72764 - Numerical Methods

Course Unit Page

Academic Year 2019/2020

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

First Part

  • Key idea: accuracy, precision, truncation and round-off errors, condition numbers, operation counts, convergence and stability.
  • Numerical Linear Algebra: direct and iterative methods for linear systems.

  • Solution to single equations and multiple non-linear equations.
  • Interpolation and approximation: interpolating polynomials, cubic splines, least-square fitting.

  • Numerical differentiation.

  • Numerical methods for eigenvalues and eigenvectors computation.

    Exercises with Matlab on the previous topics.

Second Part

- Numerical Integration (quadrature):

- Newton-Cotes quadrature formulas

- Gaussian quadrature formulas

- Numerical solution of Partial Differential Equations (PDEs) by the Finite Difference Method:

- Elliptic PDEs: Poisson Equation

Readings/Bibliography

Some useful course materials for this course can be found at the web page

piattaforma iol    https://iol.unibo.it/

 

You can find the material for this course in many books on Numerical Analysis such as

  1. A. Quarteroni, F. Saleri, P. Gervasio, Scientific Computing with Matlab and Octave, Springer.
  2. A. Quarteroni, R. Sacco and F. Saleri
    Numerical Mathematics Springer.

 

For the second Part

- A. Quarteroni, Numerical Models for Differential Problems (3rd Edition), Springer International Publishing, 2017.

Teaching methods

The course involves practical work based on computational tools such as Matlab.

Assessment methods

Assessment is based on assignments of project works and oral discussions.

Teaching tools

Lectures, exercises, laboratory activities in Matlab.

Office hours

See the website of Fiorella Sgallari

See the website of Alessandro Lanza