•GUIDA ECONOMIA 07-08 - Università degli studi di Udine

prospectus udine
221
Bibliography
- G. GIORGI, Elementi di Matematica, Giappichelli,
2004.
- R. ISLER, Matematica generale, Edizioni
Goliardiche, Trieste.
- L. PECCATI, S. SALSA, A. SQUELLATI,
Matematica per l’economia e per l’azienda,
third edition, Egea, Milano, 2004.
- A.GUERRAGGIO, Matematica, Mondadori,
Milano, 2006.
Every week the lecturer will recommend
some excercises to solve, which can be
found on the ‘Sindy, Materiale Didattico’
site.
Texts and solutions of past written examinations
are available in ‘Student tutor
office’.
MATHEMATICS
(CdL BF, EC, SCSBM)
Prof. Marcellino Gaudenzi
Contents
Sets, ordered sets, real numbers, functions
Sets. Logical implications and equivalences.
Ordered sets. Real numbers.
Extended real numbers. Functions,
inverse functions and composed functions.
Cartesian products and the graph
of a function. Real functions of one real
variable. Monotone functions. Minimum,
maximum, infimum and supremum
of a function assuming real values.
Analytic geometry, exponential and logarithmic
function, trigonometric functions
The Cartesian coordinate system on the
line and on the plane. Lines in the plane.
The Cartesian coordinate system in
space. Planes of space. Circles and
spheres. Outlines of conic sections:
canonical equation of ellipses, parabolas,
hyperbolas. Neighbourhoods and their
properties. Powers, exponential and logarithmic
functions. Trigonometric functions:
sine, cosine and tangent functions
and their inverses.
Combinatorics
Permutations and combinations with and
without repetition. Binomial coefficients.
Newton’s binomial formulae and Pascal’s
triangle.
Limits, continuous functions, series
A general definition of limit. Algebraic
theorems on limits and indeterminate
forms. Basic theorems on the limit of
functions and sequences. Series: sum,
series with non-negative terms, geometric
series.
Continuous functions. Basic theorems
on continuous functions: The Weierstrass
theorem and the intermediate
value theorem, continuity of the inverse
function.
Differential calculus
The derivative of a function. The geometric,
physical and economic meaning of
the derivative. The tangent line. The rules
of derivation. The chain rule and the
derivative of the inverse function. Derivatives
of order greater than one. Local maxima
and minima. Rolle’s theorem, Fermat’s
theorem and the mean value theorem.
Sign of the derivative and the study
of the monotonicity of a function. Primitive
functions. L’Hospital’s rule and Taylor’s
formula. Convex functions. Inflection
points, asymptotes, elasticity.
Integral calculus
Riemann’s integral: definitions, properties
and geometric meaning. Integrability
of continuous functions and monotone
functions. The definite integral. The fundamental
theorem and the fundamental
formula of integral calculus. Calculus of
primitive functions: immediate integrals,
integration by decomposition, integration
by parts, integration by substitution,
integration of rational functions. Volume
of solids obtained by rotation. Improper
integrals.
Multivariable calculus
Graph and level curves of a function of
two real variables. Neighbourhoods of a