Help with understanding taylor approximation

This can also be written as u = (u,v), with u representing the velocity in the x direction and v representing the velocity in the y direction. This type of approximation is commonly used in the study of fluid mechanics.
  • #1
MaxManus
277
1

Homework Statement


I'm reading about fluid mechanics and in one of the examples they have approximated the velocity field. The field is two dimensional u = (u,v)
I have never seen this before so cold someone tell me what it is called so I can look it up?
The notes I am reading are hand written so there may be small mistakes, but it seems likes some of the ts are primed.

u = u(x,y,t)



The Attempt at a Solution



u(0,0,t) = u(o,o,t) + [tex]\int_0^t[/tex]u(0,0,t')dt'[[tex]\nabla[/tex]u]x = 0
 
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  • #2
It looks like this is a two-dimensional velocity field. The notation u(x,y,t) indicates that the velocity is a function of three variables: x, y, and time t. The notation \nablau]x indicates the gradient of the velocity field in the x direction.
 

Related to Help with understanding taylor approximation

1. What is Taylor approximation?

Taylor approximation is a mathematical technique used to approximate a function by using a polynomial. It is useful for estimating the value of a function at a specific point or for simplifying complicated functions for easier analysis.

2. How does Taylor approximation work?

Taylor approximation works by using a polynomial of a certain degree to approximate a function. The polynomial is constructed based on the derivatives of the function at a given point. The more terms included in the polynomial, the closer the approximation will be to the actual function.

3. What is the difference between Taylor approximation and Taylor series?

Taylor approximation is a simplified version of the Taylor series. The Taylor series includes an infinite number of terms and can provide an exact representation of a function, while Taylor approximation uses a finite number of terms to provide an estimate.

4. When is Taylor approximation useful?

Taylor approximation is useful when dealing with complex functions that are difficult to analyze. It can provide a good approximation of the function at a specific point and can also be used to find the maximum or minimum values of a function.

5. What are the limitations of Taylor approximation?

One limitation of Taylor approximation is that it is only accurate near the point of approximation. As you move further from the point, the accuracy decreases. Additionally, Taylor approximation may not work for all functions, especially those with discontinuities or singularities.

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