Bisection Methods Aplication

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 of the graph of $f$ ...

Solutions of Equations of One Variable With The Bisection Method

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

Round-Off Error and Computer Arithmetic

The arithmetic performed by a calculator or computer is different from the arithmetic that we use in our algebra and calculus courses. From...

Taylor polynomial and Maclaurin polynomial

[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 $[a,b]$. For every $x$ in $[a,b...

Mathematical Preliminaries and Error Analysis Part 2

Review Of Calculus The integral is the other basic concept of calculus that is used extensively.The Riemann integral of the function...

Mathematical Preliminaries and Error Analysis

1.1 Introduction This part examines problems that can be solved by methods of approximation, techniques we call numerical methods. We b...