These slides contain information about Euler method,Improved Euler and Runge-kutta's method.How these methods are helpful and applied to our questions are detailed discussed in the slides.
These slides contain information about Euler method,Improved Euler and Runge-kutta's method.How these methods are helpful and applied to our questions are detailed discussed in the slides.
First principle, power rule, derivative of constant term, product rule, quotient rule, chain rule, derivatives of trigonometric functions and their inverses, derivatives of exponential functions and natural logarithmic functions, implicit differentiation, parametric differentiation, L'Hopital's rule
La manera ideal de enseñar computación cuántica sería construir entre todos un ordenador cuántico. Dado que eso está fuera de nuestro alcance, intentaremos hacer lo segundo mejor: construir entre todos un simulador clásico de un ordenador cuántico. Es decir, un programa breve, que corra en un ordenador portátil y nos permita simular el comportamiento que creemos que tendrán los ordenadores cuánticos reales, cuando sean construidos. Utilizaremos el enfoque más prometedor en la actualidad, la computación cuántica adiabática (AQC), empleada, entre muchos otros, por D-Wave.
En el seminario no asumiremos ningún conocimiento de mecánica cuántica, tan sólo conocimientos moderados de programación y de álgebra lineal. Tras la charla habilitaremos una página web de la que descargar el código descrito durante la misma.
Infomatica, as it stands today, is a manifestation of our values, toil, and dedication towards imparting knowledge to the pupils of the society. Visit us: http://www.infomaticaacademy.com/
Baking powder usually consists of a solid acid and a base. For examp.pdfpreetajain
Baking powder usually consists of a solid acid and a base. For example sodium bicarbonate and
sodium aluminum sulfate. When warm water is added to the dry baking powder, both the
acidand base go into solution and start reacting giving out carbondioxide. Hence vigorous
bubbling can be observed. NaAl (SO4)2 + 3NaHCO3 ----> Al(OH)3 + 2Na2SO4 + 3 CO2
Solution
Baking powder usually consists of a solid acid and a base. For example sodium bicarbonate and
sodium aluminum sulfate. When warm water is added to the dry baking powder, both the
acidand base go into solution and start reacting giving out carbondioxide. Hence vigorous
bubbling can be observed. NaAl (SO4)2 + 3NaHCO3 ----> Al(OH)3 + 2Na2SO4 + 3 CO2.
More Related Content
Similar to x = 0.3, and y0 = 0so, interval ==[0,0.3]step soize = h = 0.1.pdf
First principle, power rule, derivative of constant term, product rule, quotient rule, chain rule, derivatives of trigonometric functions and their inverses, derivatives of exponential functions and natural logarithmic functions, implicit differentiation, parametric differentiation, L'Hopital's rule
La manera ideal de enseñar computación cuántica sería construir entre todos un ordenador cuántico. Dado que eso está fuera de nuestro alcance, intentaremos hacer lo segundo mejor: construir entre todos un simulador clásico de un ordenador cuántico. Es decir, un programa breve, que corra en un ordenador portátil y nos permita simular el comportamiento que creemos que tendrán los ordenadores cuánticos reales, cuando sean construidos. Utilizaremos el enfoque más prometedor en la actualidad, la computación cuántica adiabática (AQC), empleada, entre muchos otros, por D-Wave.
En el seminario no asumiremos ningún conocimiento de mecánica cuántica, tan sólo conocimientos moderados de programación y de álgebra lineal. Tras la charla habilitaremos una página web de la que descargar el código descrito durante la misma.
Infomatica, as it stands today, is a manifestation of our values, toil, and dedication towards imparting knowledge to the pupils of the society. Visit us: http://www.infomaticaacademy.com/
Similar to x = 0.3, and y0 = 0so, interval ==[0,0.3]step soize = h = 0.1.pdf (20)
Baking powder usually consists of a solid acid and a base. For examp.pdfpreetajain
Baking powder usually consists of a solid acid and a base. For example sodium bicarbonate and
sodium aluminum sulfate. When warm water is added to the dry baking powder, both the
acidand base go into solution and start reacting giving out carbondioxide. Hence vigorous
bubbling can be observed. NaAl (SO4)2 + 3NaHCO3 ----> Al(OH)3 + 2Na2SO4 + 3 CO2
Solution
Baking powder usually consists of a solid acid and a base. For example sodium bicarbonate and
sodium aluminum sulfate. When warm water is added to the dry baking powder, both the
acidand base go into solution and start reacting giving out carbondioxide. Hence vigorous
bubbling can be observed. NaAl (SO4)2 + 3NaHCO3 ----> Al(OH)3 + 2Na2SO4 + 3 CO2.
