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 problems 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 prove some basic theorems. 

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 elements of Mathematical Analysis and Geometry.

Algebra and Geometry 

Sets and functions: union, intersection, complement, functions, domain, codomain, image, composition, invertible functions, right and left inverses. Injective, surjective and bijective functions.

Matrices: Operations with matrices and their properties, Gaussian form, reduced Gaussian form, rank, determinant, inverse matrix, completion of low-rank matrices.

Linear systems: reduction to row echelon form of linear systems using Gaussian elimination method, existence and multiplicity theorem for solutions of linear systems. Homogeneous systems, positive solutions of linear systems.

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

Vectors: Geometric vectors. The vector spaces R² and R³  and R^n and their properties. Bases and dimensions of vector spaces. Subspaces. 

Elements of geometry in the plane and in space: Lines, planes, conics. Cartesian form, parametric form, point-to-line and point-to-plane distance. Pencils of lines and pencils of planes. Parallel, skew and intersecting lines in 3-dimensional space.

ANALYSIS Real functions of one real variable: Basic concepts and elementary functions.

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

Derivatives and their applications: Definition and geometric meaning. Differentiation rules. Graph of the derivative. Fermat's theorem. Convexity and concavity. Function analysis.

Integral calculus: Area and estimation using finite sums: definite integral. Integrable functions and integrability of continuous functions. Fundamental theorem of integral calculus. Indefinite integral. Integration techniques and integrals of elementary functions. Examples of double integrals.

Ordinary differential equations: General integral and Cauchy problem. Separable variable equations. Second-order homogeneous and non-homogeneous equations with constant coefficients.

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

• Students  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 the booking deadline.

  The exam consists of a written test or an oral test. Precise details will be given by the instructurs.

ASSESSMENT METHODS

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.