Paola Gervasio  DICATAM  University of Brescia  paola.gervasio_at_unibs.it 




Thursday 15/03/12 (9:0012:00) Scientific Computing Laboratory. Dip.Mat. 
Matlab. Operations with scalars and arrays. Mathematical
functions: definition, evaluation, plot. Fundamentals of graphics in Matlab. Matlab
statements: forloop, whileloop, ifstatements.
Programming in Matlab: scripts, functions. 
matlab1.pdf matlab2.pdf (up to pag. 6) homework_1.pdf 
Thursday 15/03/12 (14:3017:30) Aula Seminari Dip.Mat. 
Fundamentals of numerical analysis and scientific computing. Floating point arithmetic: the floating point system, rounding errors, machine precision, propagation of rounding errors. Stability, consistency and convergence of numerical methods. Approximation (truncation) errors. About computational costs. 
intro_s.pdf rounding.pdf 
Thursday 22/03/12 (9:0012:00) Aula Seminari Dip.Mat. 
Linear systems. Direct methods: Gauss Elimination, LU and Cholesky factorizations. Iterative methods: Gradient and Conjugate Gradient methods. Condition number and stability analysis. 
LS_example.pdf LS_theory.pdf 
Friday 23/03/12 (10:3013:30) Scientific Computing Laboratory. Dip.Mat. 
Matlab Matlab statements: whileloop, ifstatements, logical operators, relational operators. Exercises and programming: propagation of rounding errors, linear systems. 
matlab2.pdf (from pag. 7) rounding_errors.pdf linearsystems.pdf 
Thursday 29/03/12 (9:0012:00) Aula Seminari Dip.Mat. 
Approximation of ODE. Approximation of the 1storder Cauchy problem: Euler methods, CrankNicolson method. Convergence, consistency and stability in approximating ordinary differential equations. 
ode_theory.pdf 
Thursday 29/03/12 (14:3017:30) Scientific Computing Laboratory. Dip.Mat. 
Exercises and programming: 1storder Cauchy problem. 
ode.pdf oscillator.pdf lotka.pdf 
Friday 30/03/12 (10:3013:30) Scientific Computing Laboratory. Dip.Mat. 
Approximation of initialboundary value problems: discretization of the 1D Poisson equation by finite differences. Discretization of the 1D heat equation. 
pde_intro.pdf pde.pdf 

Paola Gervasio September 2011 