Numerical Methods

The equation $f(x)=x^3+4x^2-10=0$ has a root in $[1,2]$ since $f(1)=-5$ and $f(2)=14$. It is easily seen from a sketch…

In this chapter we consider one of the most basic problems of numerical approximation, the root finding problem. This…

The arithmetic performed by a calculator or computer is different from the arithmetic that we use in our algebra and c…

[Taylor’s Theorem] Suppose $f\in C^{n}[a,b]$ and $f^{(n+1)}$ exists on $[a,b]$. Let $x_{0}$ be a number in $[a,b]$. F…

1.1 Introduction This part examines problems that can be solved by methods of approximation, techniques we call nu…