Post Reply 
Taylor Expansion with 2 variables
12-30-2019, 01:27 AM
Post: #1
Taylor Expansion with 2 variables
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
will give the answer:
PHP Code:
2x+y-
Equate the result to 0 and you have the equation of the tangential plane.


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) == and len(exppt) == 2):
    
pp seq(equal(vars[ii],exppt[ii]),ii,0,len(vars)-1)
    
iinnbbdd 0000
    
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 


Attached File(s)
.hpprgm  taylor2d.hpprgm (Size: 2.37 KB / Downloads: 2)
Find all posts by this user
Quote this message in a reply
Post Reply 




User(s) browsing this thread: 1 Guest(s)