CHEN 320 - Numerical Methods
Numerical Methods for Engineers
Steven C. Chapra and Raymond P. Canale
Dr. Tahir Cagin
Rm: 241, JEB Building E-mail: cagin@che.tamu.edu
Classes
12:40 13:30 MWT CHEN 104
Exams:
MON, 2/11; 7-9PM MON, 3/17; 7-9PM MON, 4/

Example on how to convert a real number into binary and into floating point notations
by
Prof. J. Seminario
1) Convert 265.302 into binary
Since 265.302 = 265 + 0.302
First we convert the integer 265 into binary by successive integer divisions recording t

Chapter 1
Introduction
Overall Course Objective
Learn how to effectively solve engineering
equations using MATLAB.
Detailed Course Objectives
Be able to classify the type of equation
undertaken.
Select the appropriate MATLAB built-in
function.
Properl

Chapter 3
Single Nonlinear Equations
Example of nonlinear equation:
Ideal gas law
P is the absolute pressure of the gas
V is the volume of the gas
n is the amount of substance of gas (moles)
T is the absolute temperature of the gas (K)
R is the ideal

Chapter 4
Systems of Linear Equations
Systems of Linear Equations
Almost all advanced numerical methods
ultimately result in a series of linear equation
solutions. Therefore, the feasibility and
computational efficiency of advanced
numerical methods is d

Chapter 2
An Introduction to MATLAB
MATLAB Overview
MATLAB: Matrix Laboratory
MATLAB provides a convenient user interface
for numerical equation solving, graphical
display and symbolic manipulation.
MATLAB uses a large set of highly optimized
FORTRAN c

CHAPTER 2
2.1
IF x < 10 THEN
IF x < 5 THEN
x=5
ELSE
PRINT x
END IF
ELSE
DO
IF x < 50 EXIT
x=x-5
END DO
END IF
2.2
Step 1: Start
Step 2: Initialize sum and count to zero
Step 3: Examine top card.
Step 4: If it says end of data proceed to step 9; otherwise,

Special Matrices and Gauss-Seidel
Chapter 11
Certain matrices have particular structures that can be exploited to develop efficient solution schemes.
A banded matrix is a square matrix that has all elements equal to zero, with the exception of a band ce

Programming and Software
Chapter 2
Objective is how to use the computer as a tool to obtain numerical solutions to a given engineering model. There are two ways in using computers:
Use available software Or, write computer programs to extend the capabil

Approximations and Round-Off Errors
Chapter 3 For many engineering problems, we cannot obtain analytical solutions. Numerical methods yield approximate results, results that are close to the exact analytical solution. We cannot exactly compute the errors

Truncation Errors and the Taylor Series
Chapter 4
Non-elementary functions such as trigonometric, exponential, and others are expressed in an approximate fashion using Taylor series when their values, derivatives, and integrals are computed. Any smooth f

Solutions of Nonlinear Equations and Systems of Equations
Why?
ax 2 + bx + c = 0 b m b 2 4ac x= 2a
But
5 + 4 + 3 + 2 + + = 0 = ? sin + = 0 = ?
Nonlinear Equation Solvers
Bracketing
Graphical
Open Methods
Bisection False Position (Regula-Falsi)
Newton Raph

Open Methods
Chapter 6
Open methods are based on formulas that require only a single starting value of x or two starting values that do not necessarily bracket the root.
Figure 6.1
Fig 6.1
Simple Fixed-point Iteration
Rearrange the function so that x is

Roots of Polynomials
Chapter 7 The roots of polynomials such as
f n (x) = ao + a1x + a2x + K + an x
2
n
Follow these rules: 1. For an nth order equation, there are n real or complex roots. 2. If n is odd, there is at least one real root. 3. If complex roo

Linear Algebraic Equations
Part 3
An equation of the form ax+by+c=0 or equivalently ax+by=-c is called a linear equation in x and y variables. ax+by+cz=d is a linear equation in three variables, x, y, and z. Thus, a linear equation in n variables is a1x1

LU Decomposition and Matrix Inversion
Chapter 10
Provides an efficient way to compute matrix inverse by separating the time consuming elimination of the Matrix [A] from manipulations of the right-hand side cfw_B. Gauss elimination, in which the forward e