While statistics has now become an irreplacable component of economic study, mathematical analysis in academic content is growing exponentially. Mathematical modelling is particularly helpful in analysing a number of aspects of economic theory.
Students need to learn mathematical application in economics and MRU is the only platform capable of teaching the same in an engaging manner. Please consider. Would be sharing the academic resources available to me as well.
Techniques of constrained optimisation.
This is a rigorous treatment of the mathematical techniques used for solving constrained optimisation problems, which are basic tools of economic modelling. Topics include: Definitions of a feasible set and of a solution, sufficient conditions for the existence of a solution, maximum value function, shadow prices, Lagrangian and Kuhn Tucker necessity and sufficiency theorems with applications in economics, for example General Equilibrium theory, Arrow-Debreu securities and arbitrage.
Bellman approach. Euler equations. Stationary infinite horizon problems. Continuous time dynamic optimisation (optimal control). Applications, such as habit formation, Ramsey-Kass-Coopmans model, Tobin’s q, capital taxation in an open economy, are considered.
Tools for optimal control: ordinary differential equations.
These are studied in detail and include linear 2nd order equations, phase portraits, solving linear systems, steady states and their stability.