AR/0021 - MATHEMATICAL ANALYSIS
Academic Year 2016/2017
Free text for the University
MARIANNA SABA (Tit.)
- Teaching style
- Lingua Insegnamento
|[80/71] ARCHITECTURAL SCIENCE||[71/00 - Ord. 2013] PERCORSO COMUNE||5||62.5|
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 logical-deductive skills acquired during the course, the student will be able to learn new methodologies necessary to address problems in different application contexts.
Basic knowledge of arithmetic and algebra.
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.
10) Integration of functions of 2 or 3 variables.
Traditional lessons (62.5 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 (25 hours) 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 type of problems is the same of the exercises solved during lessons.
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.
Testo di riferimento: Matematica per le Scuole di Architettura
Autori: A. Ratto e A. Cazzani
Casa Editrice: Liguori (Napoli, 2010)
Codice ISBN: 978-88-207-5242-2
Codice eISBN: 978-88-207-5344-3
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: 978-88-207-5511-9
Codice eISBN: 978-88-207-5512-6
The teacher will make available slides of each lesson on his web site.
The personal web page of Andrea Ratto provides ample supplementary educational material.