How to handle Initial Value Problems using numerical techniques?
#WikiCourses
https://wikicourses.wikispaces.com/Topic+Initial+Value+Problems
https://eau-esa.wikispaces.com/Topic+Initial+Value+Problems
How to find the roots of Nonlinear Equations?
Newton-Raphson method is not the only way!
How about a system of nonlinear equations?
#WikiCourses
https://wikicourses.wikispaces.com/Topic+Roots+of+Nonlinear+Equations
Numerical Response for Initial Value Problems using Newmark Method.
#WikiCourses
https://wikicourses.wikispaces.com/Topic+Initial+Value+Problems
https://eau-esa.wikispaces.com/Topic+Initial+Value+Problems
What is a multiple dgree of freedom (MDOF) system?
How to calculate the natural frequencies?
What is a mode shape?
What is the dynamic stiffness matrix approach?
#WikiCourses
https://wikicourses.wikispaces.com/Lect04+Multiple+Degree+of+Freedom+Systems
https://eau-esa.wikispaces.com/Topic+Multiple+Degree+of+Freedom+%28MDOF%29+Systems
How to handle Initial Value Problems using numerical techniques?
#WikiCourses
https://wikicourses.wikispaces.com/Topic+Initial+Value+Problems
https://eau-esa.wikispaces.com/Topic+Initial+Value+Problems
How to find the roots of Nonlinear Equations?
Newton-Raphson method is not the only way!
How about a system of nonlinear equations?
#WikiCourses
https://wikicourses.wikispaces.com/Topic+Roots+of+Nonlinear+Equations
Numerical Response for Initial Value Problems using Newmark Method.
#WikiCourses
https://wikicourses.wikispaces.com/Topic+Initial+Value+Problems
https://eau-esa.wikispaces.com/Topic+Initial+Value+Problems
What is a multiple dgree of freedom (MDOF) system?
How to calculate the natural frequencies?
What is a mode shape?
What is the dynamic stiffness matrix approach?
#WikiCourses
https://wikicourses.wikispaces.com/Lect04+Multiple+Degree+of+Freedom+Systems
https://eau-esa.wikispaces.com/Topic+Multiple+Degree+of+Freedom+%28MDOF%29+Systems
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
How to derive the finite element model using the stationary functional approach?
Application to bars and beams!
#WikiCourses
https://wikicourses.wikispaces.com/TopicX+Stationary+Functional+Approach
https://eau-esa.wikispaces.com/Topic+Stationary+Functional+Approach
Jacobi Iteration Method is Used in Numerical Analysis. This slide helps you to figure out the use of the Jacobi Iteration Method to submit your presentatio9n slide for academic use.
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
How to derive the finite element model using the stationary functional approach?
Application to bars and beams!
#WikiCourses
https://wikicourses.wikispaces.com/TopicX+Stationary+Functional+Approach
https://eau-esa.wikispaces.com/Topic+Stationary+Functional+Approach
Jacobi Iteration Method is Used in Numerical Analysis. This slide helps you to figure out the use of the Jacobi Iteration Method to submit your presentatio9n slide for academic use.
Why would a company hire a trainer? To produce a change. The trainer by default is
an agent for change. Regardless of any results a trainer may accomplish, the bottom line is a
measurable change in employees’ performance.
What is marketing?
How to find out about customers?
How to reach them?
How to get them to know about you?
What is a product life cycle?
How about Marketing strategies?
Learn more ...
http://AcademyOfKnowledge.org
Brief description of current state of drones and some future challenges.
The presentation is prepared for delivery in the "Interact with Today's World" conference held in Bibliotica Alexandria 5-6 August 2016
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
2. ENEM602 Spring 2007
Dr. Eng. Mohammad Tawfik
Objectives
• The need for a system of ODE’s will be
clarified
• Transforming a higher order linear ODE
into a set of 1st
order ODE’s
• Applying the techniques of solution to a
set of 1st
order ODE’s
4. ENEM602 Spring 2007
Dr. Eng. Mohammad Tawfik
Transformation!
• Most of the numerical methods of solving
initial value problems handle 1st
order
initial value problems
• Most of the realistic problems involve 2nd
order initial value problems!
• A transformation must be performed!!!
6. ENEM602 Spring 2007
Dr. Eng. Mohammad Tawfik
Current in an LRC circuit
( )tE
C
q
Ri
dt
di
L =++
2
2
dt
qd
dt
di
dt
dq
i =⇒=Where:
Giving: ( )tE
C
q
dt
dq
R
dt
qd
L =++2
2
OR:
( )tE
C
q
qRqL =++
7. ENEM602 Spring 2007
Dr. Eng. Mohammad Tawfik
Introducing new variables:
• Let:
• Which gives:
• In matrix form:
qxqx == 21 &
( )tEx
LC
x
L
R
x
xx
+−−=
=
122
21
1
( )
+
−−
=
tEx
x
L
R
LC
x
x 0
1
10
2
1
2
1
8. ENEM602 Spring 2007
Dr. Eng. Mohammad Tawfik
In Matrix Form
{ } [ ]{ } { }uxAx +=
( )
+
−−
=
tEx
x
L
R
LC
x
x 0
1
10
2
1
2
1
10. ENEM602 Spring 2007
Dr. Eng. Mohammad Tawfik
Euler Method (No Excitation)
• The equation is:
• Applying Euler
method:
• Or:
{ } [ ]{ }xAx =
{ } { } [ ]{ }tttt xAtxx ∆+=∆+
ttt
x
x
L
R
LC
t
x
x
−−
∆+
=
∆+ 2
1
2
1
1
10
10
01
11. ENEM602 Spring 2007
Dr. Eng. Mohammad Tawfik
R-K 2nd
Order Method
• The equation is:
• Applying R-K 2nd
order method:
• Finally:
{ } [ ]{ }xAx =
{ } [ ]{ }txAk =1
{ } { }( )21
2
1
2
1
2
kk
t
x
x
x
x
ttt
+
∆
+
=
∆+
{ } [ ] { } { }( )12 ktxAk t ∆+=
12. ENEM602 Spring 2007
Dr. Eng. Mohammad Tawfik
Summary
• Revise the numerical solution of initial
value problems
• Rewriting the second order ODE as a set
of two 1st
order ODE’s
• Applying the numerical solution
techniques to a set of 1st
order ODE’s
13. ENEM602 Spring 2007
Dr. Eng. Mohammad Tawfik
Homework #9
1. Derive the Euler
formula for a system
of initial value
problems of the
form:
2. Use the above
formula to write
down the Euler
solution of excited
circuit in matrix form
{ } [ ]{ } { }uxAx +=
( )tEq
LC
q
L
R
q =++
1
