- Docente: Hans Joachim Rudiger Achilles
- Credits: 5
- SSD: MAT/08
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: First cycle degree programme (L) in Industrial Chemistry (cod. 0882)
Learning outcomes
On successful completion of the course, students will be able to use numerical methods for the computer solution of certain classes of mathematical problems, know how computers work, and will possess practical basic computer skills. In particular, they will have knowledge on the computer representation of numbers and the propagation of errors, on numerical methods for the approximation of experimental data, on polynomial interpolation, on numerical integration and on the solution of linear systems.
Course contents
Review on complex numbers, vectors, matrices.
Computer arithmetic: floating-point numbers and arithmetic
operations with them, propagation of errors.
Nonlinear equations: conditions for convergence and
convergence rate of iterative methods (bisection method, Newton
method).
Linear systems: direct methods (LU factorization, Cholesky
factorization) and iterative methods (Jacobi, Gauss-Seidel),
perturbation analysis, condition number.
Approximation of functions and data: Lagrangian polynomial
interpolation, Chebyshev interpolation, trigonometric interpolation
and fast Fourier transform, approximation by spline functions, the
least-squares method.
Numerical differentiation and integration: finite difference
formulas, trapezoidal formula, Simpson formula.
Eigenvalues and eigenvectors: power method.
The MATLAB and Octave programming environments are used to
execute the introduced algorithms and to analyze their stability,
accuracy and complexity.
Readings/Bibliography
A. Quarteroni, F. Saleri, Scientific Computing with MATLAB and
Octave. Second Edition, Springer Berlin Heidelberg New York,
2006.
A. Kharab, K. Fahd, An Introduction to Numerical Methods: A
MATLAB Approach. Chapman & Hall/CRC, 2002.
B. Bradie, Friendly Introduction to Numerical Analysis, A:
International Edition. Pearson Higher Education, 2006.
Teaching methods
Lessons accompanied by exercise classes and laboratory activities in MATLAB/Octave programming.
Assessment methods
Written examination followed by an oral examination (discussion of a programming project).
Teaching tools
Blackboard and video projector. Exercises for homework and course material are available at http://www.dm.unibo.it/~achilles/.
Links to further information
http://www.dm.unibo.it/~achilles/
Office hours
See the website of Hans Joachim Rudiger Achilles