They basically provide an alternative path for th.pdfpreetajain
They basically provide an alternative path for the protons to re-enter. Therefore,
since the protons don\'t go through FOF1 atp synthase ATP cannot be produced. The electron
transport chain is not affected by DNP. The electrons continue to flow normally. So the correct
answer is choice a
Solution
They basically provide an alternative path for the protons to re-enter. Therefore,
since the protons don\'t go through FOF1 atp synthase ATP cannot be produced. The electron
transport chain is not affected by DNP. The electrons continue to flow normally. So the correct
answer is choice a.
Yaws- tropical infection of skin and joints etc.Spread by direct con.pdfpreetajain
Yaws- tropical infection of skin and joints etc.Spread by direct contact with the fluid of infected
person.
Archaeological evidence suggest the presence of this disease among humans for 1.6 million
years. So saying that this is because arrival of Columbus is not actually that correct.
Evidences suggest that some mutations might have helped in evolution of T. pallidum pertenue
into T. Pallidum in the temperate climate.
Solution
Yaws- tropical infection of skin and joints etc.Spread by direct contact with the fluid of infected
person.
Archaeological evidence suggest the presence of this disease among humans for 1.6 million
years. So saying that this is because arrival of Columbus is not actually that correct.
Evidences suggest that some mutations might have helped in evolution of T. pallidum pertenue
into T. Pallidum in the temperate climate..
CCl4 All the have ionic bonds. Carbon and Chlori.pdfpreetajain
CCl4 All the have ionic bonds. Carbon and Chlorine have 4 and 7 electron in their
outermost orbit. Both dont have tendency to donate an electron. Hence they share
Solution
CCl4 All the have ionic bonds. Carbon and Chlorine have 4 and 7 electron in their
outermost orbit. Both dont have tendency to donate an electron. Hence they share.
Let x moles of CF4 be formed at equilibrium. Hence at equilibrium mo.pdfpreetajain
Let x moles of CF4 be formed at equilibrium. Hence at equilibrium moles of Co2 = x and that of
COF2 = 5 - 2x
Hence x2/(5 = 2x)2 = 16
Solving this we get x = 2.22
Hence option 5
Solution
Let x moles of CF4 be formed at equilibrium. Hence at equilibrium moles of Co2 = x and that of
COF2 = 5 - 2x
Hence x2/(5 = 2x)2 = 16
Solving this we get x = 2.22
Hence option 5.
There are two types of diabetes Diabetes Insipidus and Diabetes mel.pdfpreetajain
There are two types of diabetes: Diabetes Insipidus and Diabetes mellitus. In both the forms,
large amount of urine is expelled from the body. The condition is known as polyuria.
Diabetes Insipidus (DI), is either a neurological disorder or a nephrological disorder in humans.
--In the neurologic disorder, vasopressin deficiency is there. Vasopressin is the hormone which is
released when there is less water in our body. This hormone absorbs all water from the urine and
leaves highly concentrated urine for excretion. This hormone is not released when large amount
of water is already there in the body.
--In the nephrologic disorder, vasopressin is there but the kidney\'s/nephron\'s response to
vasopressin is negligible.
In Diabetes Mellitus, excess sugar is leaked in the blood, which in turn absorbs excess water
from the body, and releases this water in the urine. This condition is known as osmotic diuresis.
In all forms of diabetes, a person feels very thirsty; so, he/she will drink large amount of water.
And because of deficiency of vasopressin, this excess water will not be absorbed. So, such a
patient produces greater volume of dilute urine.
Solution
There are two types of diabetes: Diabetes Insipidus and Diabetes mellitus. In both the forms,
large amount of urine is expelled from the body. The condition is known as polyuria.
Diabetes Insipidus (DI), is either a neurological disorder or a nephrological disorder in humans.
