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

2. 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

3. 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 at x = 1 by zero-order, first-order, and
second-order Taylor series expansions.
Figure 4.2
4-2

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

5. 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