- Docente: Fiorella Sgallari
- Credits: 12
- SSD: MAT/08
- Language: English
- Moduli: Fiorella Sgallari (Modulo 1) Alessandro Lanza (Modulo 3) Fabiana Zama (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 3) Traditional lectures (Modulo 2)
- Campus: Bologna
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Corso:
Second cycle degree programme (LM) in
Civil Engineering (cod. 8211)
Also valid for Second cycle degree programme (LM) in Chemical and Process Engineering (cod. 0929)
Second cycle degree programme (LM) in Electronic Engineering (cod. 0934)
Second cycle degree programme (LM) in Environmental Engineering (cod. 0939)
Learning outcomes
A successful learner from this course will be able to: a) deal with numerical analysis topics such as: accuracy, truncation and round-off errors, condition numbers, convergence, stability, curve-fitting, interpolation, numerical differentiation and integration, numerical linear algebra; b) deal with numerical methods for solving ordinary and partial differential equations, with finite difference and finite element methods for parabolic and elliptic partial differential equations, applications of computer programs to case studies derived from civil engineering practice.
Course contents
Numerical Methods I (Proff. F.Sgallari, A.Lanza)
- Key idea: accuracy, precision, truncation and round-off errors, condition numbers, operation counts, convergence and stability.
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Numerical Linear Algebra: direct and iterative methods for linear systems.
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Solution to single equations and multiple non-linear equations.
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Interpolation and approximation: interpolating polynomials, cubic splines, least-square fitting.
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Numerical differentiation and integration: Newton-Cotes quadrature formulas, Gaussian quadrature.
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Classification of PDEs: elliptic, parabolic and hyperbolic equations.
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Finite difference methods. Stability, consistency, and convergence theory.
Numerical Methods II (Prof. F. Zama)
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Finite Elements Methods
(formulation of the finite element method in 1-D and 2-D continuum, basic 1-D and 2-D finite elements,
modeling and programming aspects of the finite element method).
Readings/Bibliography
Some useful course materials for this course can be found at the web page http://people.ciram.unibo.it/~sgallariat the link Teaching.
You can find the material for this course in many books on Numerical Analysis such as
- A. Quarteroni, Numerical Models for Differential Problems. Springer, 2009.
- A. Quarteroni, R. Sacco and F. Saleri
Numerical Mathematics Second Ed., Springer, 2007.
Teaching methods
The course involves practical work based on computational tools such as Matlab and Freefem.
Assessment methods
Assessment is based on assignmentsof project works and oral exams.
Teaching tools
Lectures, exercises, laboratory activities in Matlab.
Links to further information
http://people.ciram.unibo.it/~sgallari/
Office hours
See the website of Fiorella Sgallari
See the website of Alessandro Lanza
See the website of Fabiana Zama