Consider the scalar IVP X= ✗ t+a x(o)=xo a>o Prove a unique solution exists for t>-a using a vector field as Lip (Ix R) for any I=[b.c] with a

Consider the following expressions for second derivatives of scalar field ø(x, y, z) and vector field A (x, y, z). State whether or not each expression makes sense, and if not, state why. Also point out any that are always equal to zero. grad(grad(ø)) div(grad(ø)) curl(grad(ø)) grad(div(A)) div(div(A)) curl(div(A)) grad(curl(A)) div(curl(A)) curl(curl(A))

Sketch the vector field on the real line and find the stability of the fixed points.