Scientific Computing
A.Y. 2021/2022
Learning objectives
The course aims to offer an enlarged vision on the various aspects - both from the theoretical and implementation viewpoints - that characterize the modern use of Scientific Computing, along with its application to problems arising in physics, biology and engineering.
Expected learning outcomes
Upon completing the course, the students will be able to apply adequate discretization techniques to handle partial differential equation problems of elliptic, parabolic and hyperbolic type. They will also be able to quantify the accuracy of the chosen method and to produce an adequate implementation in Matlab.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Distance learning (async and sync modes) only when indicated by the Dean
Course syllabus
Introduction to partial differential equation problems and their importance in the applications. Non-dimensionalization and scaling procedures. Discretization of ordinary derivative equations: multistep and Runge Kutta methods. Analysis and Matlab implementation. Partial derivative equations: theoretical properties and finite difference discretization in 1D and nD for elliptic and parabolic equations. Convection-diffusion-reaction problems with transport / dominant reaction. Introduction to inverse problems. Introduction to machine learning and the use of neural networks on selected examples of image recognition. Each topic is treated theoretically and the computer implementation in Matlab is addressed.
Prerequisites for admission
Fundamentals of Numerical Analysis, Matlab Programming, Calculus
Teaching methods
lectures and lab sessions
Teaching Resources
notes of the course, study material provided during the course
Assessment methods and Criteria
The exam is composed of 4 projects to be delivered during the term. The projects aim to verify the competences and include theoretical and coding questions
MAT/08 - NUMERICAL ANALYSIS - University credits: 6
Laboratories: 24 hours
Lessons: 36 hours
Lessons: 36 hours
Professor:
Causin Paola
Professor(s)