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lecturenotes11_14

# 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
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’)
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.
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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