Selected Topics in Mathematics
Aims of the course
The goal of this course is to provide the students with a basic understanding of the main mathematical tools used in business and economics.Course syllabus
1. Linear algebra (matrices, systems of linear equations, Gaussian elimination, determinant, vector spaces, linear independence, eigenvalues and eigenvectors, diagonalization, vector spaces with scalar product, orthonormal base, Gram-Schmidt orthogonalization, symmetric matrices, quadratic forms).2. Linear optimization (linear programs, simplex method, complementary slackness).
3. Calculus (derivative, linear approximation, partial derivative, gradient, indefinite integral, substitution, integration by parts, definite integral, multiple integral).
4. Differential equations (differential equations with separable variables, linear differential equations, classification of linear second order partial differential equations).
5. Nonlinear optimization (local and global extrema of functions of one or more variables, Lagrange multipliers, convex problems, Karush-Kuhn-Tucker conditions).
6. Analysis (implicit function theorem, fixed points theorems).
