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lecturenotes11_14 - Matlab Symbolic Mathematics November...

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Matlab Symbolic Mathematics November 14 , 2008
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Symbolic Toolbox Linear Algebraic computations Derivatives Integrals Laplace and Fourier Tranforms
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Creating Symbolic Variables Matlab needs to know you are entering a symbolic variable: >> x=sym(‘x’) or >> syms x >> syms x y z you can then create new symbolic variables from existing ones.
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Creating new symbolic variables >> y=2*(x+3)^2/(x^2+6*x+9) now, y is also a symbolic variable and can be combined again… >> z=x*y z = 2*x*(x+3)^2/(x^2+6*x+9) >> D=sym(‘A=B+C+D’)
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Creating Symbolic Equations >> D=sym(‘A+B+C’) or >> eqn=sym(‘A=B+C+D’) Note that there is a new variable type here: “sym” (see the workspace listing) The “poly” command is also useful. Consider, >>a= [1,4,-3]; >>b=poly2sym(a) b= x^2+*x-3
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Symbolic Manipulation Matlab has a number of commands designed specifically for manipulating symbolic expressions: numden , extracts the numerator and denominator expand , expands an expression factor , factors an expression collect , collects like terms in an expression See Table on Page 412 of text.
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Solving Expressions and Eqns solve function can be used to find the roots of an equation, to solve for a particular variable numerically or symbolically solve systems of linear and nonlinear equations
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