SelisOnelLectureNotes_SolNonlinEqMultiVariate

SelisOnelLectureNotes_SolNonlinEqMultiVariate - Solving...

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Solving Simultaneous Nonlinear Equations SELİS ÖNEL, PhD
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May 5,2008 SelisÖnel© 2 Quotes of the Day Nothing in the world can take the place of Persistence. Talent will not; nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not; the world is full of educated derelicts. Persistence and determination alone are omnipotent. The slogan 'Press On' has solved and always will solve the problems of the human race. Calvin Coolidge Victorious warriors win first and then go to war, while defeated warriors go to war first and then seek to win. Sun-Tzu
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May 5,2008 SelisÖnel© 3 Nonlinear Functions of Several Variables System with two nonlinear functions and two variables z=f(x 1 ,x 2 ) and z=g(x 1 ,x 2 ) Problem is more difficult to solve for more variables f(x 1 ,x 2 ,x 3 ,…,x n ) To find a zero of the system, find the intersection of the curves: f(x 1 ,x 2 )=0 and g(x 1 ,x 2 )=0 Use all the information about the problem to find the region where the curves may intersect SO…
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May 5,2008 SelisÖnel© 4 Nonlinear Functions of Several Variables Plot a 2-D or 3-D figure of the functions in MATLAB® !
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May 5,2008 SelisÖnel© 5 2-D Graphs >> x=linspace(0,2); % linspace generates a row vector of 100 linearly % equally spaced points between x1 and x2 >> y=x.*exp(-x); >> plot(y) % plots y versus their index 0 10 20 30 40 50 60 70 80 90 100 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
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May 5,2008 SelisÖnel© 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 x y y=xe -x anywhere (0.36,0.25) 2-D Graphs % ExPlot2DGraph.m x=linspace(0,2); % linspace generates a row vector of 100 linearly % equally spaced points between x1 and x2 y=x.*exp(-x); plot(x,y) % plots y agains x grid on % adds grid lines to the current axes xlabel('x') % adds text below the x-axis ylabel('y') % adds text besides the y-axis title('y=xe^{-x}') % adds text at the top of graph gtext('anywhere') %places text with mouse text(0.36,0.25,'(0.36,0.25)') % places text at the specific point
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May 5,2008 SelisÖnel© 7 2-D Graphs % ExPlot.m: This program draws a graph of sin(x) and cos(x) % where 0 <= x <= 3.14 angle=-pi:0.1:pi; % Create array xcomp=cos(angle); % Create array plot(angle,xcomp,'r:'); % Plot using dots(:) with red(r) hold on % Add another plot on the same graph ycomp=sin(angle); % Create array plot(angle,ycomp,'b-x'); % Plot using lines(-) and the symbol x % at each data point with blue(b) grid on xlabel('Angle in degrees'); ylabel('x and y components'); legend('cos{\theta}','sin{\theta}',2) gtext('cos(x)'); gtext('sin(x)'); % Display mouse-movable text -4 -3 -2 -1 0 1 2 3 4 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Angle in degrees x and y components cos(x) sin(x) cos sin
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May 5,2008 SelisÖnel© 8 2-D Graphs: Other Commands More than one function can be plotted on one graph: >>plot(x,X .*exp(-x) ,’.’,x,x*sin(x),’ - .’) More than one graph can be shown in different frames >>subplot(2,1,1), plot(x,x.*cos(x)) >>subplot(2,1,2), plot(x,x.*sin(x) Axis limits can be seen or modified >>axis >>axis([0,1.5,0,1.5]) Figure window can be cleared >>clf
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May 5,2008 SelisÖnel© 9 2-D Graphs: Other Commands Comet like trajectory of the function >> shg, comet(x,y) % shg brings up the current graphic window By using figure(n) command, it is possible to use more than one graphic window, n: positive integer Another easy way to plot a function: >>fplot(x*)
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This note was uploaded on 03/14/2012 for the course CHEMICAL E kmu 206 taught by Professor Onel,selis during the Spring '08 term at Hacettepe Üniversitesi.

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SelisOnelLectureNotes_SolNonlinEqMultiVariate - Solving...

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