--In the neurologic disorder, vasopressin deficiency is there. Vasopressin is the hormone which is
released when there is less water in our body. This hormone absorbs all water from the urine and
leaves highly concentrated urine for excretion. This hormone is not released when large amount
of water is already there in the body.
--In the nephrologic disorder, vasopressin is there but the kidney\'s/nephron\'s response to
vasopressin is negligible.
In Diabetes Mellitus, excess sugar is leaked in the blood, which in turn absorbs excess water
from the body, and releases this water in the urine. This condition is known as osmotic diuresis.
In all forms of diabetes, a person feels very thirsty; so, he/she will drink large amount of water.
And because of deficiency of vasopressin, this excess water will not be absorbed. So, such a
patient produces greater volume of dilute urine..
The difference between these two types of inflation is found in thei.pdfpreetajain
The difference between these two types of inflation is found in their causes. Both have the same
effects (increasing price level), but they are caused by different things.
Demand-pull inflation is caused by excess demand. When the people as a whole get more money
they are able to pay more for goods and services (unless more goods and services are produced).
Economists talk about more money \"chasing\" the same amount of goods and services. This
causes shortages and prices rise.
Cost-push inflation is caused by disruptions in supply. These disruptions cause increases in the
price of production. That leads to inflation. For example, a rise in the price of oil causes
practically all production to become more expensive.
There is no technical way to determine for sure which kind of inflation is going on. Analysts
must simply look around to try to see if the money supply is increasing or if there are supply
shocks. Then they have to make informed guesses about why the inflation is happening.
Why Savings equals Investment:
Using the GDP equation to explain saving and investing:
Begin with our GDP equation for an open economy:
Y = C + I + G + NX
To simplify this idea, let’s look at a closed economy, where there are no imports or exports. This
means that NX will equal 0 and will therefore drop out. This leaves us with:
Y = C + I + G
We can rearrange this equation to solve for investment (I) as a function of the other variables in
the economy:
I = Y – C – G
This equation tells us that investment in the economy will be equal to the total amount produced
(GDP = Y) minus consumption spending, and government purchases.
Now we can create a savings for the economy equation. The total amount of private savings
(savings by the private sector meaning households and firms) is going to be equal to the amount
produced (Y) plus transfer payments from the government (we will call this TR, and include
things like unemployment, social security and welfare) minus the amount spend on consumption
(C) and taxes (T).
S(private) = Y + TR – C – T
Hopefully this makes sense, the amount you save (S) will be whatever is left over (starting from
initial money of Y and TR) after you account for spending and expenses (C and T).
Now we need to consider public savings, which is how much the government saves. Public
spending depends on the amount of taxes they receive (T), the amount they spend in purchases
(G), and the amount they transfer to the population (TR). The public savings function will be:
S(public) = T – G – TR
We can find the total amount of savings (S) occurring in the economy by adding public savings
to private savings.
S(public) + S(private) = S
T – G – TR + Y + TR – C – T =S
Note that T and TR cancel out. This leaves us with savings (S) being equal to GDP (Y),
government purchases (G), and consumption (C):
S = Y – G – C
If we plug in the GDP equation for Y, or substitute C + I + G for Y we get:
S = C + I + G – G – C
Note that C and G will cancel out leaving us with:
.
The Federal Reserve is not a part of U.S. Government. It operates on.pdfpreetajain
The Federal Reserve is not a part of U.S. Government. It operates on its own and is not governed
by any government policy. The only danger of directly borrowing funds from the Federal
Reserve is that the U.S. Government (Treasury Department) will increase its national debt which
is already on the rise from the year 2000.
The yield curve is a graphic representation of interest rates for similar-quality bonds at different
maturities and is as such viewed as a reflection of expectations of future interest rates. The yield
curve also enables investors to compare the yields offered by bonds of short-, medium- and long-
term maturities when making investment decisions.
The most common shapes that the yield curve can take are represented by a normal, an inverted
and a humped yield curve. When short-term interest rates are lower than long-term interest rates,
the yield curve takes a normal shape. If the opposite holds, i.e. short-term interest rates are higher
than long-term interest rates, the yield curve is said to be inverted. Finally, when a yield curve is
humped, medium-term interest rates are higher than short-term and long-term interest rates.
