Solved Examples on Statistics
References:
SPIEGEL, M. R., and Stephens, L.J. (2008). Schaum's Outline of Theory and Problems of
Statistics. McGraw Hill, Fourth Edition.
The Range
The range of the set 2, 3, 3, 5, 5, 5, 8, 10, 12 is 12 -2 = 10. Sometimes th

Chapter 2
Numerical Methods for Parabolic PDE
2.1
Introduction
Parabolic PDE arising in scientific and engineering problems are often of
the form
u t = L (u )
(1)
nd
where L (u ) is a 2 order PD operator (linear or non-linear).
Physical examples are: d

Dynamic Behavior of Measuring System
1
Introduction
The material given in this module is taken from B. Wayne Bequette (2003).Process Control: Modeling,
Design, and Simulation.Prentice Hall
Free vibration (no external force) of a single degree-of-freedom s

Numerical Methods in Energy Science
MEP 602
Lecture 6
Parabolic Partial Differential Equations
Dr. Hesham Othman
Mechanical Power Dept.
Cairo University, Egypt
Building 17, 3rd floor, Room 303
Office hours: Monday: 13:00-14:00
Most of the materials presen

Chapter 1
FUNDAMENTALS
1.1
Classification of physical problems
The majority of the problems of physics and engineering fall naturally
into one of the following three physical categories:
Equilibrium
Problems
Eigenvalue
Problems
Propagation
Problems
Equi

Numerical Methods in Energy Science
MEP 602
Lecture 5
Elliptic Partial Differential Equations
(Cont.)
Dr. Hesham Othman
Mechanical Power Dept.
Cairo University, Egypt
Building 17, 3rd floor, Room 303
Office hours: Monday: 13:00-14:00
Most of the materials

Example of Temperature Measurement Uncertainty
Source:
Gupta, S.V. (2012). Measurement Uncertainties - Physical Parameters and Calibration
of Instruments. Springer-Verlag Berlin Heidelberg.
270
11 Uncertainty in Calibration of Some More Physical Instrumen

Numerical Methods in Energy Science
MEP 602
Lecture 3
Elliptic Partial Differential Equations
(Cont.)
Dr. Hesham Othman
Mechanical Power Dept.
Cairo University, Egypt
Building 17, 3rd floor, Room 303
Office hours: Monday: 13:00-14:00
Most of the materials

Formula sheet
=
Elliptic Partial Differential Equations
1. Taylor formulas:
2. The 2nd order centered space approximation of Laplace equation
3. The 2nd order centered space approximation of Poisson equation
Where
4. The Gauss-Seidel Method
5. The Success

FM
FORCE and PRESSURE MEASUREMENT
UNITS OF FORCE
Pound Force
- lbf
Newton
-N
Kilogram Force
- kgf
1 lbf = 0.454 kgf = 4.45 N
TYPES OF FORCE MEASURING DEVICES
Mechanical Balance
a
b
W2
c
W1
W3
From simple statics,
=
W3
=
or
1
FM
2
Proving Ring
b
F
F
r
t
Di

Numerical Methods in Energy Science
MEP 602
Lecture 4
Elliptic Partial Differential Equations
(Cont.)
Dr. Hesham Othman
Mechanical Power Dept.
Cairo University, Egypt
Building 17, 3rd floor, Room 303
Office hours: Monday: 13:00-14:00
Most of the materials

METU
Circuit Analysis
Circuit Analysis
by
Prof. Dr. Osman SEVAOLU
Electrical and Electronics Engineering Department
EE 209 Fundamentals of Electrical and Electronics Engineering, Prof. Dr. O. SEVAOLU, Page 1
Circuit Analysis
METU
What is an Electrical Cir

Post-Graduate Courses
An Approach to the Estimation of Measurement
Uncertainty
2
1 Introduction
1.1 Purpose of the Measurement Process
Measurement is the process of experimentally obtaining one or more quantity values that can
reasonably be attributed to

1.5
Uncertainty Calculations
R. H. DIECK
(2003)
The purpose of this section is to outline the fundamental methods of measurement uncertainty analysis for use as an objective
estimator of data quality. These methods apply to all test, evaluation, and proce

