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Extra Credit: Who was Knute Rockne? What sport and team was he affiliated with? (3 points)

Show that the Sturm-Liouville problem  { ϕ ″ + λ ϕ = 0 ,   0

Consider the boundary value problem involving Laplace’s equation in a semi-infinite slab { u x x + u y y = 0 , 0 0 , u ( 2 , y ) = 0 , y > 0 , u y ( x , 0 ) = 0 , 0 0 {“version”:”1.1″,”math”:”u(x,y)=A\cos(\omega x)e^{\omega y} + B\sin(\omega x)e^{\omega y} + C\cos(\omega x)e^{-\omega y} +D\sin(\omega x)e^{-\omega y},\ \omega >0″}where A, B, C, D{“version”:”1.1″,”math”:”A, B, C, D”} and ω{“version”:”1.1″,”math”:”ω”} are constants to be determined. Part (a): Find ALL values of ω{“version”:”1.1″,”math”:”ω”} that produce nonzero solution to the PDE and satisfies ALL the homogeneous BC. Also write their corresponding “eigenfunctions”. Part (b): Write a linear superposition of only the functions in the second answer box in part (a) above to use in part (c). Part (c): Apply the remaining nonhomogeneous BC to the answer you wrote in part (b) to find the function u(x,y){“version”:”1.1″,”math”:”u(x,y)”} that solves the full BVP. You must use the answer you wrote in part (b) above to get any credit here.

In physical anthropology, why is it useful to examine sexual dimorphism? [1]

In what ways do primate females differ from most other mammals their size? [1]

  From the text and in class, there is some evidence to suggest that Neanderthals [1]

You find a fossil skeleton with the following traits: eyes in the front of the skull, an opposable thumb, vertebrae (spinal column), fused frontal suture, 2.1.3.2 dental formula, lack of a reflective tapetum. It likely is a fossil species in which group [1]. It has an IMI of 50 so it is likely [2].

Consider the problem of finding the temperature distribution u(x,t){“version”:”1.1″,”math”:”u(x,t)”} of a homogeneous one-dimensional rod of length π2{“version”:”1.1″,”math”:”π2″} with perfectly insulated ends and lateral sides, no internal heat generation and a given initial temperature profile. The boundary value problem is:  { u t − u x x = 0 , 0 0 , u x ( π 2 , t ) = 0 , t > 0 , u ( x , 0 ) = 100 sin ⁡ ( x ) , 0 0 {“version”:”1.1″,”math”:”u(x,t)=e^{-\omega^2t}\Big\{A\cos(\omega x)+B\sin(\omega x)\Big\}, \quad \omega > 0″}and  u ( x , t ) = C x + D {“version”:”1.1″,”math”:”u(x,t)=Cx+D”}where A, B, C, D{“version”:”1.1″,”math”:”A, B, C, D”} and ω{“version”:”1.1″,”math”:”ω”} are constants to be determined.  Part (a): Apply only the homogeneous BC to the form u(x,t)=Cx+D{“version”:”1.1″,”math”:”u(x,t)=Cx+D”} to find if there is a nonzero solution of this form to the completely homogeneous BVP.  Part (b): Apply only the homogeneous BC to the form  u ( x , t ) = e − ω 2 t { A cos ⁡ ( ω x ) + B sin ⁡ ( ω x ) } {“version”:”1.1″,”math”:”u(x,t)=e^{-\omega^2t}\Big\{A\cos(\omega x)+B\sin(\omega x)\Big\}”} to find if there are nonzero solutions of this form to the completely homogeneous BVP. Part (c): Write a linear superposition of only the functions listed in your answer box in part(b) to use in part(d). Part (d): Apply the one nonhomogeneous BC to your answer in part (c) to find the solution u(x,t){“version”:”1.1″,”math”:”u(x,t)”} to the full BVP. You must use the answer you wrote in part (c) above to get any credit here.

The Out-of-Africa model explains [1]

Neanderthal brain size [1]