Without knowing something about differential equations and methods of solving them, it is difficult to appreciate the history of this important branch of mathematics. Further, the development of differential equations is intimately interwoven with the general development of mathematics and cannot be separated from it. Nevertheless, to provide some historical perspective, we indicate here some of the major trends in the history of the subject, and identify the most prominent early contributors. Other historical infor- mation is contained in footnotes scattered throughout the book and in the references listed at the end of the chapter. The subject of differential equations originated in the study of calculus by Isaac Newton (1642–1727) and Gottfried Wilhelm Leibniz (1646–1716) in the seventeenth century. Newton grew up in the English countryside, was educated at Trinity College, Cambridge, and became Lucasian Professor of Mathematics there in 1669. His epochal discoveries of calculus and of the fundamental laws of mechanics date from 1665. They were circulated privately among his friends, but Newton was extremely sensitive to criticism, and did not begin to publish his results until 1687 with the appearance of his most famous book, Philosophiae Naturalis Principia Mathematica. While Newton did relatively little work in differential equations as such, his development of the calculus and elucidation of the basic principles of mechanics provided a basis for their applications in the eighteenth century, most notably by Euler. Newton classified first order differential equations according to the forms dy/dx = f (x), dy/dx = f (y), and dy/dx = f (x,y). For the latter equation he developed a method of solution using infinite series when f (x,y) is a polynomial in x and y. Newton’s active research in mathematics ended in the early 1690s except for the solution of occasional challenge problems and the revision and publication of results obtained much earlier. He was...

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Incidents in the Life of a Slave Girl: Stripped from Motherhood and Womanhood
In Incidents of the Life of a Slave Girl written by Harriet Jacob’s in the 1850s, Harriet Jacobs describes her life as a slave and how she and many of the other slave women were stripped of their motherhood and womanhood on a regular basis. Many of the slave owners had children by these women, but to acknowledge this fact was a taboo subject. Harriet Jacobs explains to her readers how these women were...

...Agricultural Revolution
Back in the early years, people have their very own way to survive in this world. They went for hunting edible animals in the juggle or gather in a village or place so that they could obtain food supplies. Could we imagine how tough it was for these people merely to get food for living, so that they could continue their life and preserve the continuation of human being? But thankfully it changed in 1700s when people started to make agricultural revolution, by...

...mathematics at a deeper level.
Review of homogeneous equations
The homogeneous constant coeﬃcient linear equation an y (n) +· · ·+a1 y +a0 y = 0
has the characteristic polynomial an rn +· · ·+a1 r+a0 = 0. From the roots r1 , . . . , rn
of the polynomial we can construct the solutions y1 , . . . , yn , such as y1 = er1 x . We
can also rewrite the equation in a weird-looking but useful way, using the symbol
d
D = dx .
Examples:...

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Tyranny Tyranny
In Chapter 4 of a people’s history, "Tyranny is Tyranny" by Howard Zinn, it talks about the movement for leveling (economic equality) in the colonies. Also it talks about the causes of the American Revolution. Zinn discusses that the Founding Fathers nervous for war to disturb the societies from their individual economic troubles and discontinue popular movements, a scheme that he prerogatives the country's leaders would resume to usage in the future....

...Essay Question: Underlying causes of 1905 revolution in Russia were not political. Whatever else the revolutionaries wanted it was not to overthrow the Tsar. How far do you agree with this claim?
I agree that the underlying causes of the 1905 revolution were not only political there were also economic, social and military factors that lead to this revolution.
Firstly the social causes of this event. Even though in 1861 the Emancipation of the Serfs had occurred by the early 20th century...

...Chapter 11 ROBBER BARONS AND REBELS
1 Explain what Zinn means by a “skillful terracing to stabilize the pyramid of wealth.”
What Zinn meant by a “skillfull terracing to stabilize the pyramid of wealth” is, they believed the economic growth would be much better with the aid of blacks, whites, Chinese, and European immigrants. They had to do it together in a way to stabilize the economic wealth.
2 Explain what Zinn means by saying that the Interstate Commerce Act of 1887 “gives away...

...5.3 Discussion Questions
1. Why did Cato object to repealing the Oppian law? What was the basis of his objections?
Cato objected to repealing the oppian law because he thought that if women started to become equals with men, they would start to become their superiors. Cato referred to their ancestors and how they “permitted no woman to conduct even personal business without a guardian to intervene in her behalf,” meaning a woman can’t make her own decisions and how a man decides her...

...Name: Brianna Molnar |Date: | |
| | |
Graded Assignment
Korematsu v. the United States (1944)
Use the background information and the primary sources in the Graded Assignment: Primary Sources sheet to answer the following questions.
(5 points)
|Score |
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1. What prompted the sudden outpouring...

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