Mathematics for Economists ΙΙΙ (3rd semester for the academic year 2021-22)
The course intends to the introduction of concepts in real analysis and of methods for the solution of O.D.E. with applications in economic theory and econometrics. In this respect we examine: 1. Real sequences, accumulation points, convergence, uniqueness of limits, continuous mapping theorem, series, absolute and conditional convergence, ratio test. Power series, Taylor polynomials, intertemporal utility, moment generating functions. 2. First order O.D.E., separation of variables, exactness, Euler factors, equations with homogeneous coefficients, powers series solutions, stability of market equilibrium, Bernoulli equation and the Solow model, stability of the set of solutions, qualitative analysis and phase diagrams. 3. Higher order O.D.E, power series solutions, linear equations with constant coefficients, characteristic polynomial, particular solutions.
Indicative Course Prerequisites: Mathematics for economists Ι, Mathematics for economists ΙΙ