Paola Gervasio - Dipartimento di Matematica - Università degli Studi di Brescia - paola.gervasio_at_unibs.it
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Numerical Methods - A.A. 2011/2012
PhD Program in Natural Risks Assessment and Management (NRAM).

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Course Program

PhD Presentation


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

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