MT4512 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...View details
Math 2415 Final Exam
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.
1. (70 points) 数学考试代做
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.
5. (10 points) 数学考试代做
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
6. (a) (15 points) 数学考试代做
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)