Mathematical Methods for Economics and Finance

Matrix algebra, determinants and Euclidean spaces. Linear independence. Subspaces attached to a matrix. Limits and open sets. Limits and compact sets. Convex sets and separating hyperplanes. Concave and quasiconcave functions. Homogeneous functions and Euler’s formula. The implicit function theorem, continuous functions and compact sets. Correspondences, fixed point theorems. Derivative of functions of vectors and matrices. Unconstrained maximization, constrained maximization. The envelope theorem. Eigenvalues and eigenvectors. Difference equations: stability, forward and backward solution. The Taylor’s expansion. Fourier transform. Dynamic programming. Numerical optimization.