OVERVIEW

This course equips the students with the mathematical principles and the tools needed to study structural disciplines and design, and to understand architectural morphology, and physical, technological, economical, social and urban models. 

AIMS AND CONTENT

LEARNING OUTCOMES

The course aims is to provide  the students with the mathematical tools which are  needed to tackle any problem with a scientific approach.

AIMS AND LEARNING OUTCOMES

The course aims to provide the basic tools that allow the students to tackle any topic with a scientific approach and to stimulate the three-dimensional and aesthetic sense needed to an architect. More specifically, the aim of the course is to provide the mathematical principles and tools necessary to tackle the study and understanding of structural and design disciplines, of physical, technological, economic, social and urban planning models.

At the end of the course, students will be able to: solve linear systems, operate on vectors, recognize planes and lines in 3D, master the fundamental concepts of differential and integral calculus for one variable functions, qualitatively study the graphs of functions, solve simple differential equations, and work with complex numbers. Furthermore, we expect the ability to state and demonstrate some basic theorems of mathematical analysis.

At the end of the course we expect a critical understanding of the subject, the ability to distinguish different situations on specific examples and to make reasoned choices, justifying the chosen procedures. Some ability in the computations  and a well-argued exposition of the theory is also expected.

PREREQUISITES

A good knowledge of the mathematical topics covered in secondary school is needed. In particular, we assume well understanding of  polynomials, equations, inequalities, trigonometry, Euclidean geometry (areas and volumes of elementary geometric figures), elements of analytical geometry.

TEACHING METHODS

Lectures and exercises on the blackboard. A tutor is available for further explanations and exercises; exercises are provided for students' autonomous work.

Students who have a valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework and exams, should speak both with the teacher and with the Department of Architecture and Design's disability referent (https://architettura.unige.it/commissioni_e_referenti_dipartimento).

SYLLABUS/CONTENT

The course contains topics of Mathematical Analysis and Geometry.

GEOMETRY

Linear systems: solution of linear systems using the Gauss elimination method, existence theorem and multiplicity of solutions of linear systems

Matrices: Operations with matrices, rank, determinant, inverse matrix.

Vectors: Geometric vectors. The linear spaces R^2 and R^3 and their properties. Bases and dimension of vector subspaces of R^2 and R^3.

Elements of geometry in the plane and in space. Lines, planes, conics and quadrics.

Complex numbers. Algebraic representation, modulus and conjugate. Trigonometric representation and polar coordinates. Complex exponential. Solving equations.

ANALYSIS

Real functions of one real variable. Basic notions and elementary functions.

Limits and continuity. Definition, calculation of limits, fundamental theorems.

Derivatives and their applications. Definition and geometric meaning. Derivation calculus. Graph of the derivative. Fermat's theorem. Convexity and concavity. Qualitative study of the graph.

Integrals. Area and estimate by finite sums: definite integral. Integratable functions and integration of continuous functions. Fundamental theorem of integral calculus. Indefinite integral. Integration and integral techniques of elementary functions.

Ordinary differential equations: General integral and Cauchy problem. Equations with separable variables. Equations with constant coefficients of the second order homogeneous and not homogeneous.

RECOMMENDED READING/BIBLIOGRAPHY

M. Abate, C. de Fabritiis, Geometria analitica con elementi di algebra lineare. McGraw-Hill Libri Italia, 2006

J. Hass, M.D. Weir, G.B. Thomas, Analisi Matematica 1, Pearson, 2018  (English edition available)

C. Marcelli, Analisi Matematica 1. Esercizi con richiami di teoria., Pearson, 2019

G. Crasta, A. Malusa, Elementi di Analisi Matematica e Geometria con prerequisiti ed esercizi svolti, La Dotta,  2015

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

In agreement with the Academic calendar.

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

• The student must register at least one week in advance at https://servizionline.unige.it/studenti/esami/prenotazione. For organizational reasons, registrations will not be accepted after registration closes.
• The exam consists of a written test and an oral test.
• The written test consists of two intermediate tests or a final test. The written tests contain a part of exercises and a part of theory.
• The oral exam can be accessed only after passing the written exam. It is done at the request of the student or of the teachers and concerns the entire course program. The grade obtained at the end of the oral examination may be higher or lower than that obtained in the written test, and may possibly lead to failure to pass the exam.

ASSESSMENT METHODS

Evaluation of the written test and of the possible oral exam. The educattional goal is achieved to the extent that the student is capable of solving exercises of similar difficulty to those solved during classes and has a critical knowledge of the fundamental contents of the course.

FURTHER INFORMATION

Students with DSA certification ("specific learning disabilities"), disability or other special educational needs are advised to contact the teacher at the beginning of the course to agree on teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements and provide appropriate compensatory tools.