48 Summary

We have now come to the end of our Numerical Methods discussion. We started with approximating the output of a function with Taylor Series and learned how to approximate the error. We then turned our attention to the Trapezoid Rule and Simpson’s Rules. All of which help us approximate integrals. We also learned how to approximate the errors, both maximum and average, for these methods. We moved on to the Newton-Raphson Method for finding roots of a nonlinear equation, and we saw how the Secant Rule is an alternative to the Newton-Raphson Method when the derivative is difficult to find. Lastly, we went through Gaussian-Seidel Iteration to solve a system of linear equations.