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6). At the highest level stands the error em which occurs when forcing the physical reality (P P stands for physical problem and xph denotes its solution) to obey some mathematical model (M P , whose solution is x). Such errors will limit the applicability of the mathematical model to certain situations and are beyond the control of Scientific Computing. 6, an algebraic or differential equation, a linear or 26 1 What can’t be ignored nonlinear system) is generally not solvable in explicit form. Its resolution by computer algorithms will surely involve the introduction and propagation of roundoff errors at least.

The diagonal made of elements with indices i, i + m) has elements equal to the components of v, while the remaining elements are null. Note that this extension is valid also when m is negative, in which case the only affected elements are those of lower diagonals. For instance if v = [1 2 3] then: >> A = diag (v , -1) A = 0 0 1 0 0 2 0 0 0 0 0 3 0 0 0 0 Other special cases are the upper triangular and lower triangular matrices. A square matrix of dimension n is lower (respectively, upper ) triangular if all elements above (respectively, below) the main diagonal are zero.

Mat. mat. A file name can be specified after save or load. mat, using the command save area v1 v2 v3. help By the command help one can see the whole family of commands and pre-defined variables, including the so-called toolboxes which are sets of specialized commands. Among them let us recall those which define sin cos the elementary functions such as sine (sin(a)), cosine (cos(a)), square sqrt exp root (sqrt(a)), exponential (exp(a)). There are special characters that cannot appear in the name of a + - * / variable or in a command, for instance the algebraic operators (+, -, & | ˜ * and /), the logical (or boolean) operators and (&), or (|), not (˜), the relational operators greater than (>), greater than or equal to (>=), > >= < less than (<), less than or equal to (<=), equal to (==).

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