Homework Answers
a) Using Matlab:
Using these commands, we get our plot as:
b) We can guess that as 
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3. Finish the following problem we discussed in class today: Utt - и(х, 0) — 0,...
5. Find a solution u(x, t) of the following problem utt 0 u(0, t) — и(2,...
5. Find a solution u(x, t) of the following problem utt 0 u(0, t) — и(2, t) — 0 2 sin 3T и(а, 0) — 0, и (х, 0) — sin Tz _
3. In class we discussed the heat conduction problem with the boundary conditions a(0, t) 0, t4(1...
3. In class we discussed the heat conduction problem with the boundary conditions a(0, t) 0, t4(1,t)-0, t > 0 and the initial condition u(r,0) f(a) We found the solution to be of the form where (2n-1)n 1,2,3,. TL 20 Now consider the heat conduction problem with the boundary conditions u(0, t) 1,u(T, t)0, t>0 and the initial condition ur,0) 0. Find u(r,t). Hint: First you must find the steady state.
3. In class we discussed the heat conduction problem...
3. (20 pts). Find the solution to the vibrating-string problem: utt u(0,t) u(L,t) u2,0) 2,0) =...
3. (20 pts). Find the solution to the vibrating-string problem: utt u(0,t) u(L,t) u2,0) 2,0) = 0 = 0 2 sin(27/L) + sin(31/L) sin(72/L) 0<<L, 0<t< 0<t< oo 0<t< 0<r<L 0<r<L
5. Consider the following IBVP (initial boundary value problem utt - Curr = 0, 0<x<1, t>0,...
5. Consider the following IBVP (initial boundary value problem utt - Curr = 0, 0<x<1, t>0, with boundary conditions u(0,t) = u(1, t) = 0, > 0 and initial conditions (7,0) = x(1 – 2), 14(2,0) = 0, 0<x< 1. Use separation of variables method to find an infinite series solution of this problem. Do a complete calculation for this problem.
I think the answer that we discussed in class for this problem was D but I...
I think the answer that we discussed in class for this problem was
D but I do not know why. What indications should I be looking at to
determine that the pH range of these substances?
NH HO (1) 2. A 0.0010 Maqueous solutions of each of the substances below was prepared. Which of these solutions will have a 8 s pHS 12? CHg N NH2 OH NH2 (25 (3) (5) A C2H₂O, Only (2) C3H, NO CuloN Cat₂0 B...
2. In class, we discussed the problem of searching for an item x in a sorted...
2. In class, we discussed the problem of searching for an item x in a sorted array L with n entries. The returned value is supposed to be -1 if the value x is not in the array, and the index i such that L[i] = x if x is in the array. Assume that I does not contain duplicate values. Now consider the decision trees of algorithms for solving this problem. To make the decision tree more explicit, we...
3. (30 pts. total) We discussed the iodination of acetone in class. An alternative, but equivalent,...
3. (30 pts. total) We discussed the iodination of acetone in class. An alternative, but equivalent, way of writing the reaction is: acid H3C-C-CH3 + 131 acetone triiodide H3C-C-CH2 + 21 + H* iodoacetone iodide Is provides a more useful way to introduce 12 into the system. Iz is also useful because it absorbs visible light, and the rate of the reaction can be monitored by measuring the decrease in its absorbance at 565 nm. (Any time you can measure...
5. In class we saw that the function r(u, v) = (sin u, (2 + cos...
5. In class we saw that the function r(u, v) = (sin u, (2 + cos u) cos v, (2 + cos u) sin v), 0<u<27, 050521 parametrizes a torus T, which is depicted below. (a) Calculate ||ru x rull. (b) Show that T is smooth. (c) Find the equation of the tangent plane to T at (0,). (d) Find the surface area of T (e) Earlier in the semester, we observed that a torus can be built out of...
Problem 6 n class we discussed how expensive it is to treat Hepatitis C if you...
