# ANALYSIS OF CURVES AND SURFACES FOR ARCHITECTURE cod. 1007714

2° year of course - First semester
Professor
- Alessandra COSCIA
Analisi matematica (MAT/05)
Field
Attività formative affini o integrative
Type of training activity
Related/supplementary
40 hours
of face-to-face activities
4 credits
hub: PARMA
course unit
in ITALIAN

## 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.

## Prerequisites

The notions of Mathematical Analysis, Geometry and Drawing of the first year courses are very useful.

## Course unit content

CURVES IN PLANE
CURVATURE
CURVES IN SPACE
FUNCTIONS OF TWO REAL VARIABLES
SURFACES IN SPACE
CURVATURE OF A SURFACE
EXAMPLES OF MATHEMATICAL MODELS FOR BUILDING COVERINGS

## Full programme

TRIGONOMETRY
CURVES IN PLANE
CURVATURE
CURVES IN SPACE
FUNCTIONS OF SEVERAL REAL VARIABLES
SURFACES IN SPACE
CURVATURE OF A SURFACE
EXAMPLES OF MATHEMATICAL MODELS FOR BUILDING COVERINGS

## Bibliography

Teaching stuff (on the platform ELLY https://elly2022.dia.unipr.it):
Lecture notes.
Exercises with solution.
Examinations with solution (from 19-20 to 21-22).
Video and notes of lectures 20-21.

## Teaching methods

The course (4CFU) is organised into a series of frontal lessons and practices (four hours a week, up to the scheduled 40 hours).
The course is based on the concepts (given in an intuitive and applicative way) and on the applications and calculus.
Some practices hours are devoted to guided exercises during which the students, autonomously, solve the proposed exercises with the supervision of the teacher.
The teacher will be available one afternoon per week to discuss lectured topics.
At the beginning of the course all the material is uploaded on the Elly platform: lecture notes, examinations (from 19-20 to 21-22) with solution, exercises with solution on the whole programme.
In order to download the teaching stuff, the on-line registration is needed.
Video-lectures of the year 20-21 are also available online on the Elly platform.
The uploaded lectures are an integral part of the teaching material.
Non-attending students are advised to check the available teaching material and the information given by the teacher via the Elly platform.

## Assessment methods and criteria

Method of testing learning:
The final evaluation of the learning consists of a written and oral test; books and notes are not allowed, while a calculator machine is authorized together with curvature’s formulas.
The written test is made of five exercises up to 28 points; if the student passes the written test he/she is admitted to the oral test (6 points). The final mark is calculated up to 34 points. The exam is passed with a final mark of minimum 18/30. The student must prove he/she has understood, and is able to apply, the basic concepts of every topic in the programme.
Instead of the final test, the student will be allowed to take two written tests in itinere both made of exercises and calculated up to 34 points; if the student passes both test, the final mark is the mean value of the two test.
All tests will take place in presence in the lecture-hall.
The results of the exam will be published on the Elly platform within two weeks from the written test. The students can examine their written tests during the time specified by the teacher or by appointment.

## Other information

The course (4CFU) is mandatory for all students in Architecture.
Attending to the course is strongly recommended.