Numerical Methods in Energy Science
MEP 602
Lecture 1
Elliptic Partial Differential Equations
Dr. Hesham Othman
Mechanical Power Dept.
Cairo University, Egypt
Building 17, 3rd floor
Office hours: Tuesday: 10:15-12:15
Most of the materials presented here a

Numerical Methods in Energy Science
MEP 602
Lecture 7
Parabolic Partial Differential Equations
(Cont.)
Dr. Hesham Othman
Mechanical Power Dept.
Cairo University, Egypt
Building 17, 3rd floor, Room 303
Office hours: Monday: 13:00-14:00
Most of the material

Measurement Uncertainty Examples
1 Simple Example for Calculation of Measurement
Uncertainty
Example (Ref. [1])
Calculating the uncertainty in the length of a piece of string using a tape
measure, Figure 1.
Figure 1. Measurement of string length using a t

MEP 514 Measurements and Control
Dynamic Behavior of a Measurement System
1 Introduction
Measurement systems are often subject to inputs that vary with
time. The purpose of this module is to introduce the student to the
behavior of measuring systems when

The circuit in Fig. 4.64 represents an unbalanced bridge. If the galvano-
meter has a resistance of 40 52, nd the current through the galvanometer.
220 V
Figure 4.64 Unbalanced bridge of Example 4.13.
Solution:
We rst need to replace the circuit

Thevenin and Norton Circuits
Thevenin
Norton
A Thevenin circuit has a voltage source in series with a resistance, while a
Norton circuit has a current source in parallel with a resistance. The key point is
that both circuits will deliver the same voltage

Week 5 Temperature Measurement
After time, temperature is the second most measured physical
unit.
Temperature Sensing Techniques (see Table 16.1)
Changes in Physical Dimensions
Bimetallic Thermometers
Filled-Bulb and Glass-Stem Thermometers
Changes in

CHAPTER 13
PROBABILISTIC RISK
ANALYSIS
RANDOM VARIABLES
Factors having probabilistic outcomes
The probability that a cost, revenue, useful life,
or other economic factor value will occur, is
usually considered to be the subjectively
estimated likelihood

CHAPTER 10
DEALING WITH
UNCERTAINTY
RISK
Risk and uncertainty are similar in that
they both present the problem of not
knowing what future conditions will be
Risk offers estimates of probabilities for
possible outcomes
Uncertainty does not provide esti

CHAPTER
CHAPTER 11
$
$
INTRODUCTION
INTRODUCTION TO
TO
ENGINEERING
ENGINEERING ECONOMY
ECONOMY
$
$
WHAT
WHAT IS
IS ECONOMICS
ECONOMICS ?
?
The
The study
study of
of how
how limited
limited
resources
resources is
is used
used to
to
satisfy
satisfy unlimite

CHAPTER 11
EVALUATING PROJECTS WITH THE
BENEFIT / COST RATIO METHOD
XX
XXXXXX
XXXXXX
X
XXXXXXX
XXX
$
PRIVATE VERSUS PUBLIC PROJECTS
PURPOSE
PURPOSE
Private
Private Project
Project - Maximize
Maximize profit,
profit, minimize
minimize costs
costs
Public
P

CHAPTER 7
COST
ESTIMATION
TECHNIQUES
TECHNIQUES
TECHNIQUES FOR
FOR ESTIMATING
ESTIMATING COSTS
COSTS /
REVENUES
REVENUES
The
The Index
Index
A
A dimensionless
dimensionless number
number that
that shows
shows how
how prices
prices /
costs
costs vary
vary

CHAPTER 12
ENGINEERING ECONOMY
STUDIES IN INVESTOR-OWNED
UTILITIES
INVESTOR-OWNED UTILITIES
Investor-owned utilities provide services:
Gas
Electric power
Water
Telephone communications
Environmental Protection
Some types of transportation
Etc
UTILIT

CHAPTER 2
COST CONCEPTS AND THE
ECONOMIC ENVIRONMENT
COST ESTIMATING
Used to describe the process by
which the present and future cost
consequences of engineering
designs are forecast
COST ESTIMATING USED TO
Provide information used in setting a selling

CHAPTER 8
PRICE CHANGES AND
EXCHANGE RATES
GENERAL
GENERAL PRICE
PRICE INFLATION
INFLATION
An
An increase
increase in
in the
the average
average price
price
paid
paid for
for goods
goods and
and services
services
bringing
bringing about
about aa reduction