# NUMERICAL METHODS FOR DESIGN

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- Versione italiana
- Academic year
- 2022/2023
- 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 intermediate written tests or a single final written exam in the exam sessions.The written test is intended to test the student's ability to solve simple practical problems similar to those seen during the classroom exercises. The grade on the written test is to be integrated with the grade on the theory test. The theory test is based on the verification of theoretical concepts seen during the course and has less relevance than the written test on the exercises. There are two types of theory test that can be accessed with an average greater than or equal to 17.5.

-Theory type A: two written answers on six proposed questions, if positive it confirms the grade obtained as an average increasing it up to a maximum of 10%, if negative the exam is considered insufficient and you must repeat the whole exam.

-Theory type B: oral test on the blackboard, if positive, it can increase the average grade up to a maximum of 30%, if negative, the exam is considered insufficient and it is necessary to repeat the whole exam. #### 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).