1. Nonlinear Equations
Apply the interval Newton method to compute enclosures of the zeros of the following equations: 
   a) f(x) = sin(sqrt(x)) - x 		 with x in [0,1]
   zeros: [0.768649, 0.768649] [-0, 5.96046e-008]
   b) f(x) = -2.75x^3+18x^2-21x-12 	 with x in [-2,6]
   zeros: [4.74033, 4.74033] [2.21982, 2.21982] [-0.414689, -0.414689]
   c) f(x) = sin(10x)+cos(3x) 	 with x in [3,6]
   zeros: [5.67903, 5.67903] [5.19571, 5.19571] [5.16119, 5.16119] [4.71239, 4.71239] [4.26359, 4.26359] [4.22907, 4.22907] [3.74575, 3.74575] [3.36599, 3.36599] [3.26242, 3.26242]

2. Interval Linear Systems
Consider the interval linear system: 
   [2/5,4/5]x1 + x2 = [15/5,17/5]
   [-4/7,-2/7]x1 + x2 = [23/7,25/7]
and the initial box [-2.5,2.5]x[1.5,4.5].
   a) Use the Interval Gauss-Seidel method to solve the system without precontitioning.
   A = (([0.4, 0.8] ; [1, 1])
([-0.571429, -0.285714] ; [1, 1]))
   b = ([3, 3.4] ; [3.28571, 3.57143])
   before interval Gauss-Seidel: x = ([-2.5, 2.5] ; [1.5, 4.5])
    after interval Gauss-Seidel: x = ([-2.5, 2.5] ; [1.85714, 4.5])
   b) Compute an adequate preconditioner P.
   P = ((0.972222 ; -0.972222)
(0.416667 ; 0.583333))
   c) Obtain an equivalent system by applying de above preconditioner P.
   A = (([0.666667, 1.33333] ; [-0, 0])
([-0.166667, 0.166667] ; [1, 1]))
   b = ([-0.555556, 0.111111] ; [3.16667, 3.5])
   d)	Use the Interval Gauss-Seidel method to solve this new the system.
   before interval Gauss-Seidel: x = ([-2.5, 2.5] ; [1.5, 4.5])
    after interval Gauss-Seidel: x = ([-0.833333, 0.166667] ; [3.02778, 3.63889])

3. Nonlinear Systems of Equations (Pruning)
Apply the multivariate interval Newton method to solve the following systems: 
   a) x1^2+x1x2=10 ; x2+3x1x2^2=57   with the initial box [1.75,2.25]x[2.75,3.75]. 
   before interval Newton: x = ([1.75, 2.25] ; [2.75, 3.75])
    after interval Newton: x = ([2, 2] ; [3, 3])
   b) x^2=5-y^2 ; y+1=x^2   with the initial box [1,3]x[1,3]. 
   before interval Newton: x = ([1, 3] ; [1, 3])
    after interval Newton: x = ([1.60049, 1.60049] ; [1.56155, 1.56155])

4. Nonlinear Systems of Equations (Solving)
Compute enclosures for all solutions of the following system within the box [0,4]×[0,4]:
   x^2+y^2=10 ; 0.4y-0.1x^2=0
   solutions: ([2.63944, 2.63944] ; [1.74166, 1.74166])