Mathematics Homework Solutions

Polynomial Interpolation

please see attached pdf.

Chebyshev ploynomial of degree 4 interpolation

Calculate the five Chebyshev nodes in the interval [-1,1] which are used when interpolating with a degree four polynomial. Evaluate the function f(x)=2arcsin(x) at each of these points. Construct the degree four Chebyshev polynomial. Evaluate the resulting polynomial at x=0.8 and compare with the actual value of the function.

Cublic Splines

please see attached file. Comments welcome.

Newton-Raphson

I need to solve a system of vector loop equations, using the Newton-Raphson method and find the (x,y) coordinates of the coupler point. This problem (NEW ATTACHMENT) is listed in "Applied Numerical Methods for Engineers and Scientists" by Singiresu S. Rao: problem 2.3, page 139.

Least Squares Lines

please see attached file.

Differenetial equation

I am having difficulties gaining a solution for the following differential equation of x'=2t3 -6t2 + t1/2. Could I please get assistance with detailing my solution.

I am lost at this one.

In a linear system 2x + 3y =8 -x + 2y - z =0 3x +2 z=9 I am attempting to solve for x,y, and z using the Gaussian elimination with scaled partial pivoting. I also need to show intermediate matrices and vectors. To be honest I am at a total loss on this one.

Integers

Express and explain -15.6x10^-20 as an integer multiple of 2.3x10^-20

Solving simultaneous linear algenraic solutions

Systems of equations... (Please see attachment for questions)

Solving simultaneous linear algebraic equations

Assistance and guidance in solving the attached problem Thanks!

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