Mathematics (2008-2009)

Anno Accademico: 
Gianni Bosi
The aim of this course is to provide the students with the basic mathematical tools required for economic analysis and finance at undergraduate level.
A few aspects of logic. Essentials of set theory. Operations on sets. Quantifiers. Relations. Functions. Compositions of relations and functions. Inverse functions. Equivalences and order relations. Sequences. Some combinatorial problems. Permutations and combinations. Newton's binomial formula. Natural numbers and mathematical induction. Integers. Rational numbers. Real numbers. Axioms of an ordered field. Arithmetic operations in a field. Inequalities. Absolute values. Upper and lower bounds. Completeness axiom. Powers with arbitrary real exponent. Irrationals. Natural topology on the real line. Open and closed sets. Neighborhoods. Bounded sets. Cluster points. Convergent sequences. Functions of one variable. Basic definitions. Graphs of functions. Shifting graphs. Trigonometric functions. Function limits and continuity. Some general theorems on limits and continuity. Weierstrass' Theorem. Operations on limits. Rational functions. Infinite limits. Monotone functions. Compact sets. Cantor's Theorem. The intermediate value property. Derivatives. Differentiable functions.Simple rules for differentiation. Sums, products and quotients. Chain rule. Higher-order derivatives. Rolle's, Cauchy's and Lagrange's Theorems. Exponential functions. Logarithmic functions. Single-variable optimization. Local maxima and minima. L'Hopital's Theorem. Integration. Indefinite integrals. Definite integrals and area. Properties of definite integrals. Integration by parts and by substitution. Geometry in the plane. Conic sections. Functions of many variables. Partial derivatives with two or more variables. Surfaces and distance. Chain rules for many variables. Homogeneous functions. Multivariable optimization. Constrained optimization.
Testi consigliati: 
Knut Sydsaeter and Peter Hammond, Essential Mathematics for economic analysis, Prentice Hall
Ultimo aggiornamento: 11-12-2013 - 16:24