


Politecnico di Torino  
Academic Year 2012/13  
01NSDPW Calculus 

1st degree and Bachelorlevel of the Bologna process in Territorial, Urban, Environmental And Landscape Planning  Torino 





Subject fundamentals
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 the statistical course, or the energetic efficiency , town planning and financial evaluation of projects courses. 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, the purpose is to let the students able to understand and describe problems and solutions in future activities. The course is held in the first semester of the firs year.

Expected learning outcomes
 Knowledge of the essential mathematical tools to understand and to face problems of differential calculus and linear.
 Ability to recognize the mathematical instruments to solve simple mathematical problems or that are useful in different subjects such as town planning, urban sociology, structural and physical methodologies, and to understand and formulate simple models to describe such problems. 
Prerequisites / Assumed knowledge
Students are required to have a basic familiarity with mathematical concepts and tools, which can be acquired in high school programmes.

Contents
Linear algebra and geometry: vectors and matrices, planes and lines, algebraic systems.
Differential calculus: functions in one variable; base functions (rational and irrational, exponentials and logarithms, circular and hyperbolic functions); limits and their computation; continuous function and relative theorems; derivatives and their applications; De L'Hôpital rules; determination of extrema and convexity. Integral calculus: definite and indefinite integral and their computational rules. Functions in two variables and partial derivatives. 
Delivery modes
Every week one lecture is enterily devoted to exercises.

Texts, readings, handouts and other learning resources
 R. Monaco e A. Repaci, Algebra Lineare, Celid, Torino
 P. Marcellini e C. Sbordone, Calcolo, Liguori Editore, Napoli 
Assessment and grading criteria
The exam consists in a written work of six exercises which cover the whole program of the course; time allowed is two hour. Each student in one of further days is then called for a oral colloquium where he can control the correction of his work and answer eventually to questions. At the end the teacher communicates the final note. During the written work the use of a formulary is allowed.

