A Scheme Of The Department Of Education

A Scheme Of The Department Of Education
Part A: Scheme of work
The basis of this essay will discuss at a scheme within mathematics. Per the Department of Education (DfE) (2013) "mathematics is a creative and
highly interconnected disciplines that have been developed over centuries......... It is essential to everyday life, critical to science, technology and
engineering, and necessary for financial literacy and most forms of employment." The substance of maths is divided into five reasons; significance it
has in everyday life, its use within other curricular areas, the pupil can develop intellectually, pupil's enjoyment of learning and has a distinctive place in
pupil's human knowledge and culture (Haylock & Manning 2014). The scheme is based on six lessons it will consider EAL learners, ability based
differentiation, assessment and motivation. The second section of the essay will explore further in to motivation and how and why this is important to
the teacher, pupils, classroom for effective learning of the subject. It will then look at the consider the implications within the class and to personal
development as a teacher.
The scheme is based on a year 2 class, looking at place value through partitioning, one more, one less and ten more, ten less. I have chosen this due to it
being the key focus within the curriculum for key stage 1 learners. The aim by the completion of Key stage 1 stands that pupils have a strong
understanding, confidence and mental fluency with whole numbers, counting and place value (DfE,
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Phd In Computational Engineering Statement
STATEMENT OF PURPOSE– PhD in Computational Engineering??
"In this mighty world many blabber about their dreams, but who identified their paths and persistently stuck on their words are the few ones, who are
known famous to the world. Being remained unknown would be my greatest regret. My path to chase my dreams is Mechanical Engineering, for a
proud mechanical engineer can say, "When we rest, the world rusts!"
I have had a special interest in mechanical engineering since my childhood, as I grew up watching my father develop complicated equipment for
power plants. Hence, I opted for a mechanical engineering course for my UG program. The concept of computational science and engineering which
uses numerical approaches to characterize, predict and simulate physical events and engineering systems using the laws of mechanics fascinated me. To
understand their advanced methodologies, I have pursued a Master's degree in CAD/CAM from VIT .
The courses in my PG program included Finite element methods, Applied engineering mathematics, Advanced stress analysis, Advanced strength of
materials, Advanced vibration engineering, Computational methods in heat and fluid flow etc. which gave me a greater knowledge in mechanical and
mathematical field. As a part of my Master's degree internship ... Show more content on Helpwriting.net ...
I have accumulated valuable experience in Multi physics analysis. Computational mechanics is a fascinating field in which learning feels like never
ending adventure. After exploring CAE tools like ANSYS Mechanical, ANSYS CFX etc., the thought like rigid body deflection of deflector due to
fluid velocity, is still not numerically solved. I feel that time has come for me to research in refining the problem solving approach than to solve
engineering

The Effect Of Chewing Gum On Cognitive Processing
Some reports have suggested that chewing gum might improve the performance in memory task, although other studies have not confirmed this effect
of chewing. Little is known about the brain activity and the task performance while chewing gum. Near–infrared spectroscopy is a spectroscopic
method that uses the near infrared region of the electromagnetic spectrum(what does this mean). Put in my own words, describe what it
means.Near–infrared spectroscopy is a useful tool for investigating brain function and can measure brain activity during bodily movements. Wadi et
al.'s purpose of the study was to "clarify the effects of chewing gum on cognitive processing during and after chewing gum, using NIRS–based
measurement of cerebral hemodynamic response." They investigated the effect of chewing on the hemodynamic changes in this brain region, using
NIRS (Hoshi et al., 2000), and the performance of subjects in a short–term memory task involving serial recall of random eight–digit numbers. The
study asked for 30 healthy volunteers(is this enough to make conclusive) with no history of neurological, psychiatric, temporomandibular joint
disorders. The volunteers were asked to recall random eight digit numbers. They sat in a dimly lit room in front of a PC monitor and the a series of 8
digit numbers flashed on the screen for two seconds. They were then told to type out the numbers and the PC proceeded to flash a new 8 digit number
when they had finished typing the previous number. The

Analysis Of Ryan 's ' The Flies '
Similar to a circle, Ryan 's face is rounded just enough for his Aunt to love it. Despite a chubby face and fingers, his body is small. Fragile. In the
six years of his life he has come to enjoy learning new concepts. He understands that to draw a house he must start with a square base. A roof is
nothing more than a triangle on top. Add two squares for Windows and a rectangle for a door and Ryan has drawn a squiggly lined house. Red.
Yellow. Green. One plus two equals three. Ryan understands these concepts, because they 're easy to control.Understanding becomes hard when the
shapes are replaced by feelings, and the colors and numbers are replaced by people. Why is it hard to be understanding towards one another? How
come it is difficult to put myself into someone else 's shoes and say they had every right to mock me. Could it be because I am too simpleminded
to understand? Or, is it because I am too unwilling to let myself be carried away by someone else 's life. If they refuse to accept my world, then
why should I try to understand theirs? It 's that kind of thinking that keeps me from truly enjoying life. When I fail to see the rough aspects in
others lives, it not only makes them, but also me, feel frustrated as well. I know how it feels to be unheard. I know how it feels to have someone
watch me talk, but ignore my words; like I wasn 't there to begin with. Who am I if my peers are willing to treat my voice as if it was nothing more
than a gust of air? I crash

Evaluation of Various Numerical Methods for Option Pricing...
In finance, a derivative is a financial instrument whose value is derived from one or more underlying assets. An option is a contract which gives the
owner the right, but not the obligation, to buy or sell the asset at a specified strike price at the specified date. The derivative itself is just a contract
between two or more parties. Its value is determined by fluctuations in the value of the underlying asset. This price is chosen so that the value of the
contract to both sides is zero at the outset, which means that the price is fair, so neither party is taking advantage of the other. Hence, numerical
methods are needed for pricing options in cases where analytic solutions are either unavailable or not easily computable. The subject of ... Show more
content on Helpwriting.net ...
This method is widely used as it is able to handle a variety of conditions. Finite difference methods were first applied to option pricing by Eduardo
Schwartz in1977. In general, finite difference methods are used to price options by approximating the differential equation that describes how the
option price moves over time by a set of difference equations. This method arises since the option value can be modeled by partial differential
equations, such as the Black–Scholes PDE. This approach has the same level of complexity tree methods. The application of Monte Carlo method to
option pricing was by Phelim Boyle in 1977. In terms of theory, Monte Carlo valuation relies on risk neutral valuation. The technique is to generate
several thousand possible random price paths for the underlying asset and via simulation, and to calculate the average payoff of each path. This
approach is particularly useful in the valuation of options with complicated features, which would be difficult to value through straightforward
Black–Scholes style or tree model. ( reference [3] Valuation of Options)
Each of these methods has its own advantages and disadvantages. The comparison of accuracy and consistence are presented and suitable method for
each situation is discussed.
Then the report briefly goes through some exotic options and implements the numerical solutions with binomial tree method. These options, includes
American option which can be exercised any time before the

Examples Of Josephus Problem
The next base the essay will explore is base 3 also known as ternary, this is the base that was used in the original Josephus problem. By exploring this
base and a few more bases, I will find a pattern and derive an equation to solve Josephus problem with any number of people in any number base.
Josephus problem in base 3 is when each person kills the person who sits two seats away from him and the following diagram will demonstrate how it
happens, the numbers on the inside show the order of the people that are gone which will make it easier to follow.
Figure 7 An example of how Josephus problem works in base 3 with 12 people
I will now create the same table as I did for the problem in a binary form.
Table 3 Analyzing the Josephus problem in base 3 when1в‰¤nв‰¤12
Number of people
()
Order in which people are gone
The winning number
1
1
1
2
1,2
2
3
3,1,2
2
4
3, ... Show more content on Helpwriting.net ...
Applying the equation to Josephus problem, to find we have to find as . We know how to solve as there are only 2 people and starts meaning he has to
skip and therefore dies first and wins. Now we know that , we can see from the table above the answer is correct however we have to do it once more
to find .

