1015723 - METODI MATEMATICI PER L'INGEGNERIA
Expected Learning Outcomes
The course aims to provide the basic knowledge concerning Fourier series and integral transforms, with a brief introduction about distributions, to introduce the main equations of mathematical physics (wave equation, heat equations and Poisson equation) and the most relevant methods of numerical analysis.
The teaching method of the course consists of lectures, programming elements in Matlab or similar language and computer exercises.
In particular, the course aims to allow the student to acquire the following skills:
Knowledge and understanding: knowledge of results and fundamental methods in mathematical physics and numerical analysis. Skill of understanding problems and to extract the major features of the tackled problems. Skill of reading, undertanding and analyzing a subject in the related literature and to present it in a clear and accurate way.
Applying knowledge and understanding: skill of elaborainge new example or solving novel theoretical exsercise, looking for the most appopriate methods and applying them in an appropriate way.
Making judgements: to be able of devise proposals suited to correctly interprete complex problems in the framework of mathematical physics and numerics. To be able to formulate autonomously adequate judgements on the applicablity of mathematical models to theoretical or real situations.
Communication skills: skills of presenting arguments, problems, ideas and solutions in mathematical terms with clarity and accuracy and with procedures suited for the audience, both in an oral and a written form. Skill of clearly motivating the choice of the strategy, method and contents, along with the employed computational tools.
Learning skills: reading and analyzing a subject in the engineering literature involving applied mathematics. To tackle in an autonomuous way the systematic study of arguments not previously treated. To acquire a degree of autonomy such that the student can be able to start with an autonomuos reserach activity.
Course Structure
Mainly frontal lectures. Moreover, the theoretical acquired competencies will be applied in a laboratory where study cases will be tackled in a MATLAB enviroment.
Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, in line with the programme planned and outlined in the syllabus.
Learning assessment may also be carried out on line, should the conditions require it.
Required Prerequisites
Detailed Course Content
Fourier series and integral transforms. An introduction to distributions and Dirac's delta. out relevant equations of mathematical physics: wave equation, heat equation, Poisson's equation. Introduction to programming in Matlab or similar language. Numbering systems. Linear systems. Zeros of nonlinear equations. Methods of interpolation and approximation. Quadrature formulas. Numerical differentiation. Numerical methods for ordinary differential equations. Boundary problems for ODEs and finite elements. Introduction to the main numerical methods for partial differential equations.
Textbook Information
Main textbook: V. Romano, Metodi matematici per i corsi di ingegneria, CittàStudi edizioni
Further readings
A. Quarteroni, Modellistica numerica per problemi differenziali, Springer
A. Quarteroni, R, Sacco, F. Saleri, Matematica Numerica, Springer
V. Comincioli, Analisi Numerica: metodi, modelli, applicazioni, McGraw-Hill
Course Planning
| Subjects | Text References | |
|---|---|---|
| 1 | Elements of programming in MATLAB. | Notes of the lecturer |
| 2 | Fourier series and integral transforms. Introduction to distributions and Dirac's delta. Main equations of mathematical physics: wave equation, heat equation and Poisson's equation. Element of MATLAB programming. Systems of numeration. Nu erica methods for Linear system and non linear equations. Intyerpolation methods and approximation of data and functions. Quadrature formulas. Numerical derivatives. numerical schemes for ODEs. Introduction to the main numerical methods for PDEs. | Text 1 |
Learning Assessment
Learning Assessment Procedures
The exam can be performed online if necessary as a consequence of the restriction due to the pandemic wave.
Examples of frequently asked questions and / or exercises
Fourier series
Fourier transforms
Dirac's delta
Classification of the partial differential equations of the second order
Dirichlet and Neumann boundary conditions
Heat equation
Wave equation
Poisson's equation
Newton's method for nonlinear equations
Method of Newton-Raphson for nonlinear systems
Lagrange fundamental polynomial
Least square approximation
Accuracy of an interpolation formula
Order of the Simpson quadrature formula
Finite difference approach for differential equations with boundary data
Most common Runge-Kutta schemes
Finite difference scheme for the Poisson equation
Finite difference scheme for the heat equation
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