How to compute a Taylor expansion for f(x,y) using Mathematica?

In summary, When computing a Taylor expansion for f(x,y) using Mathematica's Series function, it is common to encounter terms like O[y+2]^2, which represent unspecified higher order terms in the expansion. To eliminate these terms, use the Normal function on the series.
  • #1
chinaman209
3
0
Can someone pls explain hot to compute a taylor expansion for f(x,y) using mathematica
 
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  • #3
When I expand like that i get some zero terms like 0(y+2)^2.. and so one repeated a finite number of times. When i try to simplify the answer the zeroes don't go away. So are these really zero?
 
  • #4
Those are not 0 (number zero) they are O (letter "Oh"). The term O[y+2]^2 means an unspecified term of order (y+2)^2 to represent all of the higher order terms in the expansion. If you want to get rid of it then just use:

Normal[Series[...]]
 

What is Taylor Expansion in Mathematica?

Taylor Expansion in Mathematica is a method of approximating a function by a polynomial of infinite degree at a specific point. It is a powerful tool for solving complex mathematical problems and is commonly used in physics, engineering, and other scientific fields.

How do you use Taylor Expansion in Mathematica?

To use Taylor Expansion in Mathematica, you first need to define the function you want to approximate. Then, specify the point at which you want to expand the function. Finally, specify the desired order of the expansion. The output will be a polynomial expression that approximates the original function at the specified point.

What is the purpose of Taylor Expansion in Mathematica?

The purpose of Taylor Expansion in Mathematica is to approximate a function at a specific point by a polynomial expression. This allows us to simplify complex functions and make them easier to work with. It also enables us to approximate solutions to differential equations and other mathematical problems.

What is the difference between Taylor Expansion and Maclaurin Expansion in Mathematica?

Taylor Expansion and Maclaurin Expansion are both methods of approximating a function by a polynomial at a specific point. The main difference is that Taylor Expansion can be used at any point, while Maclaurin Expansion is specifically for approximating a function at x=0. Additionally, Taylor Expansion uses derivatives of the function at the specified point, while Maclaurin Expansion uses derivatives at x=0.

Can Taylor Expansion be used for functions with multiple variables in Mathematica?

Yes, Taylor Expansion can be used for functions with multiple variables in Mathematica. The process is similar to the one-variable case, but instead of taking derivatives with respect to a single variable, you take partial derivatives with respect to each variable. The resulting polynomial will approximate the function at the specified point in the multi-dimensional space.

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