We can always consider position and we have to repeat the equation until getting to the required number. This solution can be very frustrating as you
must do the same thing over and over, however it can be programmed very easily and save a lot of time.
This method is the third and the last method to solve the Josephus problem, it is the most useful method as it works for all bases however it is the
most complicated one. In order to compare between this method and the other two methods, we first have to write the equation in base

Essay About My Math Teaching Experience
My math teaching experience went with students who are in third grade. In my group I had four students, where was one ELL student. They were
struggling in math as per their teacher, especially in subtracting big numbers with zeroes. I had to reteach subtraction, three or two digit number, as
needed, from three digit number. And concentrate on subtractions from zeroes. Everything started great, the kids were exiting, as of they are going
out of the room. We sat down in the hall and it was not comfortable.The kids were sitting near the wall, I was sitting in front of them in the middle
of the walking area. As of kids were sitting on the floor and me too, we were several times distracted by other kids or adults, who was walking
through the hall, it was always disturbing us. I started my lesson with math solving problem and my students easy were able to figure out what
operation that needs to do. They all said subtraction. I said great. Then, I asked them to solve this problem independently. Student 1, was just sitting,
Student 2 used her fingers to count, Student 3 did very fast, but not correctly and Student 4 just copied that incorrect answer. Then, I asked to share
their answers. Student 3 raised her hand and said, it was easy, we have 0–9, will be 9. Then 0–5, will be 5. Then 4–2 will be 2. So, the answer is 259.
From this answer I understood, that my students understand that ones must be under one, and tens under tens, hundred under hundred, but students

A flat plate solar collector has a dynamic behaviour in...
A flat plate solar collector has a dynamic behaviour in response to variations in the intensity of solar radiation at different times of the day and also
variations in weather conditions. The characteristics governing the input–output behaviour of a flat plate collector can be described by a mathematical
model which serves as a prerequisite for simulation and control. The steady state and transient characteristics of flat plate solar collectors have been
studied in cite{Hilmer1999Solar,Dhariwal2005Solar,deRon1980,RodriguezHidalgo2011,Refaie1980}. Depending on the complexity of the flat plate
solar collector under observation, deriving a mathematical model may lead to a high order model which requires high computational effort and longer...
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Improvements to the original frequency weighted balanced truncation by Enns have been described in
cite{Ghafoor2007PFE,SreeramSahlan2012,SreeramSahlanMudaPFE2013}. Schelfhout and Moor pointed out that many specifications and robustness
requirements yield natural frequency domain weighting functions but in other cases time domain weighting functions are more appropriate which led
to the introduction of time weighted controllability and observability gramians for the balanced truncation algorithm cite{SchelfhoutMoor1995}.
Sreeram had defined the frequency response error bounds for time weighted balanced truncation cite{TimeWeightedSreeram2002}. More recently
Shaker and Tahavori had introduced time weighted balanced stochastic truncation cite{TahavoriShaker2012,TahavoriShaker2011}. Cross gramians
matrices contain information regarding both controllability and observability of a system in a single matrics
cite{FernandoNicholson1983,FernandoNicholson1984}. Instead of computing two separate gramians for controllability and observability, states
which are the least controllable and observable can be identified from a single cross gramian matrics and these states can be truncated. Model reduction
using cross gramians does not involve balancing which is an advantage since balancing may be ill conditioned for systems with almost uncontrollable
and unobservable states cite{Aldhaheri2006}.

Description And Description Of A Calculator
<!DOCTYPE html> CALCULATOR body{ margin: 0px; padding:0px; } main section{margin: 20px;} #calc_body, #calc_header{ background
–color:
#BFBABE;} main section table {padding: 20px; border–radius: 10px; border–spacing:0px; border–collapse:collapse;} table, th, td
{display:inline–block; padding:0;float:left;} #heading{ text–align: center; font–size:23pt; color: black; font–weight:bold; text–transform: uppercase;}
main section table tr td button{ height: 70px; display:block; width: 90px; font–size: 22pt; border:0; } .longbutton{ height: 70px; width: 180px; margin:
0; text–transform: uppercase; font–size: 22pt;} main section table tr td button:hover{ background–color: #E990C0; font–weight: bold; } #display
{width: 540px; height: 80px; background–color: #B0EEDB; font–size: 25pt; border:none; outline:none; text–align:right; margin–bottom:15px;} #expr{
width: 540px; height: 80px; background–color: #B0EEDB; font–size: 13pt; border:none; outline:none; } #Trig{font–size: 26pt;}
.orangebuttons{background–color:#F99B58; } .orangebuttons:hover{ background–color:#FBB888;} .operators{ background–color:#7B8EF8;}
.operators:hover{ background–color:#B6C0FA;} #equalsign{background–color:#343436; color:white;} #equalsign:hover{
background–color:#959699;} Calculator log2 Rads

Thinking, Fractions And Decimals
Teaching students effectively in areas of multiplicative thinking, fractions and decimals requires teachers to have a true understanding of the concepts
and best ways to develop students understanding. It is also vital that teachers understand the importance of conceptual understanding and the success
this often provides for many students opposed to just being taught the procedures (Reys et al., ch. 12.1). It will be further looked at the important
factors to remember when developing a solid conceptual understanding and connection to multiplicative thinking, fractions and decimals.
When teaching mathematical concepts it is important to look at the big ideas that will follow in order to prevent misconceptions and slower
transformation ... Show more content on Helpwriting.net ...
C., 2015, p. 3).
Symbolic representation using base–ten and expanded algorithms is a way to show students the written connection to the visual models used. The
partial–products algorithm is a more detailed step–by–step process and therefore more advisable to avoid errors in students learning to grasp the
procedure (Reys ch.11.4). This process allows students to visualise the distributive property more easily. However, the standardmultiplication
algorithm is quicker and acceptable for students, if the teacher feels they have complete understanding of the steps in the partial–products algorithm.
Multiplication by ten gives students opportunity to explore larger numbers, and can also be extended on(Reys et al. ch. 11.4). In addition, multiples of
10 give students the knowledge that all digits move left one place and an additional place hundreths. This concept can be used to introduce the decimal
place which is also moving place each time something is multiplied by tens. Exposing students to a range of examples which displays patterns that
occur when multiplying by tens and hundreths will generate meaning of digits moving place (Reys et al., ch. 11.4).
Visual models known as arrays or grids can be introduced early to assist students thinking by providing a visual representation when going from adding
to multiplying. In addition, arrays are a great

