Unit MATHEMATICAL MODELS AND METHODS
- Course
- Mathematics
- Study-unit Code
- 55A00095
- Curriculum
- Didattico-generale
- Teacher
- Anna Salvadori
- Teachers
-
- Anna Salvadori
- Primo Brandi
- Hours
- 21 ore - Anna Salvadori
- 21 ore - Primo Brandi
- CFU
- 6
- Course Regulation
- Coorte 2021
- Offered
- 2021/22
- Learning activities
- Affine/integrativa
- Area
- Attività formative affini o integrative
- Academic discipline
- MAT/05
- Type of study-unit
- Opzionale (Optional)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- Mid-level course on iterative process and applications.
- 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 teachers - 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. - Prerequisites
- Analysis I, Analysis II, Geometry I
- Teaching methods
- Lessons and written test
- Learning verification modality
- Oral interview
- 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