Math Problem Statement
x = 4 cos v , y= u sinv then show that j1x j2 =1
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Parametric Equations
Jacobian
Partial Derivatives
Trigonometric Functions
Formulas
x = 4 cos(v)
y = u sin(v)
Jacobian matrix J = [[∂x/∂u, ∂x/∂v], [∂y/∂u, ∂y/∂v]]
Jacobian determinant det(J) = (∂x/∂u) * (∂y/∂v) - (∂x/∂v) * (∂y/∂u)
Theorems
Jacobian Determinant Theorem
Suitable Grade Level
Undergraduate Mathematics (Calculus, Multivariable Calculus)
Related Recommendation
Jacobian Matrix for Parametric Equations: x = 4cos(v), y = u sin(v)
Jacobian Determinant Calculation for Q-5 on Page 3
Jacobian Determinant and Double Integral in Parametric Transformation
Jacobian Computation for Transformation x = 8u + 5v, y = u - 2v
Jacobian Determinant of a Transformation: Proof and Step-by-Step Solution