change of variables

• How Does Boltzmann’s Transformation Reduce the Heat Equation?
  See how Boltzmann’s similarity variable reduces the heat equation to an ODE, with the chain-rule derivatives and an error-function example.
• How to Change Variables and Bounds in a Double Integral
  Learn how to transform a double integral correctly: map the region, derive new bounds, include the absolute Jacobian, and check the result.
• How to Change Variables in a Double Integral
  To change variables in a double integral, transform the region and integrand, then multiply by the absolute Jacobian determinant.
• How to Use Variable Substitution in a Double Integral
  To substitute variables in a double integral, transform the region and integrand, then multiply by the absolute Jacobian determinant.