Engineering Analysis (650201 & 630201)€¦ · Engineering Analysis (650201) lec(1)-Introduction Instructor: Eng. Nada Email: [email protected] Philadelphia University Faculty

Engineering Analysis

(650201)

lec(1)-Introduction

Instructor: Eng. Nada

Email: [email protected]

Philadelphia University Faculty of Engineering

Communication and Electronics Engineering

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Course Outline

Course Title: Engineering Analysis (1) (650201)

Prerequisite: Engineering Mathematics (210206)

Text Book : Advanced Engineering Mathematics By: Erwin Kreyszig 8th edition.1999.

Credit Hours :3

Level :3rd year

Providing Dept. :Communications & Electronics Engineering

Instructor :Nada N Khatib

Office No: 730

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Course Contents

Basic Concepts & Ideas (ch.1)

First Order Differential Equations (ch.1)

Second & Higher Order Differential Equations

(ch. 2)

Laplace transform (ch. 5)

Power Series Method (ch. 4)

Introduction to Partial Differential Equations

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Text Book and References

Advanced Engineering Mathematics By: Erwin Kreyszig

8th edition.1999

Boyce, William E., DiPrima, Richard C., Elementary Differential Equations, Fifth Edition, Wiley, New York, 1992.

Rabenstein, Albert L., Elementary Differential Equations with Linear Algebra, Third Edition, Academic Press, New York, 1982.

Krusemeyer, Mark, Differential Equations, Macmillan Publishing Co., New York, 1994.

Elementary Differential Equations and Boundary Value Problems by W.E. Boyce R.C. Diprima. New York, NY, U.S.A. : John Wiley & Sons, Incorporated, 1986. “

: المعادالت التفاضلية" الدكتور عبد الرحمن القواسمي و المهندسة ندى نبيل الخطيب الطبعة االولى، طبع بدعم من جامعة فيالدلفيا، مطبعة الخط العربي" تطبيقاتها الهندسية

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Course Grading First Exam → (20%)

Second Exam→ (20%)

Quizzes and Homework → (20%) Three homework assignments and 3 quizzes

There is no late homework policy

The grade of each Homework assignment is 8

The grades assigned to Quizzes will be elements of {0, 1, 2, 3, 4}

Missed quizzes cannot be made-up

Final Exam → (40%)

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What is the derivative?

Definition 1

The rate of change of a function

Definition 2

The slope of the tangent line to the graph of a function

Definition 3

The best linear approximation of a function

All of these answers are correct

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What is the Differential Equation?

Differential Equation (DE):is an

equation containing the derivatives or

differentials of one or more dependent

variables, with respect to one or more

independent variables.

DEs are used to describe phenomena that

are in movement or change with time

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What is the Differential Equation?

The DE may contains also the unknown

function itself , as well as the given

function and constants

ttxxt cos32

txdt

dx

dt

xd32943

2

2

cos

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Mathematical Model

DE are of fundamental importance in

engineering mathematics because

many physical laws & relations appear

mathematically in the form of such

equations

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Mathematical Model

DEs describe (almost) everything in the world:

physics

chemistry

engineering

ecology

economy

weather

…

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Modeling

Modeling is the process of describing

a physical situation with a DE

It is the derivation of DEs from physical

or other problems

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Population Models

How does one predict the growth of a

population?

Human populations

Population of bacteria

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Population Models/Human populations

Growth rate is proportional to the

population present

Assume that people die only of natural

causes

Death rate is also proportional to

the population present

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Population Models/Human population

if P(t) represents a population in a

given region at any time t then

= Rate at which

P(t) enters the

region

-

Rate at which

P(t) exits the

region

kppkkdt

dpp )( 21

Rate of

change of

P(t)

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Population

kdtp

dpkp

dt

dp

cktp ee ln

cktp ln

ktecp

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Population Models/Population of bacteria

Reproduce by simple cell division

Parent cell does not die, but

become two new cells

Growth rate is proportional to the

population present pk

dt

dpp 1

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Heating and cooling of Building

How long does it take to change the

building temperature substantially?

How does the building temperature

vary during spring and fall when there

is no furnace heating or air condition?

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Heating and cooling of Building

How does the building temperature

vary in summer when there is air

condition?

How does the building temperature

vary in winter when there is furnace

heating?

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Newton’s law of cooling

Newton’s law of cooling, states that

the temperature of a hot or a cold

object decreases or increases at a rate

proportional to the difference of the

temperature of the object and that of its

surrounding.

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Temperature Problems

T= the temperature of a body at any

time (inside temperature)

)( sTTkdt

dT

Ts= the temperature of the surrounding

medium (outside temperature)

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Temperature Problems

H= additional heating rate

)()()( tUtHTTkdt

dTs

U= furnace heating (+ve)

U= air condition cooling (-ve)

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Pendulums

Determine the

displacement angle,

measured from the

vertical, as a function

of time in pendulums

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Pendulums

The swinging bob in a

grandfather’s clock &

A child’s swing

Are examples of

pendulums

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Mixing problems

The mixing of a

two fluids gives

rise to a DE

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25

Newton’s 2nd law of motion

an object of mass (m) is moving with

acceleration (a) that directly proportional

to the total force (F) acting on it and

inversely proportional to its mass

Fam

atv )( ath )(

we can rewrite the acceleration, a , in one of two ways

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Newton’s 2nd law of motion

Newton’s Second Law can now be written

as a differential equation in terms of either

the velocity, v, or the position

mgtvm )(

mgthm )(

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Newton’s 2nd law of motion

To find the velocity of

the body at any time in

case of free-falling

objects, we need to

solve the DE

mgtvm )(

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Newton’s 2nd law of motion

To find the position of

the body relative to the

ground in case of free-

falling objects, we need

to solve the DE mgthm )(

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Newton’s 2nd law of motion

To find the velocity of the sky driver at

any time

Mass-spring system

The motion of a

basic mechanical

systems (a mass on

an elastic spring)

are governed by

differential

equations.

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Satellite

To determine the

distance r, you

should use Newton’s

2nd law and universal

law of gravitation

then solve DE.

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Suspended Wire

To determine the shape of a wire hanging under its own

weight, such as a wire between two telephone line

poles, we must solve nonlinear DE

Electric circuit

The electric circuits (LR, RC, LRC) models are

differential equations

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Elastic Beam

An important fourth

order Differential

equation governs

the bending of an

elastic beam such

as wooden or iron

girder in a building

or a bridge

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What is the Differential Equation?

We can write any DE in either

following forms:

explicit form

),...,,,,( )1()( nn yyyyxfy

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What is the Differential Equation?

Implicit form

0),,,,...,,( )1()( xyyyyyF nn