It unfortunate that you did not tell us how you tried "solving for the max and min x, y coordinates" since if you had we might be able to point out your mistake. All I can say is that if you have "u= x- 2y", one of the boundaries is x- 2y= 0 and the other is x- 2y= 4, u= 0 and 4 pretty much leaps out at you- u= x- 2y= 0 and u= x- 2y= 4!Feodalherren said:
A Jacobian transformation is a mathematical method used to transform the coordinates of a vector or set of variables from one coordinate system to another. It is commonly used in multivariable calculus and differential equations.
Jacobian transformation allows us to simplify the calculation of integrals and derivatives in different coordinate systems. It is especially useful in physical and engineering problems where different coordinate systems may be used.
The Jacobian transformation is calculated by taking the partial derivatives of the new coordinates with respect to the old coordinates. These derivatives are then used to create a Jacobian matrix, which is used to transform the variables.
Finding new limits in Jacobian transformation is important because it allows us to express integrals and derivatives in terms of the new coordinates. This can make the calculations simpler and more efficient.
Yes, Jacobian transformation can be applied to any coordinate system as long as it is a one-to-one mapping. This means that each point in the original coordinate system corresponds to a unique point in the new coordinate system.