Teachings
AR/0021  MATHEMATICAL ANALYSIS
Academic Year 2017/2018
Free text for the University
 Professor

MARIANNA SABA (Tit.)
 Period

First Semester
 Teaching style

Convenzionale
 Lingua Insegnamento

Informazioni aggiuntive
Course  Curriculum  CFU  Length(h) 

[80/71] ARCHITECTURAL SCIENCE  [71/00  Ord. 2017] PERCORSO COMUNE  5  50 
Objectives
The aim of the course is to provide students with the practical knowledge necessary to reason independently on various topics of basic mathematics.
In this section of the integrated course we develop basic tools in the area of calculus.
A) Knowledge and understanding
The student will be able to represent functions of one variable and to qualitatively describe the graph of a function. The student will know calculus for function of one variable and several variables; he will be able to solve differential equations.
B) Applying knowledge and understanding
The acquisition of mathematical and methodological knowledges will allow the student to critically study and reason on scientific texts on these fields: physical technique, statics, science and structural engineering. The student will be able to solve different scientific problems correctly using learned mathematical tools.
C) Making judgements
The student will be able to choose the more appropriate mathematical tools and methodology to address applicative problems linked to science of architecture.
D) Communication skills
The student will be able to understand mathematical language and to use it to communicate scientifically correct.
E) Learning skills
Based on the knowledge and logicaldeductive skills acquired during the course, the student will be able to learn new methodologies necessary to address problems in different application contexts.
Prerequisites
Preliminary mathematical knowledge required: elementary arithmetic and algebraic operations (necessary).
The first week is devoted to the illustration of the required preliminary mathematical knowledge to address the topics of the course. Therefore, there is no required specific prior knowledge. On the other hand, the course requires that the student possess, at least up to a reasonable extent, the skill of understanding verbal and logical reasoning. More specifically, students with special initial difficulties can refer to the book: Matematica: 2^3 capitoli per tutti" shown below.
Contents
Real analysis:
1) Real numbers and cartesian coordinate system. Functions. Functions of one real variable. Graphs, symmetries, increasing and decreasing functions. Basic trigonometric functions. Inverse function.
2) Limits. Continuity. Fundamental limits. Sequences and series.
3) Derivatives. Physical and geometrical interpretation of derivative. Calculus of derivatives. De l'Hospital theorem.
4) The complete study of a function of a real variable.
5) The fundamental theorems of differential calculus (Rolle, Lagrange). Taylor serie.
6) Integration. Fundamental theorem of calculus. Techniques of integration: by parts and by substitution.
7) Differential equations. Cauchy problem. Linear first order differential equation; linear second order differential equation with constant coefficients; separable differential equation.
8) Functions of several variables. Limits and continuity. Partial derivatives and gradient. Schwarz theorem.
9) Optimization.
10) Integration of functions of 2 or 3 variables.
Teaching Methods
Traditional lessons (50 hours) at the blackboard, possibly with the help of projections of digital slides on a screen. Each lesson begins with a brief summary of the concepts covered in previous lessons and ends with the assignment of homework. The course is also supported by tutorial activity addressed to improve the ability to solve mathematical questions, and specifically conceived for the preparation of the written examination.
Verification of learning
Written test on the entire program. The test consists in solving a series of exercises, each of which is assigned a score.
The maximum total score is 32. The mark 30 cum laude is attributed to Students which obtain a final score greater or equal to 31.
The type of problems is the same of the exercises solved during lessons. More details can be found on the website people.unica.it
Students who regularly attend classes may take the exam divided into two partial tests, the first of which will take place in about half of the course, while the second at the end of the course.
Texts
Testo di riferimento: Matematica per le Scuole di Architettura
Autori: A. Ratto e A. Cazzani
Casa Editrice: Liguori (Napoli, 2010)
Codice ISBN: 9788820752422
Codice eISBN: 9788820753443
Testo per recupero conoscenze argomenti delle scuole superiori: Matematica: 2^3 Capitoli per tutti
Autori: S. Montaldo e A. Ratto
Casa Editrice: Liguori (Napoli, 2011).
Codice ISBN: 9788820755119
Codice eISBN: 9788820755126
More Information
The teacher will make available slides of each lesson and exercises on her web site.
The personal web page of Andrea Ratto provides ample supplementary educational material.