The lectures will be held in C4 Bldg., Lecture Room 002 (Mondays
and Wednesdays from 11:10 to 13:00).
Tutorials will be taken every friday from 12:10 to 13:00 at the
Applied Physics Department (B5 Blgd.).
Practicals will be announced in short.
Syllabus.
Floating point representation. Error propagation. Stability of
algorithms. Introduction to Fortran-95 and Matlab.
Interpolation and approximation of functions. Lagrange and
Hermite-Birkoff polynomial interpolation. Runge phenomenon. Orthogonal
polynomials. Generalized Fourier series. Discrete Fourier
transforms. Aliasing and Gibbs phenomenon. Convolution sums.
Zeros and minima of functions of a single variable. Iterative
techniques: fixed point, bisection, chord, Newton-Raphson and Brent
methods. Minimization with Derivative-free methods. Golden's
rule and Brent method. Minimization using derivatives.
Numerical differentiation and integration. Differentiation
matrices. Newton-Cotes formulae. Gaussian quadratures.
Numerical linear algebra. Direct methods for linear systems
solving (LU, QR, pivoting, Gaussian elimination). Iterative methods
(Jacobi, Gauss-Seidel and SOR). Singular value decomposition.
Numerical integration of ordinary differential
equations. One-step methods (Runge-Kutta). Applications to boundary
value problems. Shooting.
Basic references.
Quarteroni, A., Sacco, R. and Saleri, F., Numerical
Mathematics (2nd Ed.), Springer 2007.
Dahlquist, G. and Bjorck, A., Numerical Methods, Dover 1974.
Higham, D. J. and Higham, N. J., Matlab Guide, SIAM 2000.
fa.upc.edu Office: B5 (010)