- Docente: Andrea Brini
- Credits: 5
- SSD: SECS-S/06
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in STATISTICS, ECONOMICS AND BUSINESS (cod. 8056)
Learning outcomes
The student will learn the basic concepts and techiques of
multivariate differential calculus. More specificfally, the student
will be able to calculate partial derivatives,
to find maxima and minima a nd to use the Lagrange multiplicator
method.
Course contents
Introduction to metric topology. Complete sapces. Connected spaces.
Spaces of limited functions. pointwise and uniform convergence
for sequences of limited functions.
Normed and Banach spaces. Compact spaces.
Total convergence for series in Banach spaces. Spaces with inner product.
Partial derivatives and differentiable functions. The total differential theorem.
Multivariate Taylor expansion. Hessian matrices, local
extrema.Implicit functions: Dini's theorem.Simple, open and regular
curves in R^n and tangent vectors. Differentiable manifolds in
R^n.
Jacobian matrices. Tangent spaces and normal spaces. The
method of Lagrange multipliers for optimality in constrained
problems.
Teaching methods
We will introduce general concept and methods
pertaining to the Differentil Calculus for functions in several
variables.
We also analyze some concrete problems, in order to stimulate the
student to find solutions in an autonomous way.
Assessment methods
The examination consists of an oral examination lasting 45 minutes. Will occur 'the student's Competency both in terms of acquisition of concepts and methods, with application to concrete cases.
Office hours
See the website of Andrea Brini