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Extra resources for Symbolic math toolbox for use with MATLAB - user's guide
Sample text
2*besselj(1,x)/x + besselj(0,x) 0 gamma(x+1)–x*gamma(x) 0 cos(x)^2 + sin(x)^2 1 simple The simple function has the unorthodox mathematical goal of finding a simplification of an expression that has the fewest number of characters. Of course, there is little mathematical justification for claiming that one expression is “simpler” than another just because its ASCII representation is shorter, but this often proves satisfactory in practice. The simple function achieves its goal by independently applying simplify, collect, factor, and other simplification functions to an expression and keeping track of the lengths of the results.
The symbolic simplification problem involves the verification that these three expressions represent the same function. It also involves a less clearly defined objective—which of these representations is “the simplest”? 1-47 1 Tutorial This toolbox provides several functions that apply various algebraic and trigonometric identities to transform one representation of a function into another, possibly simpler, representation. These functions are collect, expand, horner, factor, simplify, and simple.
5 −4 −6 −4 −2 0 x 2 4 6 1-39 1 Tutorial indicates that the global minima occur near x = -π and x = π. We can demonstrate that they occur exactly at x= ±π, using the following sequence of commands. First we try substituting -π and π into f'''(x). simple([subs(f3,x,–pi),subs(f3,x,pi)]) The result ans = [ 0, 0] shows that -π and π happen to be critical points of f'''(x). We can see that -π and π are global minima by plotting f2(–pi) and f2(pi) against f2(x). m1 = double(subs(f2,x,-pi)); m2 = double(subs(f2,x,pi)); plot(-pi,m1,'go',pi,m2,'go') text(-1,-4,'Global minima') The actual minima are m1, m2 ans = [ –4, –4] as shown in the plot on the following page.
Symbolic math toolbox for use with MATLAB - user's guide by MathWorks
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