## Learning objectives

Knowledge and understanding:

The aim of the course is to provide basic knowledge of curves, of curvature and of functions of two real variables, with particular attention to the study of surfaces that the student will learn to recognise mathematically and to draw, linking them to roof coverings. During the formative activity the student can consolidate some knowledge of Mathematical Analysis, of Geometry and Drawing he had acquired during the first year of his degree course.

At the end of the course the student is expected to be able:

Knowledge and understanding:

- to know the basics of trigonometry

- to recognize a curve in plane and in space and its features

- to know the theory of tangent and normal vectors and unit vectors

- to know the theory of tangent and normal lines

- to have understood the concept of curvature and the theory to compute it

- to know basic notions of functions of two real variables (law, domain, graph)

- to know general equations and features of all surfaces showed in the course

- to have understood how to shape a surface as a roof covering

Applying knowledge and understanding:

- to calculate sine and cosine of a known angle

- to analyse and draw with great accuracy a curve in plane and in space

- to determine and draw tangent and normal vectors and unit vectors

- to determine tangent and normal lines equation

- to compute the curvature and the radius of curvature of a curve; to determine and draw the circle of curvature

- to determine the domain and the graph of a function of two real variables

- to recognize the surface given by the graph and its features and to draw it with great accuracy

- to determine sections of a given surface

- to draw with great accuracy a building given the base and the covering, computing the necessary z-coordinates and proportions.

Making judgments:

- to have increased the ability to reckon critically which surface has been used in the covering of an already existing building or in the realization of a design object he wants to examine

- to invent solutions, adapting geometries learnt during the course to projects he is attending to

- to have developed the precision in organizing his work

- to be able to check the credibility of the results.

Communication skills:

- to have improved the ability to show clearly analysis and concepts.

Learning skills:

- to be able to use autonomously the geometric forms applicable to design and architectural planning

- to face, in the future, an autonomous analysis of possible applications in a study or in a project.