


Politecnico di Torino  
Academic Year 2007/08  
16ACFEW, 16ACFFG, 16ACFJC Mathematical analysis I 

1st degree and Bachelorlevel of the Bologna process in Civil Engineering In Water Management  Mondovi' 1st degree and Bachelorlevel of the Bologna process in Mechanical Engineering  Mondovi' 1st degree and Bachelorlevel of the Bologna process in Electronic Engineering  Mondovi' 





Objectives of the course
The aim of this course is to train students at the university system, and to teach them the basis of differential and integral calculus for variable functions, with applications on first order ordinary differential equations and on second order linear equations. Complex numbers are studied as well and they are applied to represent the solutions of second order ordinary differential equations.
To represent ordinary differential equations it is necessary to know the concept of a partial derivative and basic concepts on continuity of functions of many variables and on partial derivatives. Many applications of differential and integral calculus are studied. 
Expected skills
Skills in understanding logical reasonings; understanding of differential and integral calculus of the function of one variable. To be good in figures. Skills in reading a technical text.

Syllabus
References to: numerical sets, equations and inequalities, trigonometry. Functions and their properties.
Differential calculus: limits, continuity, infinity and infinitesimal; differential calculus for functions of one variable and their applications. Taylor's formula. Integral calculus: integral calculus for functions of one variable and their applications; improper integrals. Functions of many variables: continuity, partial derivatives and gradient. Curve integral. Differential equations: complex numbers. 1storder differential equations; 2ndorder differential equations, linears and constant coefficients. 
