# chapter 11 calculus. symbolic expressions required: > symbolic math toolbox > use symbolic variables

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• Chapter 11Calculus

• Symbolic ExpressionsRequired:> Symbolic Math Toolbox> Use Symbolic Variables

• 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.

• Symbolic Expression Example>>syms x y>>s=x+y;>>r=sqrt(x^2+y^2);

• Symbolic Expression Example>>n=3;>>syms x;>>A=x.^((0:n)*(0:n))>>A=[1, 1, 1, 1][1, x, x^2, x^3][1, x^2, x^4, x^6][1, x^3, x^6, x^9]

• Manipulating ExpressionsUse the expand command:>>syms x y>>expand((x+y)^2)ans=x^2+2*x*y+y^2>>expand(sin(x+y))ans=sin(x)*cos(y)+cos(x)*sin(y)

• Evaluating ExpressionsUse subs(E, old, new) or double(y):>>syms x>>E=x^2+6*x+7;>>G=subs(E,x,2)G= 23

• Multiple Variables>>syms x y z>>E=x^2+6*y+2*z;>>subs(E,{x,y,z},{2,2,3})ans = 22

• Using Double Command Example>>sqroot2=sym(sqrt(2));>>y=6*sqroot2y=6*2^(1/2)>>z=double(y)z=8.4853

• Plotting ExpressionsUse ezplot command:>>syms x>>E=x^2-6*x+7;>>ezplot(E,[-2 6])

• 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

• Laplace Transformslaplace(exp) Returns Laplace transform.

ilaplace(exp) Returns inverse Laplace.

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