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+--- Thread: Taylor Expansion with 2 variables (/thread-14267.html)
Taylor Expansion with 2 variables - hamorabi - 12-30-2019 01:27 AM
I'm sharing a little function I wrote that returns the Taylor expansion of functions of two variables. The Taylor function included in the prime only works for single variable functions.
Function definition:
PHP Code:
taylor2d(ff,vars,exppt,ordr)
For example, to return the second order polynomial that approximates the function sin(2x)+cos(y) at the point x=0, y=0:
PHP Code:
taylor2d(sin(2x)+cos(y),[x,y],[0,0],2)
You can also use this function to find the equation of the tangential plane to a surface. Since the tangential plane is a first order approximation, just set the parameter ordr to 1:
PHP Code:
taylor2d(ln(2*x+y),[x,y],[-1,3],1)
PHP Code:
2x+y-1
PHP Code:
#cas
def taylor2d(ff,vars,exppt,ordr):
"""
taylor2d(sin(2x)+cos(y),[x,y],[0,0],2)
taylor2d(x*e^y+1,[x,y],[1,0],2)
"""
if (type(vars) != DOM_LIST) and (type(exppt) != DOM_LIST):
return taylor(ff,equal(vars,exppt),ordr,polynom)
elif (len(vars) == 2 and len(exppt) == 2):
pp = seq(equal(vars[ii],exppt[ii]),ii,0,len(vars)-1)
ii, nn, bb, dd = 0, 0, 0, 0
while (ii<=ordr):
bb = binomial(ii,nn)/(ii!)*((vars[0]-exppt[0])**nn)*((vars[1]-exppt[1])**(ii-nn))
dd += subst(diff(diff(ff,vars[0],nn),vars[1],ii-nn),pp)*bb
if (nn==0):
ii += 1
nn = ii + 1
nn -= 1
return dd
else:
return "Error!"
#end