So u-substitution is used to make an effective change of variables in one-dimensional calculus. Jacobian determinants are used to make a change of variables in two or higher-dimensional calculus. Can a u-substitution be thought of as a one-dimensional Jacobian determinant? And on an entirely unrelated note, does anyone know how to make vertical dots in matrix? I was going to draw out the Jacobian determinant, but I couldn't figure that out.