Numerical Methods - A.A. 2011/2012
PhD Program in Natural Risks Assessment and Management (NRAM).

Lectures plan and slides

Thursday 15/03/12 (9:00-12:00) Scientific Computing Laboratory. Dip.Mat.	Matlab. Operations with scalars and arrays. Mathematical functions: definition, evaluation, plot. Fundamentals of graphics in Matlab. Matlab statements: for-loop, while-loop, if-statements. Programming in Matlab: scripts, functions.	matlab1.pdf matlab2.pdf (up to pag. 6) homework_1.pdf
Thursday 15/03/12 (14:30-17:30) 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 (9:00-12:00) 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 (10:30-13:30) Scientific Computing Laboratory. Dip.Mat.	Matlab Matlab statements: while-loop, if-statements, 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 (9:00-12:00) Aula Seminari Dip.Mat.	Approximation of ODE. Approximation of the 1st-order Cauchy problem: Euler methods, Crank-Nicolson method. Convergence, consistency and stability in approximating ordinary differential equations.	ode_theory.pdf
Thursday 29/03/12 (14:30-17:30) Scientific Computing Laboratory. Dip.Mat.	Exercises and programming: 1st-order Cauchy problem.	ode.pdf oscillator.pdf lotka.pdf
Friday 30/03/12 (10:30-13:30) Scientific Computing Laboratory. Dip.Mat.	Approximation of initial-boundary 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

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