of Economics and Business 
Grao en Administración e Dirección de Empresas 
Subjects 
Mathematics II 
Contents 



Identifying Data  2019/20  
Subject  Mathematics II  Code  611G02010  
Study programme 


Descriptors  Cycle  Period  Year  Type  Credits  
Graduate  2nd fourmonth period 
First  Basic training  6  

Topic  Subtopic 
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. Continuity. 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.  Firstorder necessary conditions. Secondorder conditions. The convex case. Sensitivity analysis. 
7. Equalityconstrained optimization  Formulation. Firstorder necessary conditions: the Lagrange theorem. Secondorder conditions. The convex case. Sensitivity analysis. 
8. Linear programming.  Formulation of linear programs. Basic feasible solutions. Fundamental theorems. The simplex algorithm. 