Essay On Fourier Analysis
In numerical analysis, explicit and implicit approaches are used to obtain numerical approximations of time dependent ordinary and partial differential
equations. Fractional order differential equations are used widely for finance market analysis. Implicit solution methods require more computational
efforts and are complex to program. In order to overcome these difficulties, explicit method for fractional order differential equation has been
introduced which is one of the most recently developed areas in the world of finance. The main aim of this paper is to investigate stability of
Fractional Explicit method for qth order time fractional Black–Schols equation by the well known Fourier analysis method and a numerical experiment
is presented for comparison of European call option prices for different values of 'q'.
Keywords– Fractional calculus; Fractional Explicit Method; stability; European call options; time fractional Black–Schols equation; Fourier analysis.
MSC 2010 No.: 26A33, 65M06, 65TXX.
Introduction
In Numerical analysis, the use of Fractional calculus is increasing day by day. The field of fractional calculus is not new for mathematicians. It is as
old as in the year 1695 , when L'Hopital sent a letter to Leibniz asking him an important question about the order of the derivative, " What would be the
result if order of derivative is ... Show more content on Helpwriting.net ...
After introduction 1, the next section 2, will review the working of Fractional Explicit method. Section 3 is based on the stability analysis of the
method. In section 4, there is a numerical experiment analyzing the performance of Fractional Explicit method for different values of 'q'. Data for
this experiment is taken from historical data section of NSE website of jet airways of the period from 1st November 2016 to 30th November 2016.
Graphical representation is given for the more precise comparison. Finally in section 5 there is concluding remarks for the

Assignment 1: Finite Element Analysis Essay
[pic] ENGD3016 Solid Mechanics Assignment 1: Finite Element Analysis Name: Wei Zhang ID: P14021978 Date: Dec17th 2015 Abstract 1.0
Introduction 2.0 Objectives 3.0 Matlab 4.0 Solidworks 4.1 Model of truss 1 4.2 Model of truss 2 5.0 Comparison of the two trusses 6.0 Comparison
between MATLAB and SOLIDWORKS 6.1 Comparison of results 6.2 Advantages and disadvantages 7.0 Conclusion Appendix Abstract The purpose
of this report is to based on two different 2D pictures of trusses to finite element analysis from two ways. First carried... Show more content on
Helpwriting.net ...
To construct a part to be analysed on Algor software and to find relevant deflections stresses and strains using the software. To compare the two
methods of finite element analysis outlining strengths and drawbacks of each. To decide on an appropriate box size, and material for the truss taking
into account its intended use. 3.0 Matlab First, the truss of materials selection, use of the material information shown in the following tableAISI 4130
Steel, annealed at 865C |Elastic |Poisson's Ratio|Shear Modulus |Mass Density |Tensile |Yield Strength |Thermal |Specific | |Modulus | | | |Strength |
|conductivity |Heat | |2.05e+011N/m^|0.285N/A |8e+010N/m^2 |7850kg/m^3 |560000000N/m^2 |460000000N/m^2 |42.7W/(mВ·K) |477J/(kgВ·K) |
|2 | | | | | | | | E = 2.05E11 The thickness of the steel pipe 2mm, so that the outer diameter of 20mm, an inner diameter of 16mm. Architecture sectional
area A=20*20–16*16=144 mmВІ=0.000144

Identifying Error Patterns Of Computation
Identifying Error Patterns in Computation
According to Ashlock, not only do students need to understand computations of arithmetic, but also need to have computational fluency, in other
words, conceptual understanding. As stated in Principles and Standards for School Mathematics: Knowing basic number combinations – the single–digit
addition and multiplication pairs and their counterparts for subtraction and division – is essential. Equally essential is computational fluency – having
and using efficient and accurate methods for computing.
The following examples demonstrate fictitious students and the common error patterns they exhibit along with the suggested instruction on how to
teach the students to correct the errors. In the first ... Show more content on Helpwriting.net ...
To verify that Albert multiplied correctly, have him use a calculator to compute each partial product, making sure the correct values are multiplied; for
52 Г— 312, multiply 50 Г— 312 then 2 Г— 312. If needed, provide instruction to Albert to ensure he knows how to operate the calculator.
To further emphasize multiplication for one place value at a time, teacher Albert to apply a paper mask. The composition of the mask consists of a
piece of with a hole in the middle allowing the student to view the multiplier as multiplying the entire multiplicand. Once the completion of the
multiplication of the units (ones) digits, move the mask to the left to allow the visibly of only the tens digit. This process continues until each place
value has been multiplied to the multiplicand. Continue to remind Albert to complete the multiplication problem with each digit and placement of each
digit in the appropriate place value.
The second error pattern shows Rosanne making errors starting with the incorrect place value in a long division problem. Although, Rosanne
demonstrates understanding her multiplication facts, her errors show a misconception of where to start dividing the divisor into the dividend as shown
in the examples below.
Rosanna
By estimating the quotient before computing it, allows Rosanna to determine if her answer is reasonable. Once Rosanna estimates and computes the
answer for a

Questions On Learning And Teaching
Task #4: Mathematics Learning & Teaching
Competency 662.1.4: Aligning Learning Activities to National Standards
Competency 662.1.5: Standards and Best Practices in Teaching and Learning
Competency 662.1.7: Differentiated Instruction
Jennifer Moore
Western Governor's University
Part A: The "Equivalent Fractions and Decimals Lesson Plan" is aligned to NCTM's content and process standards. The content standard that this lesson
is addressing is numbers and operations. This entire lesson is about students using fractions and decimals to solve problems. This lesson also has
several process standards addressed in the lesson plan. One of the process standards used in this lesson is Connections. Throughout this ... Show more
"The Show or the Ad" activity has students using word problems that talk about television programs and commercials. The teacher has made the
students connect that math is even in the TV shows that they watch. The teacher then makes it even more the students own connections by allowing
them to be creative and writing their own word problem about TV and commercials. The teacher also uses these types of problems on the summative
assessment. The teacher uses connections even in the homework that is assigned to the students. The teacher assigns students to watch their favorite
television show, and as they watch the show to record how many minutes the commercials are. All of this shows the students understanding of the
concept while allowing the students to relate this to something they enjoy. The one NCTM process standard that I would add to this lesson plan
would be the reasoning and proof standard. This is the only standard that is rarely used in this lesson plan. "The Reasoning and Proof standard
emphasizes the logical thinking that helps us decide if and why our answers make sense" (Walle, p. 5). This lesson needs to allow students to justify
the reason for their answers. This lesson only has them justifying their answers on one question, throughout the entire lesson. I would add more to the
questions than just the answers. One part of this lesson I would change to incorporate the reasoning and proof standard is on the "The Show or the

Justifications : Warm Up : Shared Book Essay
Justifications: Warm–up: Shared Book Description:Justification: The warm up for this lesson is reading a book called, "Earth Day – hooray!" I chose
to incorporate reading as a math warm–up because it is an effective way to explore mathematical concepts, which are both engaging and informative for
the students. Integrating elements of literature into the lesson supports problem solving and allows students to be fully immersed in the story, solving
themselves the mathematical issues that the characters fall into. Ministry of Education, 2016, endorses this idea stating that applying visual elements
of picture books aid in illustrating mathematical concepts, which are difficult to teach with other resources, or challenging for students to comprehend.
This particular book introduces properties of place value, discussing the idea that 10 tens is equal to 1 one hundred, which all groups need assisting
with. Picture books contextualize mathematical ideas in meaningful ways for students, while creating stories, which are relatable and spark curiosity
and enthusiasm (McGrath, 2014). McGrath further explains that learners will respond positively when stories are not written with the intention of
teaching children mathematics and will be more receptive to learning the math message, if the thinking is second nature. As the cappuccinos are
learning about place value this warm–up is a great launching point for furthering exploring this concept and prompts ideas for discussion and