When the yield curve is normal, investors expect interest rates in the future to be higher. The
higher interest rates would be a result economic growth and higher inflation in the future. A
normal yield curve also tells investors that long-term bonds yield a higher return than short-term
bonds. Hence, investors with longer investment horizons might prefer to invest in long-term
rather than short-term bonds. However, taking into account expectations of inflation as reflected
in the shape of the yield curve, the higher return on a long-term security will in fact give an
investor lower buying power as future cash flows are discounted at higher interest rates due to
inflation. Moreover, the cash invested as principal will have a substantially lower purchasing
power when it is returned in the future (say in 20 years), when interest rates are significantly
higher. As a means of protecting against inflation, investors might consider altering their fixed
income portfolio allocations and shifting some of their holdings into securities that are immune
to inflation, such as TIPS. TIPS (Treasury Inflation Protected Securities) pay a principal at
maturity that is adjusted for inflation and they also pay coupons as a percentage of the adjusted
principal.
Solution
The Federal Reserve is not a part of U.S. Government. It operates on its own and is not governed
by any government policy. The only danger of directly borrowing funds from the Federal
Reserve is that the U.S. Government (Treasury Department) will increase its national debt which
is already on the rise from the year 2000.
The yield curve is a graphic representation of interest rates for similar-quality bonds at different
maturities and is as such viewed as a reflection of expectations of future interest rates. The yield
curve also enables investors to compare .
The correct answer is InductionInduction is the process in which .pdfpreetajain
The correct answer is Induction:
Induction is the process in which one cell or tissue acts as an inducer and signals the
neighbouring cells or tissues to develop. These cells are called organizers. When the eye tissue
was transplanted in the tail of the tadpole; what might have occurred is that due to presences of
inducer cells, they must have secreted some protein, which signalled brain to activate the
neighbouring cells and start developing an eye on the tail of tadpole.
Pattern formation: It is the process in which cell fate is decided based on the genes. Pattern
formation is done by the genes. Pattern formation is related to the morphogenesis.
Potentiation: The strength of the never impulse is increased based on the previous actions. Thus
this process helps to signal the body to perform certain task with more effectiveness and
encountered again. So when tadpole was transplanted with an eye tissue, they must have
signalled for its development more effectively than the previous time. But the whole process of
development of an eye cannot be initiated by potentiation.
Positional information: the pattern formation is based on the positional information. A pattern of
the embryogenesis is formed based on the information obtained from the position of the cells. So
when the system is well organized, the pattern is formed based on the position of the genes. This
cannot occur on our tadpole, since transplantation of eye tissue on the tail was not the
information available in the genes.
Solution
The correct answer is Induction:
Induction is the process in which one cell or tissue acts as an inducer and signals the
neighbouring cells or tissues to develop. These cells are called organizers. When the eye tissue
was transplanted in the tail of the tadpole; what might have occurred is that due to presences of
inducer cells, they must have secreted some protein, which signalled brain to activate the
neighbouring cells and start developing an eye on the tail of tadpole.
Pattern formation: It is the process in which cell fate is decided based on the genes. Pattern
formation is done by the genes. Pattern formation is related to the morphogenesis.
Potentiation: The strength of the never impulse is increased based on the previous actions. Thus
this process helps to signal the body to perform certain task with more effectiveness and
encountered again. So when tadpole was transplanted with an eye tissue, they must have
signalled for its development more effectively than the previous time. But the whole process of
development of an eye cannot be initiated by potentiation.
Positional information: the pattern formation is based on the positional information. A pattern of
the embryogenesis is formed based on the information obtained from the position of the cells. So
when the system is well organized, the pattern is formed based on the position of the genes. This
cannot occur on our tadpole, since transplantation of eye tissue on the tail was not the
information ava.
Step1 Reverse the 2nd equation and add to the first equation Ste.pdfpreetajain
Step1 Reverse the 2nd equation and add to the first equation
Step2 C2H4(g) + H2O(l)----> C2H5OH(l) ;Change of H= -1411.1+1367.5= 43.6 kj
Step3 Reactants
Products
Solution
Step1 Reverse the 2nd equation and add to the first equation
Step2 C2H4(g) + H2O(l)----> C2H5OH(l) ;Change of H= -1411.1+1367.5= 43.6 kj
Step3 Reactants
Products.
