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Write about Numerical Approximation in Matlab and also answer questions from the file Questions.pdf

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NUMERICAL APPROXIMATION IN MATLAB

1. Theory and Background
The main theory is numerical calculations in Matlab. Unlike formal Mathematics, which is exact, Matlab does not know how to store real numbers. Thus all the calculations have rounding errors and this is what will be examined in this report.

In the first part we examine how to solve a system of linear equations that represent the forces applied to a certain system. We can solve this by inverting a matrix and we also examine how Matlab stores variables in vector or matrix form.

In the second part, the issue of computing complex functions like sine is examined. One of the ways to compute an approximation of the sine function numerically is by using its Taylor Series. The more we increase the number of terms, the more accurate the approximating function becomes. We then examine the error that results from using the approximation instead of using the exact function. We then go onto study how to compute the derivative of a function numerically by decreasing the step size. As the step size diminishes, we will see that the error decreases. However, when the step size becomes really small, of the order of 10-9, the rounding error kicks in and we lose accuracy....

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