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Descrizione dell'insegnamento |
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The course of Mathematics aims to provide students the understanding of the basic analytical instruments, focusing also to the tools currently used in the economic analysis. The main topics of the course are the study of the functions, derivates of functions, intregrals, and matrices. Those course is the basic step to collect the tools necessary to attend statistics and other economic courses. |
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Prerequisiti |
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Analytic geometry on the plane. Elementary functions. Algebraic, trigonometric, exponential and logarithmic equations and inequalities. |
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Scopi |
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• Calculus of limits; • Differentiating one-variable real functions, in particular elementary real functions; • Study of the behaviour of any one-variable real function; • Calculus of integrals. |
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Contenuti |
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• Elementary logic. Sets, relations, functions. Transformations on graphics. Compositions of functions; inverse functions. • Limits and continuity. Calculus of limits. Discontinuities. Asymptotic. Sequences. Landau symbols. Basic results on limits and on global properties of continuous functions. • Derivatives and derivation rules. Second derivatives and convexity. Differential calculus results (Fermat, Rolle, Lagrange, Cauchy, De L’Hopital Theorems). Taylor approximations. • Primitives and definite integrals. Integration rules. Improper integrals. symbols. Basic results on limits and on global properties of continuous functions.
• Derivatives and derivation rules. Second derivatives and convexity. Differential calculus results (Fermat, Rolle, Lagrange, Cauchy, De L'Hopital Theorems). Taylor approximations.
• Primitives and definite integrals. Integration rules. Improper integrals. |
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Testi |
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• Advanced Engineering Mathematics, A Jeffrey; Harcourt/Academic Press; 2002; • R. Bartle & D. Sherbert, Introduction to Real Analysis, Wiley, 1982; • R. Haggerty, Fundamentals of Mathematical Analysis, Addison-Wesley, 1992; • Dolciani, M. et al : Introductory Analysis , Houghton Mifflin , Boston , 1991. |
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Esercitazioni |
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The exercises follow the macro arguments on which the course is structured. However, there are few insights to better understand some topics not intuitive. In particular, given the broad class of knowledge and related techniques, contained in systematic qualitative study of a real function of a real variable, it presents a detailed method for how to properly follow the study. |
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Docente/Tutor Responsabile insegnamento |
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Clemente Cesarano
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