Given the heat conduction problem in the rod as follows: Length of the rod is equal 15 and heat conductivity coefficient is equal 3. The heat flow at the left hand end of the rod equal t - sint and the heat at the right hand end is given as tcost At initial time temperature of the rod was as 12cos There is the heat source inside of the rod expressed by the function 71x 710x 7cos 2 2510x 6cos +5(t - sint) 6 10tcost (x - 3)2 x2 (1 - sin2t) + 3 6 (cost tsint) Your task followings: 1. Specify the problem as mathematical model. Problem for u(x,t). 2. Write appropriate Transformation v(x, t) for the Step 1. 3. Finalize Step 1 and specify the problem for v(x,t). 4. Find v(x,t). 5. Find the solution of the problem u(x,t). 6. Draw the graph u(x, 10) which is the temperature of the rod at the time t = 10. 7. Draw the graph u(1,t) which is the temperature of the rod at point x = 1 in the time interval 0