By Kiusalaas J.
Numerical equipment in Engineering with MATLAB is a textual content for engineering scholars and a reference for training engineers, specially those that desire to discover the ability and potency of MATLAB. the alternative of numerical tools used to be in line with their relevance to engineering difficulties. each process is mentioned completely and illustrated with difficulties concerning either hand computation and programming.
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The corresponding changes in the ith row are Ai j ← Ai j − λAk j , j = k, k + 1, . . 8b) To transform the entire coefﬁcient matrix to upper triangular form, k and i in Eqs. 8) must have the ranges k = 1, 2, . . , n − 1 (chooses the pivot row), i = k + 1, k + 2 . . , n (chooses the row to be transformed). The algorithm for the elimination phase now almost writes itself: for k = 1:n-1 for i= k+1:n if A(i,k) ˜= 0 lambda = A(i,k)/A(k,k); A(i,k+1:n) = A(i,k+1:n) - lambda*A(k,k+1:n); b(i)= b(i) - lambda*b(k); end end end In order to avoid unnecessary operations, the above algorithm departs slightly from Eqs.
The equations are then solved by back substitution. 1—multiplying one equation (say, equation j ) by a constant λ and subtracting it from another equation (equation i ). The symbolic representation of this operation is Eq. (i ) ← Eq. (i ) − λ × Eq. 6) The equation being subtracted, namely Eq. ( j ), is called the pivot equation. We start the elimination by taking Eq. (a) to be the pivot equation and choosing the multipliers λ so as to eliminate x1 from Eqs. (b) and (c): Eq. (b) ← Eq. 5) × Eq. (a) Eq.
If greater detail about the variables is required, type whos. Variables can be cleared from the workspace with the command clear a b . . which clears the variables a, b, . . If the list of variables is omitted, all variables are cleared. 26 Introduction to MATLAB Assistance on any MATLAB function is available by typing help function name in the command window. 9 Plotting MATLAB has extensive plotting capabilities. Here we illustrate some basic commands for two-dimensional plots. The example below plots sin x and cos x on the same plot.