Facoltà di Ingegneria - Guida degli insegnamenti (Syllabus)

Mathematics I

The aim of the course is that of providing the theoretical, methodological and practical elements of numerical analysis. The objective is that of managing efficiently the modeling problems which arise in the analysis of production and logistic processes and, more generally, of business processes and technology organization problems, which arise in firms operating in both the industrial and the services fields. In particular, the course aims at providing the student with: understanding the difference between the analytical and the numerical approach to mathematical problems; the abality of analysing and justifying the algorithms employed; determine the solutions of the problems under study and estimate the errors induced by the numerical approximation

: The main classical results of Numerical Analysis, accompanied by numerous applications, will be introduced, in order to develop the students ability to model, analyze and solve problems. This path will lead the student to achieving the capability of: quantitatively modelling decisional problems by means of mathematical programming; choosing the numerical method best suited to the problem under scrutiny; using mathematical and scientific software as supporting tools for the solution of numerical problems of engineering science.

The expertise acquired in this course will be needed in order to study the material of later courses. Individual and collective problem-solving sessions, aimed at detecting, formulating and solving engineering management problems, will improve the ability to develop independent thought and learning capabilities. Oral presentations of the topics taught in the course, with the language proper of the basic disciplines of the degree course will help developing communication skills.

LINEAR ALGEBRA - Vectors, matrices, linear systems and transformations, Gauss elimination, diagonalization, eigenvalues and eigenvectors. DIFFERENTIAL EQUATIONS - First order differential equations, n-th order differential equation with constant coefficients, variation of constants method, order reduction method NUMERICAL ALGORITHMS - Lagrange interpolation, spline, numerical integration and differentiation, Euler's method for initial value problems, iterative methods for solving linear systems, least square method, iterative methods for calculating eigenpairs, iterative methods for non-linear systems, numerical methods for boundary values problems. Some of the algorithms will be illustrated also through the implementation of electronic spreadsheet.

The exam consists in a written and an oral test. If the written test is passed, the student can sustain the final oral test. The student must sustain the oral examination within the date of the next written exam.

In the written exam the student must show to know how to practically and independently use the tools described during lectures to solve simple problems. In the oral examination he must show to know the theoretical fundations of such tools, and to be able to implement the numerical algorithms described during lectures using a programming language or spreadsheet.

Written examination consists in 3 problems on linear geometry, linear algebra and differenital equations. Each problems is evaluated up to 4 points. The exam is passed if the student collects a total of 6 points, but he must collect at least one point in each problem. Oral examination is a discussion on an algorithm chosen by the student and implemented on an electronic spreadsheet or computer language. Then, the discussion will be driven by the teacher on the theoretical subjects of the course topics.

Final mark is in thirties, with possible honours. It is given by weightening the resuls of oral and written examinations. Oral examination has a higher weight.

M.Bramanti, C.D. Pagani, S. Salsa Matematica - Calcolo infinitesimale e algebra lineare. Zanichelli. R.L Burdem, J.D. Faires Numerical Analysis. Cengage Learning

- Ingegneria Gestionale (Corso di Laurea Triennale Fuori Sede (DM 270/04))

**Università Politecnica delle Marche**

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