CHAPTER 3
LU Decomposition and Matrix Inversion
1
LEARNING OUTCOME
At the end of the lecture students should be able to
solve linear equation system and finding matrix
inverse using LU decomposition.
2
LU DECOMPOSITION
Gauss elimination is designed to sol

CHAPTER 6
Gauss Quadrature
MOTIVATION
In the last lecture we studied the numerical
integration known as the Newton-Cotes equations.
A characteristic of these formulas was that the
integral estimate was based on evenly spaced
function values. Consequently,

Chapter 2
Roots of Equations
- Bisection Method
Roots of Equations
The
two major classes of methods
available to find roots of equations.
These methods can be distinguished by
the type of initial guess. They are
f (x)
1. Bracketing Methods
2. Open Method

CHAPTER 6
Numerical Differentiation
MOTIVATION
We have already introduced the concept of numerical
differentiation in Chapter 1. Recall that we employed
Taylor series expansions to derive finite-divideddifference approximations of derivatives. We develope

CHAPTER 5
Spline Interpolation
LEARNING OUTCOME
At the end of the lesson students should be able to
apply Cubic Spline to evaluate the value of f(x) for
any intermediate value of x.
INTRODUCTION
In the previous lecture, nth-order polynomials were used to

CHAPTER 6
Romberg Integration
MOTIVATION
In the last lecture we presented algorithm for
multiple-application of the trapezoidal rule and
Simpsons rule.
It shows that the estimate is getting closer to the
actual value as we progressively used more
segments

CHAPTER 5
Interpolation
LEARNING OUTCOME
At the end of the lesson students should be able to
use the Newton interpolation technique to evaluate
the value of f(x) for any intermediate value of x using
a set of the data points.
INTRODUCTION
oInterpolation i

CHAPTER 8
Boundary Value Problems and Fourier Series
SUPERPOSITION PRINCIPLE
If u1, u2, ., uk are solutions of a homogeneous linear partial
differential equation, then the linear combination
where c1, c2, ., ckuare
is also a solution.
c1uconstants,
1 c2 u

CHAPTER 8
Heat Equation and Laplaces Equation
D E R I VAT I O N O F T H E H E A T
C O N D U C T I O N E Q UAT I O N
The conduction of heat in a uniform bar (or in a thin wire)
depends on the initial distribution of temperature and on the
physical propert

CHAPTER 8
Finite Difference Method: Parabolic Equations
MOTIVATION
In the previous lectures we obtained the solution of the wave
equation
2
2
as
u ( x, t ) u ( x , t )
,
t 2
x 2
8
u ( x, t ) 2
0 x 20,
t 0,
c 1
1
n
nx
nt
sin
sin
cos
2
2
20
20

Chapter 2
Roots of Equations
- False-Position Method
Learning Outcome
At
the end of the lecture student should
be able to use the False-Position Method
to estimate the root of the equation.
False-Position Method
Let f (x)
be real and continuous function

CHAPTER 8
Partial Differential Equations
INTRODUCTION
An equation involving partial derivatives of an unknown function
of two or more independent variables is called a partial
differential equation, or PDE. For example:
2u
2u
2 xy 2 u 1
x 2
y
.(1)
3u

CHAPTER 7
Heuns Method
MOTIVATION
A fundamental source of error in Eulers method is
that the derivative at the beginning of the interval is
assumed to apply across the entire interval.
True solution of
differential
equation
True
Error
Predicted
slope
dy

Numerical Methods For
Engineers
Chapter 1 Error Analysis
Introduction
Numerical methods are techniques for solving problems
numerically using computer or calculator (in old days by
hand)
This method is capable in solving mathematical
problems which are

CHAPTER 3
Special Matrices
SPECIAL MATRICES
Banded Matrix:
A banded matrix is a square matrix that has all elements
equal to zero, with the exception of a band centered on the
main diagonal.
The dimensions of a banded system can be quantified by two
param

CHAPTER 7
Numerical Methods For Ordinary Differential
Equations
Eulers Method
LEARNING OUTCOME
After completing this chapter, students should have
greatly enhanced their capability to confront and
solve ordinary differential equations.
MOTIVATION
In descr

