Applied Numerical Methods PowerPoint to accompany Applied Numerical Methods With MATLAB® for Engineers and Scientists First Edition Steven C. Chapra Chapter 4 Copyright © 2005. The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

An example from marksmanship illustrating the concepts of accuracy and precision: (a) inaccurate and imprecise, (b) accurate and imprecise, (c) inaccurate and precise, and (d) accurate and precise. Figure 4.1 4-1

The approximation of f(x) = –0. 1x4 – 0. 15x3 – 0. 5x2 – 0. 25x + 1 The approximation of f(x) = –0.1x4 – 0.15x3 – 0.5x2 – 0.25x + 1.2 at x = 1 by zero-order, first-order, and second-order Taylor series expansions. Figure 4.2 4-2

Graphical depiction of (a) forward, (b) backward, and (c) centered finite-divided-difference approximations of the first derivative. Figure 4.3 4-3

A graphical depiction of the trade-off between round-off and truncation error that sometimes comes into play in the course of a numerical method. The point of diminishing returns is shown, where round-off error begins to negate the benefits of step-size reduction. Figure 4.4 4-4