数学代码代写 MT4512代写 自动机、语言和复杂性代写
118MT4512 Automata, Languages and Complexity 数学代码代写 EXAM DURATION: 2 hours EXAM INSTRUCTIONS: Attempt ALL questions. The number in square brackets shows the maximum marks obtainable for tha...
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数学考试代做 To get full credit you must show ALL your work. The problems must be solved without any assistance of others or the usage of unauthorized material
To get full credit you must show ALL your work.
The problems must be solved without any assistance of others or the usage of unauthorized material or information. This is a “closed book” exam: no texts, notes or calculators allowed.
Consider a metal rod encased in a thermal insulator. Suppose the rod is immersed in boiling water so that its temperature is 100˚C throughout, and then removed from the water at time t = 0 with one of its ends immediately put in ice and kept at temperature 0˚C, and insulated on the other end.
Mathematically, this situation can be modeled as follows:
Show the details of your construction of the solution. You must show all the steps of your calculation for full credit.
Which of the following is the general solution of the equation
(a)y(t) = ce−t − te−t ?
(b) y(t) = tet + cet ?
(c) y(t) = te−t + ce−t ?
(d) y(t) = e−t + ce−t ?
(e) y(t) = te−t + cte−t ?
(f) None of the above
Find a differential equation whose general solution is: y(x) = c1ex + c2e-3x, where c1, c2 are arbitrary real numbers.
The function E(t) is T-periodic, defined in one periodic window by
Determine the Fourier series for E(t)
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