Using Adaptive Response Surface Regression
3 Methodology
The developed optimisation routine makes use of adaptive response surface regression to use a limited initial amount of FE models to feed an
optimisation routine which is specifically designed for general thermal problems where parameters linked to the general heat equation can be optimised
or estimated using experimental input data. The algorithm uses a pan and zoom function to move through the design space and delivers faster
predictions with fewer iterations than standard updating routines [35, 41].
3.1 Adaptive response surface method
The adaptive response surface optimisation routine is used to optimise numerical models with a lot of data points and the time reducing by the
algorithm increases as the number of parameters rises [40]. The routine is designed to handle multiple–output time series data [35]. The optimisation
procedure can be divided into following steps:
1. Starting reference simulation points are ran and a correct object function is built of the difference between the FE model and the target value
(experiment or validation model).
2. The FE model is replaced by a meta–model of response surfaces to decrease the optimisation time but remains an accurate approximation.
3. The optimisation routine is run on a specific object function. It is possible to use multiple objective functions or build an objective function related to
multiple outputs.
4. The estimated parameter values are used as input parameters for a new FE model that corrects the

The Military Sector Of The Marine Corps
We are losing some of our best Machinists and Welders after their first enlistment due to the lucrative options available in the civilian sector and the
lack of opportunities to display their innovative nature in the Marine Corps. An additive and subtractive fabricator in the trenches would serve to be an
asset to commanders, because he/she will not be limited by technology or lack of expertise. Both of these specialties present an opportunity to exploit
manufacturing capabilities. After all, exploitation is a human endeavor and until unmanned technologies take over completely, is it not the Marines
using the technologies that are the assets? In the civilian sector, experience is often necessary in most fields; however, machining and ... Show more
Thus, the opportunities to exploit machining and welding capabilities disappear along with the opportunities to pass down their knowledge and skills
through guidance and mentoring. Interestingly enough the current manpower structure places these two MOS' side by side in every ESB,
Maintenance battalion and Ground Ordnance Vehicle Battalions. In an effort to challenge the status quo and to continue on with the Commandant
guidance; what benefits could arise if these two specialties are aligned together and be allowed to merge at the fifteen year mark?
These two specialties share similar skills in terms of fabrication and metallurgy, including a thorough understanding of the physical and mechanical
properties of metals. They both have a strong understanding of structural design and manufacturing regardless of material. And one particular aspect
that is often overlooked is the ability to be critical thinkers, as this is inherent with artistic creation (White, Robinson 2001). Additionally, all the
processes used in machining and welding require a level of critical thinking and creativity in order to maximize efforts and resources. The current
employment of these two specialties is minimal while in garrison; however, while forward deployed, these specialties become an integral part of
combat innovation. Their creativity and ingenuity have made a significant impact in the

Diagnosis Of Attention Deficit Hyperactivity Disorder
Assessment 1 Specific Difficulty in the Number Strand Chloe has a difficulty in completing vertical subtraction algorithms, particularly when
there is a zero in the minuend. Learner Profile Chloe is an 11 year and 10 months old girl who lives on Sydney's North Shore with her mother,
father and two younger brothers. Her first language is English and she is currently in Year 7 at a comprehensive systemic girls Catholic high school
located in Chatswood. Chloe excels at Dance and Music, and has been a member of the Australian Girls Choir for four years. She has a history of
ongoing difficulties with Maths. Chloe was born with Morning Glory Anomaly in her left eye; a congenital condition that results in the failure of the
optic nerve to fully develop. In late 2015, her left retina completely detached resulting in almost total blindness. Her visual acuity is normal in the right
eye. Chloe has a diagnosis of Attention Deficit Hyperactivity Disorder (predominantly inattentive), clinically significant levels of anxiety and a
specific learning disorder with impairment in written expression. Her ADHD is managed through a low chemical diet and she is not medicated.
Chloe's most recent review of cognitive and learning abilities was completed in early 2014. The key findings include stronger verbal intellectual skills
(average) than non–verbal intellectual skills (low average); the abstract reasoning that is needed for many maths tasks. Whilst her working memory and
processing speed

Mathematics : Computational Mesh And Grid
LITERATURE REVIEW:
COMPUTATIONAL MESH AND GRID
DEPENDANCY
(Technical Report by Vignesh)
ABSTRACT
The purpose of this paper is to explain the generation of computational meshes for complex problems having intricate shapes and to study the grid
dependency for obtaining accuracy in those problems. In finite element method of numerical computation it is important to divide the domain into a
number of simple elements.
Some portion of domain may require still smaller elements so that the computation is more accurate there. A large number of algorithms have been
proposed to automate the process of mesh generation but they do not guarantee about the quality of results produced. Some methods which eliminate
the problem of intersection in elements are discussed.
INTRODUCTION
Mesh generation has received immense attention from assorted scieЕ¶tific aЕ¶d engineering branches since the emergence of numerical methods for
partial differential equations. During the past few decades, many sequential methods have been proposed, some of which are now very popular and
commercially available[1].
Several algorithms are being proposed to automate this process of grid generation.
Some of them are Sweepline algorithm,
Ruppert's algorithЕµ, BidivisioЕ¶ procedure,
Parallel mesh generation etc.
CLASSIFICATION OF MESH
Structured Mesh:
Structured meshes are those in which the topology of elements is regular. They are generally easy to compute but may require more number

The Student That I Have Been Working With Over The Past...
The student that I have been working with over the past six weeks is Brad Concordia. Brad attends Shiloh Hills Elementary School in the rural area of
the Wilson School District. Brad is a first–grade student in Mrs. Detwiler's classroom who suffers from brain damage and unfortunately he's dealt
with it since he was born. Brad is an energetic, positive kid who loves to tell stories and talk about PokГ©mon. He does not act up in class and he
tends to be very polite and well behaved. Whenever the teacher gives him an activity to do he tries his very best to accomplish it without the help of
an aid, but most times he is left with no choice due to his condition.
A couple of Brad's strengths include being able to count dots 1–34 without any issues, and he is able to comprehend the number of dots he counted and
write it down for the answer. For basic numbers such as 1–10, he is able to do it fully on his on and get all of the digits correct. For numbers greater
than 10, he is dependent on the help of one of the other teachers. His main weakness in math is his lack of ability to do problems on his own. He
relies on counting dots to add up the numbers and my goal for him is for him to be able to see a number and know how much it is "worth" rather
than using dots to count. After talking with Mrs. Detwiler, we discussed a plan to help Brad comprehend single digits numbers using his number line.
Brad has been very positive toward this intervention and he is eager to work

