Chapter 11 Calculus

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Chapter 11Calculus
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Symbolic ExpressionsRequiredgt Symbolic Math
Toolboxgt Use Symbolic Variables
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Functions for Symbolic Processingx sym(x)
Creates the symbolic
variable with name x.syms x y u v Creates
the symbolic variables x,
y, u, v.Simplify(ans) Simplifies the
expression ans.
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Symbolic Expression Examplegtgtsyms x
ygtgtsxygtgtrsqrt(x2y2)
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Symbolic Expression Examplegtgtn3gtgtsyms
xgtgtAx.((0n)(0n))gtgtA 1, 1, 1, 1 1,
x, x2, x3 1, x2, x4, x6 1, x3, x6,
x9
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Manipulating ExpressionsUse the expand
commandgtgtsyms x ygtgtexpand((xy)2)ans x22
xyy2gtgtexpand(sin(xy))ans sin(x)cos(y)cos
(x)sin(y)
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Evaluating ExpressionsUse subs(E, old, new) or
double(y)gtgtsyms xgtgtEx26x7gtgtGsubs(E,x,2)
G 23
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Multiple Variablesgtgtsyms x y zgtgtEx26y2zgt
gtsubs(E,x,y,z,2,2,3)ans 22
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Using Double Command Examplegtgtsqroot2sym(sqrt(2
))gtgty6sqroot2y 62(1/2)gtgtzdouble(y)z
8.4853
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Plotting ExpressionsUse ezplot commandgtgtsyms
xgtgtEx2-6x7gtgtezplot(E,-2 6)
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Symbolic Calculus Functionsdiff(E) Returns
the derivative of the expression E with respect
to the default independent variable.diff(E,v)
To variable v.diff(E,v,n) nth derivative
int(E) Returns the integrallimit(E)
Returns the limit
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Laplace Transformslaplace(exp) Returns
Laplace transform.ilaplace(exp) Returns
inverse Laplace.
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