## Study-unit CALCULUS

Course name Economics of tourism 20004309 ASSISI Comune a tutti i curricula Andrea Capotorti Andrea Capotorti 63 ore - Andrea Capotorti 9 Coorte 2018 2018/19 Base Statistico-matematico SECS-S/06 Obbligatorio (Required) Attività formativa monodisciplinare Italian Elementary real functions and their shifting. Differential calculus and full function’s study. Theory of integration and its meaning. Linear algebra. Hints on optimization problems in economy. F. Privilegi: “compendio di MATEMATICA PER L’ECONOMIA: Un Percorso Esaustivo ma User Friendly”, Simone Ed.M. Fedrizzi, A. Ventre, A. Oieni: “Prove scritte di matematica generale” CEDAM Ed To learn and understand basic notions for the analysis of elementary real functions and linear algebra. To learn the logical/mathematical formalism. To be able to fully understand graphics and formula. To be able to follow and understand the course it is mandatory:- to be able to compute and manipulate equalities and inequalities of I and II degree; - to manipulate algebraic expressions. Standard lectures on all the subjects and explicit solution of prototypical exercises to better understand the thoretical parts and to be able to face the written examination. For students with Specific Learning Disorders and/or Disabilities please refer to the web page: http://www.unipg.it/disabilita-e-dsa Written examinations designed to evaluate abilities to face and solve formal problems expressed in mathematical language.The eximinations contain between 3 and 5 porblems depending on the difficulty of their solutions and on the exaustiveness of the exam. The examination can be splitted in two partial parts for those who will follow the lectures, or be full for all the others. Each examination should be completed before 2 hours.Those who will receive a grade between 15 and 17 or between 27 and 30, to pass the exam should pass a further written additional test. Exercises will be on subject and of the kind explained in the lectures. Basic notions: sets; functions; composed functions; power, exponential and logarithmic functions.Differential calculus: derivative and its economic applications; elementary functions’ derivatives; derivation rules.Deepenings: functions’ local approximation; derivative and monotonicity, derivative sign study; limits; continuos functions.Economic applications: marginality, increasing rates, function’s elasticity.Integral calculus: definite and indefinite integrals; fundamental theorem of integral calculus, economic applications: cash flows, consumer and producer surplus.Optimization: optimum problems; free and constrained maxima and minima.Linear algebra: vectors operations, scalar product.