Suppose that we have the square region described by and suppose that the equilibrium temperature distribution along the boundary is given by , , and . Suppose next that this region is partitioned into an mesh using for and . If the temperatures of the interior mesh points are labeled by then show that for and . To handle the boundary points, define for and . Next let be the matrix with the identity matrix in the upper right-hand corner, a one in the lower left-hand corner, and zeros everywhere else. For example, and so on. By defining the matrix show that if is the matrix with entries , then the set of equations for and can be written as the matrix equation where we consider only those elements of with and
▯ Lecture 1.1 What was life like in the Americas before “Discovery” Pristine Myth o People thought that the land was untouched before they got there o Environment, settlement, diversity o Migration theories o 12,000-30,000 years ago What cultures were present before European Contact o Pacific northwest o Fish o Plains o Hunt buffalo and use every part o Not permanent settlement, moved with the buffalo o Southwest o Natchez, Creek, Choctaw, Cherokee o Farming o Atlantic coast o Powhatan o Farming, hunting o North o Iroquois o Farming, fortifications o Urban areas o Cahokia o Population: 10million+ in North America 90million+ in western Hemisphere why did Europeans report finding “virgin soil” disease: smallpox, typhus, influenza, diphtheria Incan conquest no Quarantine o natives didn’t believe in it, they wanted to take care of the sick person lack of immunity animals: o didn’t know how to domesticate animals o Hernado DeSoto’s Pigs Arrives in Florida Travels through southwest 95% of the Caddo Indians died from the disease from the pigs ▯ What did the Europeans want To get rich! New and expa