Problem 6 n class we discussed how expensive it is to treat Hepatitis C if you decide to purchase the 12 week treatment Sovaldi developed by GILEAD.We mentioned that one option would beto sign a contract where the patient buys the treatment in monthly payments (just like buying a house) and therefore we called it "mortgage" Suppose that the government decides this is a good idea and that the patient should pay this in monthly payments during 10 years and...
problem 5 l lbout 0 for a general solution to the given differential equation u, y(0) = 0, V,(0) = 1 . Your answer should include a grneral formula for the ncients. (Find a recursive relation. If...
problem 5
l lbout 0 for a general solution to the given differential equation u, y(0) = 0, V,(0) = 1 . Your answer should include a grneral formula for the ncients. (Find a recursive relation. If possible find Vi and 1,2). 3: Chebyshev's equation i(y + p'y-0, where p is a constant. Find two linearly Independert series solutions yi and ya. (Hint: find the series solution to the differential equation at z-0 to factor ao and ai as we...
5. Find a solution u(x, t) of the following problem utt 0 u(0, t) — и(2, t) — 0 2 sin 3T и(а, 0) — 0, и (х, 0) — sin Tz _
3. In class we discussed the heat conduction problem with the boundary conditions a(0, t) 0, t4(1,t)-0, t > 0 and the initial condition u(r,0) f(a) We found the solution to be of the form where (2n-1)n 1,2,3,. TL 20 Now consider the heat conduction problem with the boundary conditions u(0, t) 1,u(T, t)0, t>0 and the initial condition ur,0) 0. Find u(r,t). Hint: First you must find the steady state.
3. In class we discussed the heat conduction problem...
3. (20 pts). Find the solution to the vibrating-string problem: utt u(0,t) u(L,t) u2,0) 2,0) = 0 = 0 2 sin(27/L) + sin(31/L) sin(72/L) 0<<L, 0<t< 0<t< oo 0<t< 0<r<L 0<r<L
5. Consider the following IBVP (initial boundary value problem utt - Curr = 0, 0<x<1, t>0, with boundary conditions u(0,t) = u(1, t) = 0, > 0 and initial conditions (7,0) = x(1 – 2), 14(2,0) = 0, 0<x< 1. Use separation of variables method to find an infinite series solution of this problem. Do a complete calculation for this problem.
I think the answer that we discussed in class for this problem was
D but I do not know why. What indications should I be looking at to
determine that the pH range of these substances?
NH HO (1) 2. A 0.0010 Maqueous solutions of each of the substances below was prepared. Which of these solutions will have a 8 s pHS 12? CHg N NH2 OH NH2 (25 (3) (5) A C2H₂O, Only (2) C3H, NO CuloN Cat₂0 B...
2. In class, we discussed the problem of searching for an item x in a sorted array L with n entries. The returned value is supposed to be -1 if the value x is not in the array, and the index i such that L[i] = x if x is in the array. Assume that I does not contain duplicate values. Now consider the decision trees of algorithms for solving this problem. To make the decision tree more explicit, we...
3. (30 pts. total) We discussed the iodination of acetone in class. An alternative, but equivalent, way of writing the reaction is: acid H3C-C-CH3 + 131 acetone triiodide H3C-C-CH2 + 21 + H* iodoacetone iodide Is provides a more useful way to introduce 12 into the system. Iz is also useful because it absorbs visible light, and the rate of the reaction can be monitored by measuring the decrease in its absorbance at 565 nm. (Any time you can measure...
5. In class we saw that the function r(u, v) = (sin u, (2 + cos u) cos v, (2 + cos u) sin v), 0<u<27, 050521 parametrizes a torus T, which is depicted below. (a) Calculate ||ru x rull. (b) Show that T is smooth. (c) Find the equation of the tangent plane to T at (0,). (d) Find the surface area of T (e) Earlier in the semester, we observed that a torus can be built out of...
Problem 6 n class we discussed how expensive it is to treat Hepatitis C if you decide to purchase the 12 week treatment Sovaldi developed by GILEAD.We mentioned that one option would beto sign a contract where the patient buys the treatment in monthly payments (just like buying a house) and therefore we called it "mortgage" Suppose that the government decides this is a good idea and that the patient should pay this in monthly payments during 10 years and...
problem 5
l lbout 0 for a general solution to the given differential equation u, y(0) = 0, V,(0) = 1 . Your answer should include a grneral formula for the ncients. (Find a recursive relation. If possible find Vi and 1,2). 3: Chebyshev's equation i(y + p'y-0, where p is a constant. Find two linearly Independert series solutions yi and ya. (Hint: find the series solution to the differential equation at z-0 to factor ao and ai as we...
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