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A thin wire coinciding with the x-axis on the interval [L,

Differential Equations with Boundary-Value Problems, | 8th Edition | ISBN: 9781111827069 | Authors: Dennis G. Zill, Warren S. Wright ISBN: 9781111827069 202

Solution for problem 12.1.51 Chapter 12.3

Differential Equations with Boundary-Value Problems, | 8th Edition

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Differential Equations with Boundary-Value Problems, | 8th Edition | ISBN: 9781111827069 | Authors: Dennis G. Zill, Warren S. Wright

Differential Equations with Boundary-Value Problems, | 8th Edition

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Problem 12.1.51

A thin wire coinciding with the x-axis on the interval [L, L] is bent into the shape of a circle so that the ends x L and x L are joined. Under certain conditions, the temperature u(x, t) in the wire satisfies the boundaryvalue problem u(L, t) u(L, t), t 0 u(x, 0) f(x), L x L. Find the temperature u(x, t). 8

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HY 120 4/14/16 Anti-slavery Movement (continued)  Evolves overtime  During this period no one knows how to solve anything  Missouri Compromise 1819 o Missouri applies for state hood o Missouri has a lot of slavery so it wants to be a slave state o Southerners will be more in power than northern states o Shifts balance of power between the northern and southern states o Main come in as a free state  1819-1860 Americans trying to solve slavery without actually solve it o 1860-slavery explodes into civil war  American anti-slavery society o Mostly whites o Benjamin Lyndy says yes we need to gradually get rid of slavery & want to compensate slave owners Politically  Middle of political revolution Elections  1824-Andrew Jackson vs. Quincy Adams—Adams WINS  1828-same election—Andrew Jackson WINS  1832-Andrew Jackson wins again  Andrew Jackson was a WAR HERO o Killed British and Indians o Hates elite aristocrats  John Quincy Adams-elite (old revolutionary crowd)  By 1824 most states dropped qualifications for voting o White men, property owners dropped & now poor people can vote o Whoever appears to poor people (men) will win election Election of 1824  Andrew Jackson “redneck” represents common people  Most of his votes went to the white house  Henry clay votes for J.Q Adams & he makes Clay secretary of state  ADAMS WINS this election  Andrew Jackson says the elite stole his election & calls it a “Corrupt Bargain” and sides with the poor Election of 1828  Jackson runs against J.Q. Adams again  Jackson WINS  Andrew Jackson is a strong nationalist & wants strong CENTRAL GOVT. o From Tennessee & owns slaves o Big states right activist 1 issue  Jackson comes back with “Nullification”-taxes/tariffs  New England/industrialists wanted protective tariffs o Not good for consumers o Very regional conflict o North wants it o South hates it, they see it as an opportunity for the north to make them powerless o Jackson passes Bill of Rights (Congress)  1828-Tariff of Abomination o Triggers John C. Calhoun to write Exposition & Protest  Calhoun is exposing the Abomination o Encourages the state legislatures to protest the tariffs  Nullification-supreme court always win  1832-Jackson reformed tariffs & brought some of the taxes down  Passes the FORCE ACT o If you do not abide by the federal laws, we will arrest you nd 2 issue  Indian Removal- forcing Indians off U.S land  Status of Native Americans o Citizens o Not settled until 1920’s  1820’s-Native Americans had lost 200 million acres of land that U.S. stole  Policies became legitimized  Conflict about who is in charge of this (Indian Removal) Cherokee Nation vs. Georgia (1831 & 1832)  Indian went to states or got to protect them, Georgia did (against federal govt.) Supreme Court sides with Indians and against govt Worchester vs. Georgia  Native Americans are tribes under federal govt.  Who gets that authority over Indians—supreme court  Indian Removal Policy strikes up  Trail of Tears-Indians chained, and forced to give up their land (Oklahoma, Florida, Georgia, Alabama, North Carolina) 3 Issue  With Andrew Jackson  1819-Supreme Court ruled in McCullough vs Maryland o Maryland didn’t want to be taxed so they taxed the bank so heavily that it nullifies it o Supreme Court says in response YOU CAN’T DO THAT –pro bank decision  Andrew Jackson hates federal bank o Poor people (banks are destroying them) o Andrew Jackson refuses to recharter the U.S BANK o Puts in place the “PET” Banks  Local state banks Election of 1832—Jackson runs for his 2 term  Banks is the main issue-no empire, transportation if taken away  1832-major parties splintering  1860’s-third parties emerging  Jackson won election of 1832 Issues of slavery evolving around 1840’s  Nat Turner revolt-slave uprising occurs in Virginia o Nat Turner was slave in Virginia who believed that God has spoken to him and was telling that slavery was evil and he needed to put together a revolt to end it o Gov’t always tightens up on slavery-restrictions o 1830’s-40’s the incidents of violence against slaves is going to increase o Abolitionists & slavery activists sees morality  Southerner who tries to protect slaves also have morals beliefs of slavery  John C. Calhoun argues that slavery is a universal condition o Argues that the bible had slavery and is not immoral  George Fitzugh-says slavery is absolutely correct and moral (modern generation for younger people) o Refers to science and talks about the new science has proven that African Americans are inferior to whites o Points to scientific facts that whites brains are superior than Africans Americans brains  Abolitionists says slavery is immoral and is hurting the economy

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Chapter 12.3, Problem 12.1.51 is Solved
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Textbook: Differential Equations with Boundary-Value Problems,
Edition: 8
Author: Dennis G. Zill, Warren S. Wright
ISBN: 9781111827069

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A thin wire coinciding with the x-axis on the interval [L,