The solution to the logistic map .The solution now oscillates but doesn't appear to show any discernible pattern. The value of X_n seems to "jump around". This  called chaotic.

i want to design a packaging container to hold 320 sphere-shaped chocolates that each has a diameter 1.8 cm and weights about 3.2g each. i hope can get all posible shape using maple18 .

How to sketch 3D graph finite string problem of wave equation in partial differential equation using maple?

u_tt = 4u_xx

_{boundary conditions : u (0,t) = (5,t) = 0 , t>0 ,}

_{initial conditions : u (x,0) = f(x) = { 0, 0<x<4      , (5-x) , 4<x<5} 

                         u_t (x,0) = 0 , 0<x<5

how to sketch 3D graph for solution of the corresponding partial differential equations ?? 

prove that

∇ x (∅F) = ∅∇ x F + (∇∅) x F

where ∅ and F are differentiable scalar function and vector function respectively.