Topics in linear algebra. Review of basic linear algebra. Linear independence. The rank of a matrix. Main results on linear systems. Eigenvalues. Diagonalization. Quadratic forms. Quadratic forms with linear constraints. Partitioned matrices and their inverses. Linear programming. A simple maximization problem. Graphical solution procedure. Extreme points and the optimal solution. Special cases. General linear programming notation. Sensitivity analysis and interpretation of solution. Multivariable calculus. Gradients and directional derivatives. Convex sets. Concave and convex functions. Quasiconcave and quasiconvex functions. Taylor's formula. Implicit and inverse function theorems. Degrees of freedom and functional dependence. Differentiability. Existence and uniqueness of solutions of systems of equations. Static optimization. Extreme points. Local extreme points. Equality constraints: the Lagrange problem. Local second-order conditions. Inequality constraints: nonlinear programming. Sufficient conditions. Comparative statics. Nonnegativity constraints. Concave programming. Precise comparative statics results. Existence of Lagrange multipliers. Multicriteria decisions. Goal programming: formulation and graphical solution. Goal programming: solving more complex problems. Scoring models. Analytic hierarchy process AHP. Establishing priorities using AHP. Using AHP to develop an overall priority ranking. Numerical examples and application to marketing, finance, and operations management with LINGO.
Prerequisiti e modalità di esame
Closed book exam
Lecture, tutorial, and lab.
Materiale didattico e bibliografia
Knut Sydsaeter, Peter Hammond, Atle Seierstad, Arne Strom, Further Mathematics for Economic Analysis, Financial Times Prentice Hall, 2008 (chapters 1,2,3). Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, Kipp Martin, An Introduction to Management Science: Quantitative Approaches to Decision Making, Cengage Learning, 2010 (chapters 2,3,4,5,8,14).