Verizon 2:11 PM a kettering.blackboard.com C Math 305: Matlab Assignment 1 Assigned: Monday October 15th, 2018 Due: Friday November 2nd, 2018 This assignment is to be completed in groups of 2-4 people. All problems should be submitted in a single Matlah live (.mlx) file, and submitted electronically to me ncausleyCkottoring.odu. All Matlab seripts or functions which are requested should also be submitted in addition to the main project file. File names should be formatted as follows: Math 305xX_Project1asolNaze2 Nano3.nlx where "XX is your section number, and Name1, Name2, is the last name of each group member (1) Write a Matlab function to implement Newton's method. Use it, along with the functions provled, to solve Problem (2) For each the ollowing functons do the following: (i) Plot the function, and identify one (or m! root in the inteval[0.4] (ii Find the root to a precision of 10 decimal digits, with each method (when possible). ii) Commcnt on the strengths and weakness of using each cthod or this function. vOrganize your results in a tabbe the iteration count, The table should look likethis: Neton Secant False Pos. Bisection Iteration The functios aro: a)f(x)16r96+2162 -216r +81 (b) x) (c) f(x)sin(40) e5x +1.000.000 (3) Newton's nethod can b used to find complx conjugate roots, in additon to real roos By varying your initial guess, ind ll four roots of the polynomial ()37-30 HINT:2 of the roots are complex conjugates. (4) Fommalate a fixed point iteration to find the positive root of 3sin(r) + xow(z 0 in the interval Use the fixed point function with Aitken accelcration to fin ths root to 10 digits os precision (5) The main body of an airplane is to be designed, such that it is rlially symmetric, where r(r) is given by SearsHaack slender body thoory The total volume of the fuselage for a body of maxium radius R and length L is given by The wave drag, due to shock waves exting forces on the arooil ody, is given by where p1225kg is the density of air, ad U i the vekocity of the aircraft. Once designed, the aircraft has a 1312.62462m Supose that the drag force iD 961951716N when the ururaft reaches velocity U 275Tn/a Use Newtons method for linear systems to solve for the radius and length of the airplane body. Verizon 2:11 PM a kettering.blackboard.com C Math 305: Matlab Assignment 1 Assigned: Monday October 15th, 2018 Due: Friday November 2nd, 2018 This assignment is to be completed in groups of 2-4 people. All problems should be submitted in a single Matlah live (.mlx) file, and submitted electronically to me ncausleyCkottoring.odu. All Matlab seripts or functions which are requested should also be submitted in addition to the main project file. File names should be formatted as follows: Math 305xX_Project1asolNaze2 Nano3.nlx where "XX is your section number, and Name1, Name2, is the last name of each group member (1) Write a Matlab function to implement Newton's method. Use it, along with the functions provled, to solve Problem (2) For each the ollowing functons do the following: (i) Plot the function, and identify one (or m! root in the inteval[0.4] (ii Find the root to a precision of 10 decimal digits, with each method (when possible). ii) Commcnt on the strengths and weakness of using each cthod or this function. vOrganize your results in a tabbe the iteration count, The table should look likethis: Neton Secant False Pos. Bisection Iteration The functios aro: a)f(x)16r96+2162 -216r +81 (b) x) (c) f(x)sin(40) e5x +1.000.000 (3) Newton's nethod can b used to find complx conjugate roots, in additon to real roos By varying your initial guess, ind ll four roots of the polynomial ()37-30 HINT:2 of the roots are complex conjugates. (4) Fommalate a fixed point iteration to find the positive root of 3sin(r) + xow(z 0 in the interval Use the fixed point function with Aitken accelcration to fin ths root to 10 digits os precision (5) The main body of an airplane is to be designed, such that it is rlially symmetric, where r(r) is given by SearsHaack slender body thoory The total volume of the fuselage for a body of maxium radius R and length L is given by The wave drag, due to shock waves exting forces on the arooil ody, is given by where p1225kg is the density of air, ad U i the vekocity of the aircraft. Once designed, the aircraft has a 1312.62462m Supose that the drag force iD 961951716N when the ururaft reaches velocity U 275Tn/a Use Newtons method for linear systems to solve for the radius and length of the airplane body