1. Applied Numerical Methods
PowerPoint to accompany
Applied Numerical Methods
With MATLAB® for Engineers and Scientists
First Edition
Steven C. Chapra
Chapter 8
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

2. Graphical solution of a set of two simultaneous linear algebraic equations. The intersection of the lines
represents the solution.
Figure 8.1
8-1

3. Graphical depiction of singular and ill-conditioned systems: (a) no solution, (b) infinite solutions, and
(c) ill-conditioned system where the slopes are so close that the point of intersection is difficult to detect
visually.
Figure 8.2
8-2

4. The two phases of Gauss elimination: (a) forward elimination and (b) back substitution.
Figure 8.3
8-3

5. An M-file to implement naive Gauss elimination.
Figure 8.4
8-4

6. An M-file to implement the Gauss elimination with partial pivoting.
Figure 8.5
8-5

7. An M-file to solve a tridiagonal system.
Figure 8.6
8-6

8. Three reactors linked by pipes
Three reactors linked by pipes. The rate of mass transfer through each pipe is equal to the product of flow Q
and concentration c of the reactor from which the flow originates.
Figure P8.10
8-7

9. A noninsulated uniform rod positioned between two walls of constant but different temperature. The
finite-difference representation employs four interior nodes.
Figure P8.12
8-8