Politecnico di Torino
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Politecnico di Torino
Academic Year 2007/08
16ACFFC, 16ACFFA, 16ACFFI
Mathematical analysis I
1st degree and Bachelor-level of the Bologna process in Electrical Engineering - Alessandria
1st degree and Bachelor-level of the Bologna process in Plastic Engineering - Alessandria
1st degree and Bachelor-level of the Bologna process in Mechanical Engineering - Alessandria
Teacher Status SSD Les Ex Lab Tut Years teaching
Casarino Valentina       62 50 0 0 9
SSD CFU Activities Area context
MAT/05 10 A - Di base Matematica, informatica e statistica
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. 1st-order differential equations; 2nd-order differential equations, linears and constant coefficients.

Programma provvisorio per l'A.A.2005/06
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