RNA polymerase II help in repair by protecting DNA damaged by formin.pdfpreetajain
RNA polymerase II help in repair by protecting DNA damaged by forming tertiary complex . In
eukaryotic genome strand selective repair is done by gene transcribed by RNA polymerase II .
Coupling of repair of DNA governed by signal associated with RNA polymerase.
RNA polymerase II is located in nucleoplasm help in repair sometime as nucleotide repair
mechanism.
Solution
RNA polymerase II help in repair by protecting DNA damaged by forming tertiary complex . In
eukaryotic genome strand selective repair is done by gene transcribed by RNA polymerase II .
Coupling of repair of DNA governed by signal associated with RNA polymerase.
RNA polymerase II is located in nucleoplasm help in repair sometime as nucleotide repair
mechanism..
Q.1) The Hardware Layer-The hardware layer is sometimes referred t.pdfpreetajain
Q.1) The Hardware Layer-
The hardware layer is sometimes referred to as the server layer. It represents the physical
hardware that provides actual resources that make up the cloud. Since, by definition, cloud
computing users do not specify the hardware used to provide services, this is the least important
layer of the cloud. Often, hardware resources are inexpensive and are not fault tolerant.
Redundancy is achieved simply by utilizing multiple hardware platforms while fault tolerance is
provided at other layers so that any hardware failure is not noticed by the users.
The Virtualization Layer-
Often referred to as the infrastructure layer, the virtualization layer is the result of various
operating systems being installed as virtual machines. Much of the scalability and flexibility of
the cloud computing model is derived by the inherent ability of virtual machines to be created
and deleted at will.
Infrastructure as a Service (IaaS)-
The infrastructure layer builds on the virtualization layer by offering the virtual machines as a
service to users. Instead of purchasing servers or even hosted services, IaaS customers can create
and remove virtual machines and network them together at will. Clients are billed for
infrastructure services based on what resources are consumed. This eliminates the need to
procure and operate physical servers, data storage systems, or networking resources.
Platform as a Service (PaaS)-
The platform layer rests on the infrastructure layer’s virtual machines. At this layer customers do
not manage their virtual machines, they merely create applications within an existing API or
programing language. There is no need to manage an operating system, let alone the underlying
hardware and virtualization layers. Clients merely create their own programs which are hosted by
the platform services they are paying for.
Software as a Service (SaaS)-
Services at the software level consist of complete applications that do not require development.
Such applications can be email, customer relationship management, and other office productivity
applications. Enterprise services can be billed monthly or by usage, while software as service
offered directly to consumers, such as email, is often provided for free.
The Client Layer-
While this layer is not a cloud computing service, it is an essential part of the model. The client
layer acts as the user interface to which cloud computing services are delivered. Client layer
hardware can include personal computers, web browsers, mobile devices, and even telephones.
Q.2)
PaaS is designed for companies who have either an application or a set of applications and wants
to deploy those applications over the cloud. In this situation, a PaaS provider with computer
programming compatibility is the best solution. This gives you the following opportunities:
Q.3)
Answered in above question.
Q.4)
Public Cloud
With the public cloud, the infrastructure and services through which you process or store
inform.
NO2^- involves 2 bonds (one is N-O single bond, the other is N=O dou.pdfpreetajain
NO2^- involves 2 bonds (one is N-O single bond, the other is N=O double bond) and holds a
lone pair at N atom.
according to VSEPR, NO2^- has a bent shape.
Solution
NO2^- involves 2 bonds (one is N-O single bond, the other is N=O double bond) and holds a
lone pair at N atom.
according to VSEPR, NO2^- has a bent shape..
No ,the staetement is not correctReason We calculate CI for.pdfpreetajain
No ,the staetement is not correct
Reason :
We calculate CI for sample mean and not population mean
Solution
No ,the staetement is not correct
Reason :
We calculate CI for sample mean and not population mean.
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.
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
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!
