Politecnico di Torino  
Anno Accademico 2017/18  
02OHTLU, 02OHTPM Calculus 

Corso di Laurea in Architettura (Architecture)  Torino Corso di Laurea in Architettura  Torino 





Presentazione
The main purpose of this course is to provide to all students, coming from different experiences, the knowledge of the main basic mathematical concepts. In particular, the course will provide the main tools useful in subsequent courses, like other mathematical or statistical courses, building physics, statics, town planning or financial evaluation of projects. All the mathematical concepts and tools are explained in a basic and simple way, with the aim to provide knowledge about that more than to provide the ability to solve hard mathematical problems. In fact, given the present day computer technology, the purpose of this course is to let the students be capable of reading, understanding and describing mathematical problems and results, aiming more at the underlying logics than at computation complexity. The last part of the course is devoted to mathematical models of interest in Architecture and related disciplines.

Risultati di apprendimento attesi
The knowledge obtained through this course consists of the essential mathematical tools to understand and to face problems of differential calculus in one real variable, integral calculus, linear algebra, geometry and descriptive statistics. Special attention will be devoted to space visualization and its mathematical formalization. These notions are indeed of commonly used in the different fields of the Architecture programme. These skills consist on the ability to recognize the mathematical instruments (analytic, geometric and statistic) suitable to solve simple mathematical problems or useful in different subjects of planning, structural and physical methodologies, and to understand and formulate simple models to describe such problems.

Prerequisiti / Conoscenze pregresse
Standard high school mathematics is the only prerequisite. 
Programma
Linear algebra and geometry: Matrices, vectors and their operations, applicatins of vector calculus to determine straight lines and planes; systems of linear equations; eigenvalues and eigenvectors; elements of conic sections.
Differential calculus: functions and their graphical representation; elementary functions (rational and irrational functions, exponential, logarithm, trigonometric functions, hyperbolic functions), limits of functions and their calculation in simple cases; continuity of functions and reltated theorems; differentiation, calculation of derivatives and their applications; De L'Hopital rule; fundamental theorems on monotonicity, concavity and convexity; behavious at domain boundary; qualitative graph of functions. Integral calculus: definite integrals and areas; indefinite integral and simple primitives. Elementary statistics: numerical and graphical representations; position and variability indices; correlations between different sets of data. Mode, mean and median; variance. 
Organizzazione dell'insegnamento
The course includes theoretical lectures and classes devoted to solving excercises. Theoretical lectures take 60% of the total time in class.

Testi richiesti o raccomandati: letture, dispense, altro materiale didattico
Suitable textbooks are the following:
 R. A. Adams: Calculus, a complete course, Pearson Canada  Murray R. Spiegel, John J. Schiller, R. AluSrinivasan, Schaum's Outline of Probability and Statistics, McGrawHill The teachers will make further material available through internet. 
Criteri, regole e procedure per l'esame
The exam consists of two parts: a. written test that lasts 2 hours and includes exercises on all topics of the course; b. oral discussion of the written part, to which a score has been attributed. No use of calculator, notes or books is allowed. The teacher may allow the use of her or his set of notes, previously prepared for the sake of the exam.

Orario delle lezioni 
Statistiche superamento esami 
