Study-unit MATHEMATICAL MODELS AND METHODS
| Course name | Mathematics |
|---|---|
| Study-unit Code | 55A00095 |
| Curriculum | Didattico-generale |
| Lecturer | Primo Brandi |
| Lecturers |
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| Hours |
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| CFU | 6 |
| Course Regulation | Coorte 2023 |
| Supplied | 2023/24 |
| Supplied other course regulation | |
| Learning activities | Affine/integrativa |
| Area | Attività formative affini o integrative |
| Sector | MAT/05 |
| Type of study-unit | Opzionale (Optional) |
| Type of learning activities | Attività formativa monodisciplinare |
| Language of instruction | Italian |
| Contents | Medium level course on mathematical modeling, with theoretical aspects and applications in various sectors. |
| Reference texts | P. Brandi – A. Salvadori, Percorsi di Matematica, vol. II Ed. Aguaplano 2018 Michael F. Barnsley, Fractals Everywhere: New Edition (Dover Books on Mathematics), June 2012 Lecture notes by the teacher |
| Educational objectives | The course develops the basic elements of some mathematical models and discusses the related methodologies. At the end of the course the student has acquired skills to understand the numerous applications in the various sectors of science and modern technology. On the basis of the interests expressed by the students, the didactic potential of modeling with elementary tools will also be emphasized |
| Prerequisites | Analysis I, Analysis II, Geometry I |
| Teaching methods | Lessons and written test |
| Learning verification modality | oral exam lasting about 45 minutes. The interview, in addition to assessing the knowledge acquired, intends to evaluate the student's skills on mathematical modeling of reality. Students will be encouraged to present their own insights into the topics of the course For information on support services for students with disabilities and / or SLD visit the page http://www.unipg.it/disabilita-e-dsa |
| Extended program | Geodetic in spice and in time.From Archimede 's burning mirrors to optical fibres. Iterated processes with constant increase and constant ratio. Invertible elementary transformations and operators. From the curve to its linear envelope and vice versa, from the envelope to the generating curve. Field of orientors. Differential operator and its inverse. Fractal space. Affine transformations in Euclidean space. Fractal geometry. Banach fixed-point theorem . Theorem of collage . IFS fractals . Genetic code . Fractal dimension. Julia and Mandelbrot fractals. Fractals anecaos. Fractals and shapes of nature . Virtual landscapes . Applications in various fields of science and technology. Educational value of fractal geometry in High Schools. Applications we be developed supported by Computer Algebra System, GeoGebra and spreadsheet |