Clinical Engineering

ANGELA PISTOIA
GIADA VIOLA

Aim of this module is the achievement, by the students, of the basic means of Mathematical Analysis related to the study of functions of one real variable and their use for the solution of problems in Applied Mathematics, and in particular of Physical and Engineering problems. Special emphasis is devoted to qualitative study and approximate solution of these problems, by virtue of asymptotical techniques, Taylor polynomials etc.
Successful students will be able to study the behavior of numerical sequences and series; to sketch the complete graph of a function of one variable; to develop the Taylor (or MacLaurin) polynomials of functions of one variable; to study the asymptotical behavior of a function when the independent variable approaches infinity or singularities or zeros; to solve optimization problems in one variable, on bounded and unbounded intervals; to solve definite, indefinite and improper integrals; to solve some kinds of ordinary differential equations, characterizing several Physics and Engineering problems.

Knowledge and understanding
The aim of the course is to provide students with the basic tools of differential and integral calculus for functions of a real variable and their applications to the resolution of problems based on mathematical models.
At the end of the course, students will have to know the theoretical contents, the methodologies of mathematical analysis and understand the problems addressed.

Autonomy of judgement
At the end of the course, students will be able to consciously apply the concepts learned to the resolution of various types of problems, including applications, and identify the most appropriate approach to solving the proposed problems. They must be able to argue the choices made.

Basic mathematics knowledge

Aim of this module is the achievement, by the students, of the basic means of Mathematical Analysis related to the study of functions of one real variable and their use for the solution of problems in Applied Mathematics, and in particular of Physical and Engineering problems. Special emphasis is devoted to qualitative study and approximate solution of these problems, by virtue of asymptotical techniques, Taylor polynomials etc.
Successful students will be able to study the behavior of numerical sequences and series; to sketch the complete graph of a function of one variable; to develop the Taylor (or MacLaurin) polynomials of functions of one variable; to study the asymptotical behavior of a function when the independent variable approaches infinity or singularities or zeros; to solve optimization problems in one variable, on bounded and unbounded intervals; to solve definite, indefinite and improper integrals; to solve some kinds of ordinary differential equations, characterizing several Physics and Engineering problems.

Bramanti-Pagani-Salsa: Analisi Matematica I. Zanichelli ed.
Amar-Bersani: Esercizi di Analisi Matematica per i nuovi corsi di laurea. Progetto Leonardo. Esculapio.

Lectures according to the timetable published by the faculty.

suggested but not mandatory

exam tests on the web site
https://sites.google.com/uniroma1.it/angelapistoia/home-page

Study the graph of functions to find maxima and minima or to find the number of solutions to nonlinear equations. Studying functions locally via Taylor expansion. Study the convergence of series and integrals. Find the solution to Cauchy problems for differential equations with separable variables and for linear differential equations of the first and second order.