Multiplication Of Urdhva Tiryabhyam Sutra
Urdhva Tiryakbhyam Sutra is a general multiplication formula applicable to all cases of multiplication. It literally means "Vertically and crosswise". It
is based on a novel concept through which the generation of all partial products can be done with the concurrent addition of these partial products.
Power dissipation which results in higher device operating temperatures. Therefore it is time, space and power efficient. It is demonstrated that this
architecture is quite efficient in terms of silicon area/speed. Now let us take two three digit decimal numbers and understand the Urdhva technique. Let
the first number be "123" and the second the number be "456".
Step 1: Initially the unit's digit numbers are multiplied and the unit's digit of the product that is 8 is kept as the unit's digit of the result, the ... Show more
2. Let us consider the multiplication of two decimal numbers (5498 Г— 2314). The conventional methods already know to us will require 16
multiplications and 15 additions. The numbers to be multiplied are written on two consecutive sides of the square as shown in the figure. The square
is divided into rows and columns where each row/column corresponds to one of the digit of either a multiplier or a multiplicand. Thus, each digit of
the multiplier has a small box common to a digit of the multiplicand. These small boxes are partitioned into two halves by the crosswise lines. Each
digit of the multiplier is then independently multiplied with every digit of the multiplicand and the two–digit product is written in the common box.
All the digits lying on a crosswise dotted line are added to the previous carry. The least significant digit of the obtained number acts as the result digit
and the rest as the carry for the next step. Carry for the first step (i.e., the dotted line on the extreme right side) is taken to be

Fpga Based Implementation Of Digit Recognition
FPGA BASED IMPLEMENTATION OF DIGIT RECOGNITION Under Supervision of : Dr. Pavan Chakaraborty. Group members: IEC2012015
IEC2012028 IEC2012041 IEC2012089 IEC2012090 Table of Contents About platforms used:4 Xilinx ISE:4 Web Edition:4 MATLAB: [matlab]4
Feature extraction:5 Algorithm speed up using FPGA implementation:6 [parallization abitlity of NN]6 Conclusion7 Result: [Verilog outputs]4
References7 About platforms used: Xilinx ISE: "Xilinx ISE[xilinx] (Integrated Software Environment) is a software tool produced by Xilinx for
synthesis and analysis of HDL designs, enabling the developer to synthesize ("compile") their designs, perform timing analysis, examine RTL
diagrams, simulate a design 's reaction to... Show more content on Helpwriting.net ...
More than a million engineers and scientists in industry and academia use MATLAB, the language of technical computing. [3]" Feature extraction:
The method of feature extraction is based on the spatial distribution of the black and white pixels in the image space. We are assuming that the
difference of distribution of pixels for each digit are sufficient enough to classify them. All of extracted features are integer and could be
implemented with only add and subtract operation on FPGA [4]. We divide the image into multiple horizontal and vertical sections and the analysis
of accuracies can be done using this table. [insert the table of trade off] It can be observed that as we are increasing the number of sections, the
accuracy is also increasing. Taking consideration of efficient use of hardware resources four horizontal and four vertical sections can be chosen safely.
[figure showing 8 blocks] To count the number of pixels in each section 8 binary ripple Algorithm speed up using FPGA implementation: [parallization
abitlity of NN] Conclusion For the implementation

What Is An Interpolation Equation
1. INTRODUCTION OF LAGRANGE POLYNOMIAL ITERPOLATION
1.1 Interpolation:
First of all, we will understand that what the interpolation is.
Interpolation is important concept in numerical analysis. Quite often functions may not be available explicitly but only the values of the function at a
set of points, called nodes, tabular points or pivotal points. Then finding the value of the function at any non–tabular point, is called interpolation.
Definition:
Suppose that the function f (x) is known at (N+1) points (x0, f0), (x1, f1), . . . , (xN, fN) where the pivotal points xi spread out over the interval [a,b]
satisfy a = x0 < x1 < . . . < xN = b and fi = f(xi) then finding the value of the function at ... Show more content on Helpwriting.net ...
. . + ________________________________________f4 (x0 – x1) (x0 – x2)(x0 – x3)(x0 – x4)(x4 – x0)(x4 – x1)(x4 – x2)(x4 – x3)
(0.3 – 1)(0.3 – 3)(0.3 – 4)(0.3 – 7)(0.3 – 0)(0.3 – 3)(0.3 – 4)(0.3 – 7)= ________________________________________1+
________________________________________3 + (–1) (–3)(–4)(–7)1 x (–2)(–3)(–6)
(0.3 – 0)(0.3 – 1)(0.3 – 4)(0.3 – 7)(0.3 – 0)(0.3 – 1)(0.3 – 3)(0.3 – 7)
________________________________________49 + ________________________________________129 +
3 x 2 x (–1)(–4)4 x 3 x 1 (–3)
(0.3 – 0)(0.3 – 1)(0.3 – 3)(0.3 – 4)
________________________________________813
7 x 6 x 4 x 3
= 1.831

Figure 1: Example of Lagrange interpolation 4.APPLICATIONS OF LAGRANGEPOLYNOMIAL INTERPOLATION
пѓ Lagrange polynomials basis are used in the Newton–Cotes method of numerical

Ancient China Research Paper
In 1,500 bc, the mathematicians of China were using numbers. Long before the people of India invented the number zero, Chinese people were using
base ten counting systems. The base ten method they used is different than the one we use today, using ancient Chinese math, the number 465 would
be written as four one hundred markers, six ten markers, and five one markers. They were also advanced in geometry, this was proved in 600 BC,
when the Tangram was invented. The Tangram is an amazing math game, that allows you to explore geometry to huge extents. This essay tells the
fascinating story of how the game is played, how it was used, and how it became known to the western world. China is often thought of as one of the
wealthiest countries in... Show more content on Helpwriting.net ...
In ancient times, believe it or not, they were used to tell stories. The pictures made by Tangrams can be put in order to make a scene. You can
arrange the shapes in any way, and trace the picture onto paper, and make a new figure. The traced pictures can look just like comics. You actually
can think of Tangrams as the comic books of the ancient world. Quite truly, you can make any story, from superheroes to mathematics. This is
actually quite important, creating a story using geometric shapes can actually improve your skills in geometry. That probably explains why they were
so popular in China. "Scholars and artists thrown together are often annoyed at the puzzle of where they differ. Both work from knowledge; but I
suspect they differ most importantly in the way their knowledge is come by. Scholars get theirs with conscientious thoroughness along projected lines
of logic; poets theirs cavalierly and as it happens in and out of books. They stick to nothing deliberately, but let what will stick to them like burrs
where they walk in the fields." –Robert Frost. This quote highlights the fact that both scholars and artists take an interest in Tangrams. "Tangrams are a
great thing to incorporate into the mathematics classroom because they are fun, interesting, and

Math Observation
In the beginning of my observations the students in the classroom had been practicing their addition and subtraction in a one digit numbers. However,
as the year went on my cooperating teacher started to get her students to be solving two–digit addition and subtractions problems. Before she started
with two–digit she wanted to be certain that her students felt confident along with concrete knowledge and examples in their one digit equations
because if not, they would fall apart for two digit equations. My teacher had opened with two–digit addition, by developing knowledge on base ten
blocks for approximately two weeks, then progressed her students to the standard algorithm. My classroom is set up for their numeracy portion of the
class that... Show more content on Helpwriting.net ...
My student at the beginning of two–digit addition struggled with being organized in his base ten block drawings and would get the answer wrong
because he would circle 11 ones instead of 10. When he got the opportunity to work with the actual base ten blocks he had a strong concept of
regrouping. Before the lesson my cooperating teacher taught them how to do the standard algorithm, which my case study student took to excellent.
During the process of the standard algorithm I asked him to walk me through what he was doing and the process. He explained that he carried the one
over because it was making a new ten and then counted twenty plus thirty plus ten instead of 1 plus two plus three, which I felt like the was
understanding the place value. I thought during the lesson if my student was advancing ways to challenge him on this assignment would be to have
him add three two digit numbers or have him add one two digit and one three digit number. Then if I felt like my student was starting to struggle I
could have his partner help him solve the process, bring out the base ten blocks, or have him just add one two digit and one digit numbers until he got
the concept

