DIFFERENTIAL EQUATIONS: A SIMPLIFIED APPROACH‚ 2nd Edition DIFFERENTIAL EQUATIONS PRIMER By: AUSTRIA‚ Gian Paulo A. ECE / 3‚ Mapúa Institute of Technology NOTE: THIS PRIMER IS SUBJECT TO COPYRIGHT. IT CANNOT BE REPRODUCED WITHOUT PRIOR PERMISSION FROM THE AUTHOR. DEFINITIONS / TERMINOLOGIES A differential equation is an equation which involves derivatives and is mathematical models which can be used to approximate real-world problems. It is a specialized area of differential calculus but it involves
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Multi-Regional Continuity: The Fossil Evidence With regards to the multi-regional continuity model of human evolution‚ there is without a doubt a preponderance of fossil data that supports the diverse origins of Homo sapiens in different regions of the globe. Skulls displaying a wide variety of mixed modern and archaic features have been found in every corner of the world. The mere existence of these fossils is evidence enough to prove that human evolution was far less cut-and-dried a process
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Ancient Egypt was one of the many civilizations existing in the ancient world. Lasting from 8‚000 BCE to 525 BCE‚ it was one of the longest lasting civilizations in the history of the world. Its pyramids and other monuments can still be found in modern day Egypt‚ with its birthplace being along the Nile River. However‚ Egypt went through a lot of changes before becoming the huge civilization that we all think of. Namely‚ Egypt had several developments in agriculture‚ religion and social structures
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the official date of the Roman Empire’s demise. The Franks took over what is now France while the Eastern Goths took over the western Balkans‚ Greece‚ and Italy. The Saxons conquered areas of southern England. Western Europe was heavily based upon the feudal system during this period in time. The feudal system was at its height after the death of the Carolingian Emperor‚ Charlemagne‚ when his successors split up the empire between themselves. Manorialism was also present during this period in time
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the Archaic Age set the stage for the period of great cultural achievement known as the Classical Age. Urban life‚ literacy‚ and maritime trade disappeared as both food production and population declined‚ causing many Greeks to migrate to Ionia. Between 750 and 650 B.C.E.‚ many economic and cultural innovations were introduced to the Greeks from their contacts with Middle Eastern peoples‚ the most valuable of which was the Greek adoption of the Phoenician alphabet. A new form of social and political
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The alliances between China‚ Persia‚ and other Central Asian regions brought about a clash of civilizations‚ which often involved the Byzantine Empire and/or the Roman Empire as a result of increased trade relations during the first centuries A.D. During this time‚ the struggle to control the trade routes became a geopolitical struggle that created military conflicts between civilizations. For instance‚ the Nisibis War of the 290s A.D. defines
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Leibniz’s Spatio-temporal Continuity: Most people agree that the spatiotemporal continuity is a good guide to determine a person’s identity‚ but philosophers want more. The theory says that spatiotemporally continuous stays with the body not the mind. For example if two people switch bodies like they do in Freaky Friday then they are then the mind in the daughter’s body is the daughter and the mind in the mother’s body is the mother’s. Locke’s Psychological Continuity: According to Locke’s theory
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BCE to 1450 CE the spread of religion continued along the Silk Road. While continuity is seen in the patterns of interaction along the Silk Road‚ during the time period 200bce to 1450ce in diffusion of religion through the Eurasian continent‚ clear changes is also seen. These changes include nomadic invasions influence on interaction of cultures and the surrounding regions effect on specific Products traded. Continuity is shown in
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------------------------------------------------- Changes and Continuities in labor systems in Russia Between 1750 and 1914‚ England‚ Germany‚ and Western Europe were all expanding. England was gaining land and trust in the Middle East‚ Germany was becoming an established nation‚ and Western Europe was thriving due to the Industrial Revolution. After recognizing all of this‚ Russia decided it was time for reform or be left in the dust. This caused major changes in Russia’s labor system such as
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Kunal Pathade 11/10/13 10-6 WHAP Hebrew Essay: Continuity and Cultural Diffusion The Jews lived to preserve their culture; that essentially represented the fundamental goal of life to the Jews. The Jews observed the decadence of the Sumerians as a cause of cultural diffusion‚ and wanted to make sure that same thing would not happen to them. Eventually‚ the Jews did become vulnerable to cultural diffusion around the 4th century CE when the Greek-Macedonians from the West came; the great and
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