OVERVIEW

Mathematical methods play an important role in both traditional (mechanical, electronic) and more recently established engineering sectors such as bioengineering, the result of the confluence of engineering culture and areas of knowledge such as biology and medicine . The teaching highlights the training and application roles of mathematical methods in the creation of models with good representation and prediction skills and in their simulation through analytical and numerical techniques.

AIMS AND CONTENT

LEARNING OUTCOMES

To provide a complex of knowledge that allows the understanding and use of the main mathematical tools for numerical calculation, the treatment and analysis of experimental data, the interpretation and the formulation of models in a physical-mathematical key.

AIMS AND LEARNING OUTCOMES

Aims Attendance at lectures in the classroom and participation in lectures in the computer room, supported by individual study will allow the student to gain a good knowledge of the mathematical tools necessary for the formulation of models in macro (eg robotics) and micro (eg. neurostructures) scale, to the application of these models and to their numerical simulation.

Learning outcomes At the end of the course the student will be able to

- describe and apply the basic mathematical tools for numerical calculation, processing and analysis of experimental data;

- to choose the appropriate methods for the formulation and treatment of physical-mathematical models;

- discuss the fundamental methods for the treatment of problems of variational calculus and apply these methods;

- recognize the types of partial differential equations and choose the appropriate methods (analytical and / or numerical) for their solution in the field of physical-mathematical modeling;

- apply numerical calculation tools such as MATLAB for the study of models in the areas listed above.

PREREQUISITES

Basic knowledge in the fields of mathematical analysis, geometry, physics.

TEACHING METHODS

80 hours approx. of classroom lectures and 12 hours of computer training. The exercises are carried out in informatics laboratory with the use of the MATLAB program under presence control. They concern the verification and application of the topics presented in class.

Participation in training sessions contributes to the formulation of the exam mark.

SYLLABUS/CONTENT

Normed spaces, orthonormal spaces, operators. Function approximation in a normed space, best uniform approximation. Numerical differentiation and integration. Numerical solution of ordinary differential equations (ODE). Compatibility of linear systems. Least squares solution. Singular value decomposition (SVD) of a matrix with applications. Variational calculus: Euler-Lagrange equations. Variational formulation of physical-mathematical models. Classification of partial differential equations (PDE). Hyperbolic, parabolic, elliptic second-order linear PDEs. Examples of PDE-based models. Separation of variables. Approximate solution of linear and nonlinear PDEs by weighted-residual methods. Applications: traffic models, nonlinear propagation (solitons).

RECOMMENDED READING/BIBLIOGRAPHY

Teaching material provided by the teacher (pdf notes on lectures and tutorials)

Reference text in Italian: Mauro Parodi, "Mathematical methods for engineering", Levrotto & Bella ed., Turin, 2013.

TEACHERS AND EXAM BOARD

Exam Board

MAURO PARODI (President)

ALBERTO OLIVERI

LUCA ONETO

MARCO STORACE

LESSONS

LESSONS START

The lessons begin in September and end in the following May according to the timetable of the lessons prepared by the Polytechnic School.

Class schedule

MATHEMATICAL METHODS FOR ENGINEERS

EXAMS

EXAM DESCRIPTION

Oral examination in official appeals.

Possibility of intermediate oral tests concerning the successive fractions of the program carried out in class. The sum of the scores obtained in these tests and of the one assigned for the frequency of the exercises form a score that is proposed as a final result.

ASSESSMENT METHODS

Each exam, both in the complete form of the official appeals and in the form of intermediate tests, is oral. In each one the ability to critically expose the knowledge acquired on methods of approximation, on the treatment of experimental data, on numerical calculation, on variational methods and on partial differential equations. The ability to apply this knowledge to the formulation of physical-mathematical models in the sectors considered during the lessons will be evaluated. Where possible, the ability to choose the most suitable numerical methods for data processing and model simulation will be evaluated.

For each answer the evaluation parameters will be: the ability to synthesize, the quality of the exposure, the correct use of the specialized lexicon, the capacity for critical reasoning.

Exam schedule

FURTHER INFORMATION

Sending educational material and information regarding the course and checks is done via the Aula Web.