Mathematics : A Scheme Within Mathematics
The basis of this essay will discuss at a scheme within mathematics. Per the Department of Education (DfE) (2013) "mathematics is a creative and
highly interconnected disciplines that have been developed over centuries......... It is essential to everyday life, critical to science, technology and
engineering, and necessary for financial literacy and most forms of employment." The substance of maths is divided into five reasons; significance it
has in everyday life, its use within other curricular areas, the pupil can develop intellectually, pupil's enjoyment of learning and has a distinctive place in
pupil's human knowledge and culture (Haylock & Manning 2014). The scheme is based on six lessons it will consider EAL learners, ability based
differentiation, assessment and motivation. The second section of the essay will explore further in to motivation and how and why this is important to
the teacher, pupils, classroom for effective learning of the subject. It will then look at the consider the implications within the class and to personal
development as a teacher.
The scheme is based on a year 2 class, looking at place value through partitioning, one more, one less and ten more, ten less. I have chosen this due to
it being the key focus within the curriculum for key stage 1 learners. The aim by the completion of Key stage 1 stands that pupils have a strong
understanding, confidence and mental fluency with whole numbers, counting and place value (DfE, 2013). Moreover, place value

How Milling Is Metal Removal Process
2.1 Introduction Milling is metal removal process distinguished from drilling and other machining operation. It is used in most high productive
manufacturing industries, where quality is essential for parts. In milling operation, Metal removal takes place due to the cutting action of a revolving
milling cutter, when work piece is fed on it. But for producing quality side surface of parts, end milling operation carried out. Drill bit can cut in axial
order only, while a milling bit can generally cut in all directions, although some cannot cut axially. End mills are used in milling applications such as
plunging, side milling and profile milling. 2.2 Optimization The main purpose of most engineering design procedure is to improve productivity with
reduction in cost. The algorithm of an optimization is a one type of procedure which executed optimum solution by comparing various solutions till the
satisfaction level. In conventional method, solutions were accepted by comparing few designated answers in many industrial process design activity.
This is very simple approach and no guarantee for an optimum solution. To get the proper values of optimization, user must have to apply one or more
design solutions to check relative search space between algorithm techniques. The role of controllable cutting parameters (Speed, feed, depth of cut,
width of cut etc.) for economical machining process, optimization have been recognized. F. W. Taylor (1907) showed that an optimum

The Optimization Problems Of The Constraint Optimization...
1. Introduction
In this paper, the problem we consider is the constrained optimization problem, as follows:
(P) min f (x)
s.t. gi(x) в‰¤ 0, i = 1, 2, . . . , m, x в€€ X,
Where X вЉ‚ Rn is a subset, and f , gi: X в†’ R, i в€€ I = {1, 2, . . . , m} are continuously differentiable functions. Let X0= {x в€€ X|gi(x) в‰¤ 0, i =
1, 2, . . . , m} be the feasible solution set. Here we assume that X0 is nonempty. The penalty function method provides an important approach to solving
(P), and it has attracted many researchers in both theoretical and practical aspects (see e.g. [1,8,9,11,12,18,25]). In 1967, Zangwill [25] first proposed
the classic l1 exact penalty function:
F(x, Пѓ ) = f (x) + Пѓmв€‘i=1max{0, gi(x)}, (1)
Where Пѓ > 0 is a penalty parameter, it is known from the theory of ordinary constrained optimization that the l1 exact penalty function is a better
candidate for penalization. The obvious difficulty with the exact penalty functions is that it is not a smooth function. Which prevents the use of efficient
minimization algorithms, and causes some numerical instability problems in its implementation when the value of the penalty parameter becomes
larger. Hence, in order to use many efficient algorithms, such as Newton Method, it is very necessary and important to smooth exact penalty function to
solve constrained optimization problems. In fact, almost all penalty function algorithms need to change the value of the penalty parameter in
computational process. So do the exact

The Definition Of Allusion Problems
subsection{parameter uniform 2010} There are many papers in the literature dealing with the numerical approximation of the solution for time
dependent singularly perturbed reaction diffusion problems. In cite{186,188,189}, 1D problems are considered, in cite{185,187} the case of 2D
parabolic problems is analyzed and coupled linear systems are solved in cite{190}. Different techniques have been used to prove the uniform
convergence of the numerical method defined for each problem. In some papers the totally discrete method is directly considered and the analysis of
the convergence is based on appropriate bounds for the truncation error and the discrete maximum principle for the totally discrete operator.
Nevertheless, this technique... Show more content on Helpwriting.net ...
There exist number of papers where similar problem is studied. In cite{170}, first order uniform convergence was proved for the central finite
difference scheme constructed on a Shishkin mesh; this result was improved in cite{171} showing that the central difference scheme really is an
almost second order uniformly convergent scheme. In cite{172}, for reaction diffusion systems with an arbitrary number of equations, second order
of uniform convergence of central differences scheme was proved. In cite{173} the analysis was extended to a parabolic reaction diffusion system of
equations, proving first order uniform convergence for the scheme combining the Euler method in time and central differences in space. In the context
of FEM, up to our knowledge only the $p$ and $hp–$version approximates the solution at an exponential rate of convergence. In cite{174} some
numerical results showing the efficiency of this method were giving for the case of two equations. On the other hand, in cite{175} an arbitrary number
of equations is considered, proving the convergence in the simpler case of equal diffusion parameters. subsection{Monotone iterative 2011} In
cite{191}, a monotone iterative methods for solving semilinear singularly perturbed parabolic problem is presented. The

Simulation: Questions And Answers
05 – PERMUTATIONS AND COMBINATIONS
( Answers at the end of all questions )
Page 1
(1)
If the letters of the word SACHIN are arranged in all possible ways and these words are written out as in dictionary, then the word 'SACHIN' appears
at serial number ( a ) 601 ( b ) 600 ( c ) 603 ( d ) 602 [ AIEEE 2005 ]
(2)
The value of
50
C4 +
55
r =1
в€‘
6
56

–r C 3
is
( a ) 55 C 4
(b)
C3
( c ) 56 C 3
(d)
56
C4
[ AIEEE 2005 ]
(3)
How many ways are here to arrange the letters in the word GARDEN with the vowels in alphabetical order ? ( a ) 120 ( b ) 240 ( c ) 360 (d ) 480 [
AIEEE 2004 ]
(4)
The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is (a) 5 ( b ) 21 (c) 3
8
( d ) 8 ... Show more content on Helpwriting.net ...
пЈ¬ пЈ·! пЈё пЈ 2 пЈё [ C 0 2 – 2C 12 + 3C 2 2 – ... + ( – 1 )n ( n + 1 ) C n 2 ], n! where n is an even positive integer, is equal to (a) 0 (b) (–1) ( e ) none
of these n/2 (n + 1)
(c) (–1) (n + 2)

n
(d) (–1) n [ IIT 1986 ]
n
( 23 )
Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the
chairs marked 1 to 4, and then the men select the chairs from amongst the remaining. The number of possible arrangements is (a)
6
C3 Г— C2
4
(b)
4
P2 Г— P3
4
(c)
4
C2 Г— P3
4
( d ) none of these

