The course provides the basic notions of mathematical analysis useful for the analysis and understanding, through mathematical models, of economic phenomena.
T.U. C1-C2. KNOWLEDGE AND UNDERSTADING: Graph of elementary functions and their transformations in the Cartesian plane. LEARNING SKILL: knowing how to evaluate simple situations and translate them into a linear and non-linear mathematical model; be able to process information and use calculation methods; knowing how to construct simple problem solving procedures with linear and non-linear relationships. LINK / APPLYING KNOWLEDGE AND UNDERSTADING: linear and non-linear models used in Economics, in the Business and in Statistics: functions of cost, revenue, profit, demand functions, supply and price of equilibrium, linear regression, simple interest rate, compound interest rate.
T.U. C3.KNOWLEDGE AND UNDERSTADING: average variation rate from a table, from a formula, incremental ratios, instantaneous variation rate, slope of the tangent equaled to the rate of variation, calculation of the derivative by algebraic way, analyze the continuity / discontinuity of a function both algebraically and graphically, asymptotes. LEARNING SKILL: knowing how to recognize algebraically and graphically when the continuity / discontinuity domain of a function (even at times). knowing recognize from the graph of a function if the function is derivable; knowing how to calculate simple limits of linear and non-linear functions (finite and infinite); knowing how to enunciate a theorem and recognize the necessary / sufficient conditions expressed by a theorem. LINK / APPLYING KNOWLEDGE AND UNDERSTADING: non-linear models used in Economics: cost, revenue and marginal profit.
T.U.C4.KNOWLEDGE AND UNDERSTADING: Acquire the calculation techniques related to the derivation for the product and the ratio of functions, chain rule; right tangent of an explicit and implicit function. LEARNING SKILL: knowing how to draw graphs of a function from that of its derivative and vice versa; knowing how to use the concept of derivative in the sphere of geometry and economics; know how to model simple phenomena with increasing or decreasing trend
over time. LINK/ APPLYING KNOWLEDGE AND UNDERSTADING: Cobb-Douglas production function
T.U. C5. KNOWLEDGE AND UNDERSTADING: maximum and minimum of a function; unlimited domain; singular point; concavity and convexity of a function; Fermat's theorem and theorems on second order n / s conditions. LEARNING SKILL: being able to calculate the extreme points of a function; given the function graph to recognize the extremes (local and global) points, the concavity and convexity domain; knowing how to apply the theorems of the first and second order conditions on the excellent; to qualitatively succeed in drawing the graph of a function using the acquired tools; knowing how to draw the graph of a function given the properties of it (max / min, concavity / convexity, domain and asymptotes). LINK / APPLYING KNOWLEDGE AND UNDERSTADING: minimize the average cost and consumption of raw materials, maximize revenue and profit; acceleration of sales.
T.U. C6. KNOWLEDGE AND UNDERSTADING: domain of multi-variable functions, surface analysis, constrained domains, Lagrange multiplier method; level curves. LEARNING SKILL: being able to calculate with the Lagrange multiplier method the optimum of a 2-variables function with an equality constraint; extrema problem of 2-variables function as function of one variable. LINK / APPLYING KNOWLEDGE AND UNDERSTADING: profit maximization with a Cobb-Douglas function (consumer utility).