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Lecturer:
Luisa Donatella Marini
Course name: Calcolo numerico (ca)
Course code: 062025
Degree course: Ingegneria per l'Ambiente e il Territorio, Ingegneria Civile, Ingegneria Meccanica
Disciplinary field of science: MAT/08
L'insegnamento costituisce attività di base per: Ingegneria per l'Ambiente e il Territorio, Ingegneria Civile, Ingegneria Meccanica
University credits: CFU 6
Course website: http://www.imati.cnr.it/marini
Specific course objectives
Aim: to give the students the basic ideas of numerical algorithms to tackle various practical problems. The course covers the basics of the subject and provides a foundation for more advanced work
Course programme
All the classical subjects of a Numerical Analysis textbook will be presented, with more enphasis on the practical use and implementation than on the theoretical approximation results:
Nonlinear equations/systems
Approximation of functions and data
Numerical Derivation and Integration
Solution of linear systems of equations
Ordinary differential equations/systems
Nonlinear equations/systems
- Bisection and Newton methods, convergence and order of convegence
- stopping criteria
Approximation of functions and data
- Lagrange interpolation, global and piecewise
- convergence analysis
- least square approach for the data-fitting
Numerical Derivation and Integration
- Approximation of derivatives
- Basic integration formulae
- error analysis and practical use
Solution of linear systems of equations
- Direct methods (Gaussian elimination and LU factorization, Choleski
factorization), implementational aspects and costs
- Iterative methods (Jacobi and Gauss-Seidel), convergence analysis,
implementational aspects, stopping criteria
Ordinary differential equations/systems
- one-step methods (Euler backward and forward, Crank-Nicolson, Heun)
- consistence, 0-stability and A-stability, convergence and orders of convergence.
- computational aspects and application to systems
Course entry requirements
Integral and differential calculus for real functions; complex numbers; vectors and matrices
Course structure and teaching
Lectures (hours/year in lecture theatre): 28
Practical class (hours/year in lecture theatre): 24
Practicals / Workshops (hours/year in lecture theatre): 0
Project work (hours/year in lecture theatre): 0
Suggested reading materials
A. Quarteroni, F. Saleri. Calcolo Scientifico - IV Edizione. Springer-Verlag Italia, Milano 2008..
Testing and exams
Two written tests (midterm and final) or one written final exam. Oral exam (not compulsory) after a sufficient grade in the written part
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