[ IIT 1982 ]
( 24 ) Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then, the number of words which have
at least one letter repeated is ( a ) 69,760 ( b ) 30,240 ( c ) 99,748
5
( d ) none of these
[ IIT 1980 ]
( 25 ) The value of the expression (a)
47 C 5
47
C4 + (c)
j=1
в€‘
52 – j C 3
is equal to [ IIT 1980 ]
( b ) 52 C 5
52 C
4
( d ) none of these
( 26 ) n Cr – 1 = 36 n C r = 84 and n Cr + 1 = 126 , then r is (a) 1 (b) 2 (c) 3 ( d ) none of these [ IIT 1979 ]

( 27 )
There are 27 points in a plane. 5, 10 and 15 points are collinear on distinct lines. By joining

Volume Estimates of the Heart through the Use of Simpson's...
Table of Contents
1.Introduction and Objectives3
2.Simpson's rule3
2.1First proof of Simpson's rule4
2.2Second proof of Simpson's rule6
2.3Error in Simpson's rule7
2.4Number of slices for the approximation to be exact up to a certain number7
3.Application of the Simpson's rule to measuring the volume of the heart8
3.3.2 Sample calculation.10
4.Conclusion11
5.Bibliography12
6.Appendix12
Introduction and Objectives
I was looking at a program on discovery channel where there were treasure hunter ships.They would scan the seabed it. I noticed then when the seabed
came up on the computer screen it was imaged one part at a time, this made me think of integration with the trapezoidal rule where separate ... Show
more content on Helpwriting.net ...
Finally, I will draw the main conclusions from this project.
Simpson's rule
A way that we can see the trapezoidal (or midpoint) rule is that we approximate a function using a first degree polynomial. Following this line of
thinking we can say that by using Simpson's rule we approximate a function using a second degree polynomial. In the graph here above f(x) represents
the function that we are trying to approximate
P(x) is the second degree polynomial that we use to approximate the function
The Simpson's rule can be derived in various ways described in the two following subsections.
First proof of Simpson's rule
(based on the proof in the book Calculus, Larson Hostetler Edwards's fifth edition)

в€«_a^bв
–’в–€(f(x)dx=@ ) в€«_a^bв
–’гЂ–(AгЂ— x^2+Bx+C)dx
Integral is taken
в€«_a^bв
–’в–€(f(x)dx=@ ) [(Ax^3)/3+(Bx^2)/2+C] x = b– a
в€«_a^bв
–’в–€(f(x)dx=[(A(b^3
–a^3))/3+(BгЂ–(bгЂ—^2–a^2))/2+C(b–a)]@ )
By inverse distribution
в€«_a^bв
–’f(x)dx=((b–a)/6)[2A(a^2+ab+b^2 )+3B(b+a)+6C]
в€«_a^bв
–’f(x)dx=((b–a)/6)[(Aa^2+Ba+C)+4[A((b+a)/2)^2+B((b+a)/2)+C]+ (Ab^2+Bb+C)]
в€«_a^bв
–’f(x)dx=((b–a)/6)[f(a)+4f((b+a)/2)+f(b)]
To use Simpson's rule you divide the interval into n equal subintervals each of width в€†x=(b
–a)/n. N is required to be even because for Simpson's rule
we use coordinates to draw a polynomial of the least degree to pass through. For a polynomial to be determined we need three coordinates, we reuse
the last coordinate of the previous polynomial to create our next one.

Using A Dynamic Programming Method
Table of Contents
2OBJECTIVE2
3BACKGROUND2
4CONVEX OPTIMIZATION2
4.1INTRODUCTION2
4.2THEORY2
4.3ALGORITHM2
5NON CONVEX OPTIMIZATION2
5.1INTRODUCTION2
5.2THEORY2
5.3ALGORITHM2
6LAGRANGIAN RELAXATION FLOW CHART2
6.1INTRODUCTION2
6.2ALGORITHM FOR A UNIT COMMITMENT PROBLEM2
7RESULTS AND SIMULATIONS2
7.1TEST SYSTEM2
7.2RESULTS2
8CONCLUSIONS2
9FUTURE SCOPE3
10REFERENCES3
OBJECTIVE
BACKGROUND
CONVEX OPTIMIZATION
INTRODUCTION
THEORY
ALGORITHM

NON CONVEX OPTIMIZATION
INTRODUCTION
THEORY
ALGORITHM
LAGRANGIAN RELAXATION FLOW CHART
INTRODUCTION
Using a Dynamic Programming method would be a tedious search of all the the possible combinations. This reduction in possible combinations would
make the problem complicated and would consume a greater amount of time. This problem of reducing combinations can be eliminated by using
Lagrangian relaxation method.
The Lagrangian Relaxation algorithm being implemented in basically an extension of Non – Convex Optimization to a power system. In this project,
we have taken up the cost functions of each of the generators under consideration and developed the cost function to be minimized keeping the mind
the generator limits as well as the load balance.
Loading constraints:Pt_load=в€‘_(i=1)^Ngв
–’гЂ–Pit*Uit=0 гЂ— Generating limits: Uit*Pit_minв‰¤Pitв‰¤Uit*Pit_max
The objective function to be minimized i.e, the overall cost function of the generator would be the sum of cost function of each

The Advantage And Disadvantages Of CNC Machining
Advantages of Custom CNC Machining There are various businesses that can exploit PC numerical control machine hardware, now and then known
as CNC machining. The hardware is utilized to manufacture littler pieces, and in addition to make bigger pieces that are to a great degree exact. The
gear that is utilized with CNC machining removes at the undesirable material of the bigger piece keeping in mind the end goal to create a littler part. It
is a procedure that advantages both the producer and the end–client. What are a portion of the particular advantages of custom CNC machining?
Effortlessly Customizable – The product which drives the machine that is making the parts is anything but difficult to tweak. By basically rolling out a
few improvements to the... Show more content on Helpwriting.net ...
This takes into consideration the assembling of various items. It additionally makes it workable for numerous bits of diverse materials to be delivered
for the same item at the same area. Moderateness – The sum that you will spend on modified CNC machining is frequently a great deal not exactly
what you will pay for fast prototyping. Fast prototyping makes utilization of 3–D CAD information through a procedure known as added substance
layer assembling (3–D printing). In spite of the fact that this has its place in numerous commercial ventures, you may find that it is more moderate to
have tweaked parts fabricated through the utilization of CNC machining. Resistance – In various assembling commercial enterprises, there is a sure
level of resilience which is allowed when assembling parts. This is something that may vary, contingent on the thing that is being produced. At the
point when redone CNC machining is used, it holds to tight resistances, which makes a predictable piece that will be of advantage to your

Advantages And Disadvantages Of Market Based Optimal Power...
Optimal power flow is defined as fulfilling the power requirements of consumer's with least outlay of power generation. OPF is a functional unit that
reduces the production expenditure, bus voltage divergences and losses which enhances the structure functionality by fulfilling some restraints. The
nature of some of the variables follows continuity with real output of power and voltage and few other variables in OPF is discrete with phase shifters,
reactive injections and tap settings in transformers which is considered to be major problem. OPF problem was resolved by several traditional
optimization techniques.
Market–based optimal power flow
In this a power pool model is developed which includes the one–sided auction market in OPF. A hourly price bid is represented in the form of marginal
cost by each market participant. Locational Marginal Price (LMP) is used to minimise Hourly Social Cost (HSC) was minimised by the bids which
are taken as inputs to the OPF. A bilateral contract between thewind supplier and storage owner is used to purchase the curtailed wind power. By using
the generation bids HSC function is formulated. The main objective of market–based optimal power flow is as follows ... Show more content on
Helpwriting.net ...
Point Estimation Method is a simple numerical method which is used to calculate the moments of nonlinear function. Two point estimation method
(2PE) a modification of PE is adapted here which is a variation of point estimate method to design the unpredictability of wind speed and load. This
method evaluates high accuracy level when examined with several methods. The input and output arbitrary variables and the analogous nonlinear
function are evaluated as equations (4.12), (4.13) &

