# Equations, linear algebrae, interpolation, quadrature, Numerical DEs

Equations, linear algebrae, interpolation, quadrature, Numerical DEs 150 150 Affordable Capstone Projects Written from Scratch

Quiz 1 – Equation

Choose any equation from questions 7. Show how to solve it using each of the methods:

(a) Direct iteration,

(b) Newton-Raphson method,

(c) Secant method,

(d) Bisection method,

(e) Method of false position.

Write down all the calculator commands you used, and all the output you obtained. If you wrote or used some programs, list them.

Quiz 2 – Linear Algebra

(1) A single 3 × 3 example from questions 1, 2 or 3, (picture above) for both Gauss-Seidel and Jacobi methods.

(2) A single 4 × 4 example from questions 2 or 3, (picture above) for both Gauss-Seidel and Jacobi methods.

(3) One of your choices from questions (1) and (2) but using LU factorization.

Quiz 3 – interpolation

1. Find the interpolating polynomial through the points:

x:   −2     −1      1     3      4

y:   101    26    −4    6     71

using

(a) Lagrange’s formula,

(b) divided differences.

1. Using Neville’s method, find y(2) from the data given in question 1.
2. Use the Newton-Gregory formula to find the interpolating polynomial through the points

x:     −3          −1         1          3               5

y :   185       −31     −39      −367      −1159

1. Find an approximation to the sum of the series

1. Choose either integral I1 compute both the trapezoidal and Simpson’s rule with 10 intervals.

1. integral of I2, compute it using Romberg integration.

1. Compute of I3 using Gaussian quadrature of orders 2, 3 and 4.

Quiz 5 – Numerical DEs

TO GET THIS OR ANY OTHER ASSIGNMENT DONE FOR YOU FROM SCRATCH, PLACE A NEW ORDER HERE