Numerical Differentiation
Chapter 1 Lecture 3
At the end of this session students should be able to
estimate the derivative using forward, backward and
centered finite divided difference.
Numerical Differentiation
The Taylor Series expansion (Forward Ta

CHAPTER 7
Multistep Methods
MULTISTEP METHODS
The one-step methods described in the previous
lecture utilize information at a single point xi to
predict a value of the dependent variable yi+1 at a
future point xi+1.
MULTISTEP METHODS
Alternative approache

CHAPTER 5
Lagrange Interpolating Polynomials
1
MOTIVATION
The Lagrange interpolating polynomial is simply a
reformulation of the Newton polynomial that avoids
the computation of divided differences. That is, the
Lagrange interpolating polynomial can be
de

CHAPTER 3
Linear Algebraic Equations
Learning Outcome
At the end of the lecture students should be able to solve
the linear equations by Nave Gauss Elimination.
Matrix notation
A rectangular arrangement of numbers (real or complex)
in m row and n column

Chemical Engineering Department
CCB 2033 - Heat Transfer Design
Assignment 1
Submission deadline: 24th June 2013
Considering the outside day temperature variation, find the maximum and minimum rate of heat
transfer in IRC, UTP.
What is the total heat tran

Heat Transfer Design
Conduction Heat Transfer
Dr. Rajashekhar Pendyala
Chemical Engineering Department
University Teknologi PETRONAS
Instructional Objectives
Explain Fouriers law for steady state one dimensional heat
conduction
Explain conduction in dif

Heat Transfer Design
Boiling and Condensation
Heat Transfer
Dr. Rajashekhar Pendyala
Chemical Engineering Department
University Teknologi PETRONAS
INSTRUCTIONAL OBJECTIVES
Explain the mechanisms for heat transfer
involving phase change, viz boiling and
c

Radiation Heat Transfer:
Funamentals
Dr. Khashayar Nasrifar
Department of Chemical Engineering
Universiti Teknologi Petronas
Learning Outcome
In this lecture, you will learn the fundamentals of
radiation heat transfer. In particular, radiation heat
transf

Radiation Heat Transfer
Dr. Khashayar Nasrifar
Department of Chemical Engineering
Universiti Teknologi Petronas
1
10/15/16
Course outcome
Define view factors (shape factors), and
understand its importance in radiation heat
transfer calculations
Develop vi

Lecture # 4
HEAT EXCHANGERS
Objectives:
Analysis of variable properties
Heat exchanger design consideration
1
10/15/16
Analysis for Variable Properties
Heat exchanger design depends on heat transfer coefficient
and the latter is a strong function of flui

Radiation Heat Transfer
Dr. Khashayar Nasrifar
Department of Chemical Engineering
Universiti Teknologi Petronas
Course Outcome
Calculate radiation heat transfer between black
surfaces.
Determine radiation heat transfer between diffuse
and gray surfaces in

Condensation Heat
Transfer
CONDENSATION AND
BOILING HEAT TRANSFER
Dr. Khashayar Nasrifar
Department of Chemical Engineering
Universiti Teknologi Petronas
Condensation
2
Condensation occurs when a saturated vapor comes
to contact with a solid whose surfac

This chapter deals with optimization
problems where constraints come into
play. The problems where both objective
function and the constraints are linear
will be discussed. For such cases, a
method called the linear programming
which could be used to solv

CHAPTER 6
Numerical Differentiation and Integration
LEARNING OUTCOME
After completing the lesson students should be able
to solve numerical integration problems and
appreciate their application for engineering problem
solving.
MOTIVATION
Calculus is the m

Chapter 4 Distillation Design
Subject: 1304 332 Unit Operation in Heat transfer
Instructor: Chakkrit Umpuch
Department of Chemical Engineering
Faculty of Engineering
Ubon Ratchathani University
1
What are you going to learn in this chapter?
4.1 Vapor-Liqu

SETTING UP THE LINEAR
PROGRAMMING PROBLEM
Suppose that a gas-processing plant receives a fixed
amount of raw gas each week. The raw gas is
processed into two grades of heating gas regular
and premium quality. These grades of gas are in high
demand (they a