Singularly Perturbed Problem Essay
section{Parameter Uniform} In the context of singularly perturbed problems posed on non–rectangular domains, the finite element method is a
natural choice for many researchers (e.g. cite{118}). However, in the context of singularly–perturbed convection–diffusion problems, it is difficult to
construct monotone methods on highly anisotropic meshes, which are desirable when thin layers are present. Moreover, energy norms or other norms
based on the $L^2–$norm, are the natural norms associated with variational methods. Error analysis in the pointwise norm is not straightforward in a
finite element framework, especially when one is dealing with a problem that is not self–adjoint. Given that their interest lies in parameter uniform
numerical... Show more content on Helpwriting.net ...
The presence of a convective term means that the data of the problem across the entire domain has an influence on the outflow boundary layer, in
contrast to reaction diffusion problems where it is only the data local to a boundary that has an influence on the boundary layer. Hegarty and O'Riordan
cite{115} constructed a parameter–uniform numerical methods for the singularly perturbed problem posed on a circular domain. Asymptotic
expansions for the solutions to such a problem have been established in cite{120,121,122,123}. Analytical expressions for the exact solution, in the
case of constant data, are given in cite{123} as a Fourier series with coefficients written in terms of modified Bessel functions. In cite{120,121,122}
sufficient compatibility conditions are identified so that the accuracy of the asymptotic expansion can be estimated in the $L^2–$norm or in a suitably
weighted energy norm. These expansions are derived without recourse to a maximum principle. The smooth case, where significant compatibility is
assumed, is examined in cite{120}; the non–compatible case with a polynomial source term is studied in cite{125} and for a more general source
term in cite{122}. Based on these asymptotic expansions, a numerical method is constructed in cite{124} for the problem, which uses a
quasi–uniform mesh (which is, hence, not layer–adapted). By enriching the finite element subspace, with certain exponential boundary–layer basis

Questions On Grasp Problem Solving Method
GRASP Problem Solving Method
Given – You need to figure out the important information in the question.
Required – What do I have to do to answer the question?
Application – What is my plan to solve the question?
Solve – Use your plan to solve the problem.
Paraphrase – Write a couple of sentences about your answer and how you found it.
Example: Shane is setting up for his birthday party. There are 50 people coming to the party. If each table holds 6 people, how many table does he need?
Given –1 table = 6 people 2 tables = 10 people 3 tables = 14 people
Required – We need to find out how many table he needs.
Application – We could use –repeated addition –make a chart –draw pictures –make a graph
Solve – Use a chart
# of tables # of people
16
210
314
418
522
626
730
834
938

1042
1146
1250
Paraphrase – we found out that Shane needs 12 tables for 50 people. We know this because we made a chart and increased the chart until we reached
50 people and see how many tables are needed.
BEDMAS
BEDMAS is an acronym for the order of operations used to solve a math equation that has more than 1 operation.
A math equation is a math sentence (e.g. 2 + 2 = 4).
BEDMAS tells us the order we need to use to complete the operations in an equation.
Brackets
Exponent
Division
Multiplication
Addition
Subtraction

Global Finite Element Matrix Construction Based on a...
Introduction
Many physical phenomena in stationary condition such as electrical and magnetic potential, heat conduction, fluid flow and elastic problems in static
condition can be described by elliptic partial differential equations (EPDE). The EPDE does not involve a time variable, and so describes the steady
state of problems. A linear EPDE has the general form as presented in Eq. (1), where a,b,c are coefficient functions, the term f is a source (excitation)
function and u is the unknown variable. All of this function can vary spatially (x,y,z).
в€‡(cв€™в€‡u)+bв€™в€‡u+au=f(1)
EPDE can be solved exactly by mathematical procedures like Fourier series [1]. However, the classical solution frequently no exists and for those
problems where is possible the use of these analytical methods, many simplifications are done [2]. Consequently, several numerical methods have been
developed to efficiently solve EPDE such as the finite element method (FEM), finite difference and others.
The FEM have several advantages over other methods. The main advantage is that it is particularly effective for problems with complicated geometry
using unstructured meshes [2]. One way to get a suitable framework for solving EPDEs by using FEM is formulate them as variational problems also
called weak solution.
The variacional formulation of an EPDE is a mathematical treating for converting the strong formulation to a weak formulation, which permits the
approximation in elements or subdomains, and the EPDE

Why I Learned Mathematics For Teaching Mathematics
Introduction This report follows the progress of an eight year old, grade three child's progress, through a mathematical diagnostic assessment
pertaining specifically to number placement, and proceeds through the relevant stages of mathematical learning, mapping the strategic points involved
in teaching mathematics whilst following the progress of the child, and the areas with which they required improvement. The partitioned focus, of
this report is on specific areas such as the mechanics of learning numbers specifically, counting and the developmental appropriate learning stages of
a neurotypical child. Succeeding the initial factual proponent of the report (Part A), is an account of the experience of tutoring (Part B) the grade
three child, whom shall be known as "Boris" (a neighbours child). A permission slip was attained a copy of which may be found within the
appendices. This portion of the report will explain any errors Boris made, why Boris made those errors, and what was done to rectify them. Pictorial
evidence of the tutoring sessions may be found within the body of the Part B text. Part A Rationale In order to teach well, there must be an observance
of the student, and how that student may best learn. The commonsense within the points, which make up the components of the "professional
judgement circle (Department of Education, (DoEWA) 2013. p. 2.)" describe well the necessary stages for the development of student learning, as
opposed to teacher teaching and a

Engineering Design And Manufacture By Looking At...
1.0 – Summary
In this assignment I have demonstrated an understanding of engineering design and manufacture by looking at traditional manufacturing processes and
non–contact processes. I have selected the right process/process and its suitable materials, economics, quality issues, dimensional accuracy and they're
advantages/disadvantages. I have given a thorough conclusion on what method I believe is the best depending on the quantity of lathe carrier body's
being made and also value for money.
Table of Contents
1.0 – Summary1
2.0 – Introduction1
3.0 – Task 12
Method of manufacturing2 3
Suitable materials3
Economic consideration3
Advantages & dis–advantages4
4.0 – Task 24
Suitable materials4
Economic consideration5
Advantages & disadvantages5
5.0 – Comparison of processes5
6.0 – Conclusion5
7.0 – References6
Bibliography6
8.0 – Table of figures6
2.0 – Introduction
In this assignment I am going to cover many different ways of manufacturing a lathe carrier. I am going to base all my knowledge and research on two
main processes. These are going to be non–contact processes and traditional manufacturing processes. I am going to demonstrate a good understanding
of engineering design and manufacture. I shall prove this by considering all the important factors which include economy, quality, suitable

manufactures, surface finish, dimensional accuracy, advantages/disadvantages...etc. After careful consideration then I shall compare and contrast the
methods

A Scheme Of The Department Of Education

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