Mathematics Homework Solutions

Cubic Splines : Natural and Clamped

Please see the attached file for the fully formatted problems.

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.

Systems of Equations : Gaussian Elimination with Scaled Partial Pivoting

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.

Integers

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

Solving Simultaneous Equations Using MATLAB

Please see the attached file for the fully formatted problems.

Solving simultaneous linear algebraic equations

Assistance and guidance in solving the attached problem Thanks!

Obtaining a Target Number

Using the numbers 3, 3, 8 and 8 once and only once, obtain the target number of 24. (You have to use 3 twice and 8 twice - 3 x 8 = 24 is not acceptable). You may use only addition, subtraction, multiplication and division (eg. no factorial). Hint: no addition in the equation.

Use Monte Carlo integration to estimate the value of the double integral, try to find....

Use Monte Carlo integration to estimate the value of the double integral (x^2+y^2)/(1+y^2) over the unit circle. Try to find a 95% confidence interval in which the true value lies? What is the exact value?

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