# NUMERICAL METHODS FOR DESIGN

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- Versione italiana
- Academic year
- 2020/2021
- Teacher
- LORENZO PARESCHI
- Credits
- 6
- Didactic period
- Primo Semestre
- SSD
- MAT/08

#### Training objectives

- The course aims to provide the basis for the knowledge of the main numerical techniques in computer graphics. To this end, the first part of the course will deal with topics of basic mathematics related to differential calculus, linear algebra and numerical methods, while in the second part will deepen some algorithms aimed at the representation of curves, surfaces, and images.
#### Prerequisites

- None
#### Course programme

- Algorithms and computers.

Computational software.

Floating point numbers.

Elements of linear algebra.

Images and matrices.

Gaussian elimination and applications.

Geometric transformations in 2D and 3D.

Polynomial functions. Splines and interpolation.

Computer graphics. Bezier curves and surfaces.

Approximation of data and functions. Least squares.

Derivatives of functions. Hermite interpolation. #### Didactic methods

- Theoretical lectures and tutorials through the use of video projector and blackboard.
#### Learning assessment procedures

- During the course two written tests or one final written examination. The written test is aimed at verifying the student's ability to solve simple practical problems similar to those seen during exercises in the classroom . The grade of the written test must be integrated with that of the oral exam. The oral examination is based on the verification of theoretical concepts seen during the course and has less impact on the final grade than the written test . There are two types of oral test .

-Type A oral exam (grade larger or equal to 17.5). Two written answers out of six questions proposed. If positive it will confirm the grade obtained in the written part with a maximum increment of 10%. If negative the exam is not sufficient and also the written part must be repeated.

-Type B oral exam (grade larger or equal to 16.5). A single oral exam on the blackboard with two or three questions. If positive it will confirm the grade obtained in the written part with a maximum increment of 30%. If negative the exam is not sufficient and also the written part must be repeated. #### Reference texts

- -Teacher's handouts

-Naldi, Pareschi, Russo, Introduzione al calcolo scientifico, Mc-Graw Hill, 2003

For further information and additions we also recommend the use of the following texts:

G.Naldi, L. Pareschi: Matlab Concetti e Progetti, 3a edizioni, Maggioli Editore, (2020)

G. FARIN: Curves and Surfaces for Computer Aided Geometric Design: a practical guide, Fifth edition, Morgan Kaufmann Publishers (2002).