# Corso di Laurea in Economia e Gestione delle Imprese (Anno Accademico 2009/2010)

Calculus in one variable
Descrizione dell'insegnamento
Real functions with types, limits and continuity, derivatives, indefinite as well as definite integral, applications to differentiation and integration, simple first order differential equations.
Prerequisiti
Analytic geometry in the plane. Elementary functions. Algebraic, trigonometric, exponential and logarithmic relations.
Scopi
To reinforce the concepts of calculus like the connectivity of a behavior, the rate of change of a phenomena, extrema of a relation, composition and inverse of multiple operations, the concept of convergence and clustering in sequential steps, the concept of integration as accumulation with its vast applicability, etc.. By inducing further experimental formation, we will have satisfied the three basic objectives of calculus reform sought worldwide, namely the theoretical, the graphical and the visual aspect of such a rich subject. By completing the course, the student will have acquired a professional skill in handling phenomenal variations. It will enable him to master the vocabulary of the subject by grasping the fundamental concepts treated in calculus and treated by calculus.
Contenuti
Elementary logic, sets and real numbers, algebraic and order properties, Cartesian product, relations. Functions with classifications, geometric properties, algebraic versus transcendental, exponential, circular and hyperbolic functions, compositions of functions; inverse functions with graphing, logarithmic functions. Limits and continuity, calculus of limits of sequences and functions, one-sided limit, infinite-valued limits and asymptotes, squeeze theorem, global properties of continuous functions, intermediate and extreme value theorems. Derivatives and derivation rules, differentials, derivatives of inverse, composite and implicit functions, repeated differentiation. Applications of the derivative: Mean-value theorem and Taylor’s expansion, series and relevant convergence tests, power series, indeterminate forms and de L’Hopital rule, 2nd derivatives and convexity, functions extrema and sketch of graphs. Primitives with properties, simple differential equations. Integration by substitution, trigonometric integrals, integration by parts and reduction formulae, trigonometric substitutions and integration by partial fractions. The definite integral with properties, the integral mean value theorem, the Riemann sum with conditions of integration. Fundamental theorem of calculus and case of improper integrals.
Testi
1. Ernest F. Haeussler, Jr., Richard S. Paul, Richard Wood: Introductory Mathematical Analysis, for Business, Economics and Social Sciences, 11th edition,, Pearson, Prentice Hall, New Jersey, USA, 20052. George B. Thomas et al: Thomas’ Calculus, 11th edition, Pearson, Addison Wesley, Boston, USA, 2005
It is suggested that the exercises connected to the videolessons be carried out. During the course group and individual exercises will be organized.
Docente
Nessun Docente attualmente disponibile per questo corso
Elenco delle lezioni
 •  Lezione n. 1: Introduction to the subject Assem Deif •  Lezione n. 2: Real numbers Assem Deif •  Lezione n. 3: Real functions Assem Deif •  Lezione n. 4: Classification of functions Assem Deif •  Lezione n. 5: Basic functions Assem Deif •  Lezione n. 6: Composite functions Assem Deif •  Lezione n. 7: Inverse functions Assem Deif •  Lezione n. 8: Limits Assem Deif •  Lezione n. 9: Limit theorems Assem Deif •  Lezione n. 10: Continuity Assem Deif •  Lezione n. 11: Differentiation Assem Deif •  Lezione n. 12: Derivative of inverse - composite - implicit functions Assem Deif •  Lezione n. 13: Applications of the derivative Assem Deif •  Lezione n. 14: Infinite series Assem Deif •  Lezione n. 15: Indeterminate forms and L’Hopital rule Assem Deif •  Lezione n. 16: Function extrema Assem Deif •  Lezione n. 17: Sketching of graphs Assem Deif •  Lezione n. 18: Antiderivative or the Indefinite Integral Assem Deif •  Lezione n. 19: Integration by substitution Assem Deif •  Lezione n. 20: Integration by parts Assem Deif •  Lezione n. 21: Integration by partial fractions Assem Deif •  Lezione n. 22: The definite integral Assem Deif •  Lezione n. 23: Properties of the definite integral Assem Deif •  Lezione n. 24: The fundamental theorem of calculus Assem Deif •  Lezione n. 25: Applications of integration Assem Deif