Bildungsziele
The course belongs to the “area di apprendimento di base”,
and more specifically to the scientific area of mathematics,
informatics, statistics. It is a core course.
The course provides a general overview of scientific tools and
contents.
The educational objectives of the course are given by the
knowledge of the concepts and techniques of multivariable
differential calculus, vector functions and vector fields. Such a
knowledge is necessary for an understanding of the content of
several among the courses in the bachelor program. The
emphasis is on the ability to formulate in mathematical terms
and then solve problems involving several variables, and in
particular geometric-type problems in a three-dimensional
space, to find relative and absolute maxima and minima of
functions of two or more variables, to find constrained maxima
and minima, to calculate simple double and triple integrals, with
special attention to those of interest in mechanics and physics,
to know how to employ spherical and cylindrical coordinates, to
calculate simple curvilinear or surface integrals, both of a scalar
and a vector field. Also, an introduction to the theory of ordinary
differential equations is part of the course. For example,
students learn how to solve certain linear equations. Finally, if
there is time, the use of a software as Maple or Mathematica in
connection with the topics in the course is illustrated to the
students.
Bildungsziele und erwartete Lernergebnisse (zus. Informationen)
Knowledge and understanding:
1. Knowledge and understanding of concepts, symbolism,
and techniques of multivariable differential calculus and of
vector differential calculus.
2. Knowledge and understanding of basic mathematical
modelling and basic elements of differential equations.
Applying knowledge and understanding:
3. Applying knowledge and understanding in solving exercises
and problems (arising, in particular in engineering) that
require formalization, tools and methods learned in the
course, for example, finding absolute, relative, or
constrained maxima and minima of functions of several
variables, calculating simple double and triple integrals,
curvilinear and surface integrals of scalar fields, finding the
solutions of specific linear ordinary differential equations.
Making judgments:
4. Ability to choose a right approach and convenient tools
towards tackling problems and questions which can be
mathematically formulated.
Communication skills:
5. Ability to report on the calculations in a clear and effective
way.
Learning skills:
6. Ability to autonomously extend and adapt the acquisition
and assimilation of the symbolism, methods and tools of
this course for the understanding of the content of a
consistent part of the courses in this academic curriculum.