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
How libraries can support authors with open access requirements for UKRI fund...
x = 0.3, and y0 = 0so, interval ==[0,0.3]step soize = h = 0.1.pdf
1. x = 0.3, and y0 = 0
so, interval ==>[0,0.3]
step soize = h = 0.1
applying Euler approximation
x(n+1) = xn + h
and y(n+1) = yn + hf(xn,yn)
x(n+1) = xn + h
x1 = x0 + h
= 0.1
y(n+1) = yn + hf(xn,yn)
or, y1 = y0 + hf(x0,y0)
= 1 + 0.1(xo+yo) = 1 + 0.1(0+1)
= 1.1
so,
x1 = 0.1
y1 = 1.1
again
x(n+1) = xn + h
x2 = x1 + h
= 0.2
y(n+1) = yn + hf(xn,yn)
or, y2 = y1 + hf(x1,y1)
= 1.1 + 0.1*(x1 + y1) = 1.1 + 0.1(0.1 + 1.1)
2. = 1.22
so,
x2 = 0.2
y2 = 1.22
again
x(n+1) = xn + h
x3 = x2 + h
= 0.3
y(n+1) = yn + hf(xn,yn)
or, y3 = y2 + hf(x2,y2)
= 1.22 + 0.1*(x2 + y2) = 1.22 + 0.1(0.2 + 1.22)
= 1.363
so,
x3 = 0.3
y3 = 1.362
again
x(n+1) = xn + h
x4 = x3 + h
= 0.4
3. y(n+1) = yn + hf(xn,yn)
or, y4 = y3 + hf(x3,y)
= 1.362 + 0.1*(x3 + y3) = 1.362 + 0.1(0.3 + 1.362)
= 1.5282
so,
x2 = 0.4
y2 = 1.5282
the graph of the data set generated will yield the approximate graph of the original equation
Solution
x = 0.3, and y0 = 0
so, interval ==>[0,0.3]
step soize = h = 0.1
applying Euler approximation
x(n+1) = xn + h
and y(n+1) = yn + hf(xn,yn)
4. x(n+1) = xn + h
x1 = x0 + h
= 0.1
y(n+1) = yn + hf(xn,yn)
or, y1 = y0 + hf(x0,y0)
= 1 + 0.1(xo+yo) = 1 + 0.1(0+1)
= 1.1
so,
x1 = 0.1
y1 = 1.1
again
x(n+1) = xn + h
x2 = x1 + h
= 0.2
y(n+1) = yn + hf(xn,yn)
or, y2 = y1 + hf(x1,y1)
= 1.1 + 0.1*(x1 + y1) = 1.1 + 0.1(0.1 + 1.1)
= 1.22
so,
x2 = 0.2
y2 = 1.22
5. again
x(n+1) = xn + h
x3 = x2 + h
= 0.3
y(n+1) = yn + hf(xn,yn)
or, y3 = y2 + hf(x2,y2)
= 1.22 + 0.1*(x2 + y2) = 1.22 + 0.1(0.2 + 1.22)
= 1.363
so,
x3 = 0.3
y3 = 1.362
again
x(n+1) = xn + h
x4 = x3 + h
= 0.4
y(n+1) = yn + hf(xn,yn)
or, y4 = y3 + hf(x3,y)
= 1.362 + 0.1*(x3 + y3) = 1.362 + 0.1(0.3 + 1.362)
= 1.5282
so,
x2 = 0.4
6. y2 = 1.5282
the graph of the data set generated will yield the approximate graph of the original equation
![x = 0.3, and y0 = 0
so, interval ==>[0,0.3]
step soize = h = 0.1
applying Euler approximation
x(n+1) = xn + h
and y(n+1) = yn + hf(xn,yn)
x(n+1) = xn + h
x1 = x0 + h
= 0.1
y(n+1) = yn + hf(xn,yn)
or, y1 = y0 + hf(x0,y0)
= 1 + 0.1(xo+yo) = 1 + 0.1(0+1)
= 1.1
so,
x1 = 0.1
y1 = 1.1
again
x(n+1) = xn + h
x2 = x1 + h
= 0.2
y(n+1) = yn + hf(xn,yn)
or, y2 = y1 + hf(x1,y1)
= 1.1 + 0.1*(x1 + y1) = 1.1 + 0.1(0.1 + 1.1)](https://image.slidesharecdn.com/x0-230408123346-84299a77/85/x-0-3-and-y0-0so-interval-0-0-3-step-soize-h-0-1-pdf-1-320.jpg)
