Matlab_Tutorial_2

# Matlab_Tutorial_2 - BCB570 MatlabTutorialII February3,2010...

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BCB 570 Matlab Tutorial II February 3, 2010 1

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Outline Symbolic Math Toolbox Jacobian Matrix Eigenvectors and Eigenvalues QR Decomposition ODE Tools Example 1: Glucose (p86) Example 2: Water Formation 2
Symbolic Math Toolbox (1/2) The Symbolic Math Toolbox for Matlab enables us to create symbolic variables and expressions >> syms E S ES EP P k1 k_1 k2 k_2 k3 k_3; >> dSdt = -(k1*E*S-k_1*ES); >> dEdt = -(k1*E*S-k_1*ES)+k2*ES; ... Matlab also performs operations such as simplification, expansion, or differentiation on symbolic expressions >> syms x y; % create symbolic variables x and y >> diff(x^2/3-x+5*y,x,2) % take second derivative w/ respect to x ans = 2/3 >> expand((x-1)*(y+1)/2) % expand an expression ans = x/2 - y/2 + (x*y)/2 - 1/2 >> simplify(x/2 - y/2 + (x*y)/2 - 1/2) % simplify an expression ans = ((x - 1)*(y + 1))/2 >> pretty((x-1)*(y+1)/2) % print a more readable expression (x - 1) (y + 1) --------------- 2 3

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Plotting functions as symbolic expressions: >> f = x/(2*pi) - 2*sin(x/pi) - 5; >> zeroes = solve(f); >> f1 = diff(f) f1 = 1/(2*pi) - (2*cos(x/pi))/pi >> critical_points = solve(f1) critical_points = pi*acos(1/4) -pi*acos(1/4) >> ezplot(f) >> hold >> plot(double(critical_points),double(subs(f,critical_points)),'ro') Symbolic Math Toolbox (2/2) 4 -6 -4 -2 0 2 4 6 -6.5 -6 -5.5 -5 -4.5 -4 -3.5 x x/(2 π ) - 2 sin(x/ π ) - 5 ‘ro’ specifies color = red, marker = empty circle options for plotting points Other graphics for symbolic expressions: ezplot3, ezpolor, ezcontour, ezmesh, ezsurf, etc.
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## This note was uploaded on 03/08/2010 for the course BCB 570 taught by Professor Juliedickerson during the Spring '10 term at Iowa State.

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Matlab_Tutorial_2 - BCB570 MatlabTutorialII February3,2010...

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