The cable equation ut-γ uzz-at, with γ, α > 0, also known as the lossy heat equa- tion, was derived by the nineteenth-century Scottish physicist William Thomson to model propagation of signals in a transatlantic cable. Later, in honor of his work on thermodynamics, including determining the value of absolute zero temperature, he was named Lord Kelvin by Queen Victoria. The cable equation was later used to model the electrical activity of neurons. (a) Show that the general solution to the cable equation is given by u(t, x)-e-atu(t, z), where u(t, z) solves the heat equation tr γ'm (b) Find a Fourier series solution to the Dirichlet initial-boundary value problem vt = γ uzz _ αν, υ(0, z) = f(x), u(t,0) = 0=r(t, 1), 0 1, t>0 x Does your solution approach an equlibrium value? If so, how fast? (c) Answer part (b) for the Neumann problem

answer: i think it's a

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answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

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in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.  

its kind of blurry. can you put a clearer pic?

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do your own work and don"t cheat.

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