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Classify the diffusion equation-ะเ a 2, determine if it has any real characteristic paths and if so, find and show...
(10') Consider the equation Cut #cut = 1, 2 & R. (a) Find the characteristic curves....
(10') Consider the equation Cut #cut = 1, 2 & R. (a) Find the characteristic curves. Sketch two curves on the t-x plane. (b) Define the characteristic coordinates. (c) Solve the equation with initial condition u(x,0) = x2 + 1.
Use the 1D diffusion equation to find T(x,t): 2. A bar of length L has an...
Use the 1D diffusion equation to find T(x,t):
2. A bar of length L has an initial temperature distribution T(x,0) = a + br ( x = L are the ends of the bar). The ends are insulated. Find T(x,t) for t > 0. 0 and си oFlu сх
please provide me with full working solution. Any help is appreciated. thank you in advance Consider the diffusion equation, au(x,t u(x,t) Here u(x,t) > 0 is the concentration of some diffusing...
please provide me with full working solution. Any help is
appreciated. thank you in advance
Consider the diffusion equation, au(x,t u(x,t) Here u(x,t) > 0 is the concentration of some diffusing substance, the spatial variable is x, time is t and D is a constant called the diffusivity with dimensions [LT-11. We will consider the diffusion equation on a finite spatial domain (0<x< 1) and an infinite time horizon (t > 0). To solve the diffusion equation we must include...
Consider the plane autonomous system 4) 2 X'=AX with A (a) Find two linearly independent real solutions of the syst...
Consider the plane autonomous system 4) 2 X'=AX with A (a) Find two linearly independent real solutions of the system (b) Classify the stability (stable or unstable) and the type (center, node, saddle, or spiral) of the critical point (0,0). (c) Plot the phase portrait of the system containing a trajectory with direction as t-oo whose initial value is X(0) (0,6)7 and any other trajectory with direc- tion. (You do not need to draw solution curves explicitly.)
Consider the plane...
Show if y y(x) is a solution to an autonomous differential equation y' - f(y), then so is any "horizontal translation" of y. That is, show for any real number C, the function yc(x) - y(x...
Show if y y(x) is a solution to an autonomous differential equation y' - f(y), then so is any "horizontal translation" of y. That is, show for any real number C, the function yc(x) - y(x C) is also a solution to y'-f . y). Of course, y and yc may have possibly different initial conditions
Show if y y(x) is a solution to an autonomous differential equation y' - f(y), then so is any "horizontal translation" of y. That...
(i) Show that if X, 9X then aX+b aX + b for any real a and...
(i) Show that if X, 9X then aX+b aX + b for any real a and b. (ii) If X has zero mean and variance op, show that P(X 2 t) 2, fort > 0 (iii) Show that X, 0 if and only if EG .) +0, as n +. (iv) Let X1 X2, ... be independent and identically distributed random variables whose com- mon characteristic function satisfies '0) = in. Show that x;".
02 Comsider the linca ecomd order partia i (a) [2 marks] determine the class of the equation (b) [2 marks] Find the characteristics of the equation. 12 Marks] Sketch the characteristics in the...
02 Comsider the linca ecomd order partia i (a) [2 marks] determine the class of the equation (b) [2 marks] Find the characteristics of the equation. 12 Marks] Sketch the characteristics in the (x, y) plane (c) (d) [2 Marks] determine the characteristic coordinates (e) [9 marks] Reduce the equation to standard form (f) [3 marks] find its general solution.
02 Comsider the linca ecomd order partia i (a) [2 marks] determine the class of the equation (b) [2 marks]...
Question 4 heoWoing pradlen are so be homed on on Werbsenday: p 17. Show all wark...
Question 4
heoWoing pradlen are so be homed on on Werbsenday: p 17. Show all wark ant insdicate any lememary roe opsrations ased in sofation of syseses, caleuloion of ieweres.ete. m written in PENCIL i our own hand Skow esough work to jumty your asuners Write th reporate shevts of psper which you alach do nov wowk she probiens on th age. No peinted horwork or homewowk copved fom a solulons mamal or onine source wii be graded wnt so...
5. (2+2+3 Points) Consider the linear wave equation for-oo <エ<oo,-oo < t <oo for - oo<<oo...
5. (2+2+3 Points) Consider the linear wave equation for-oo <エ<oo,-oo < t <oo for - oo<<oo for utt-c2uzz = f(x, t) tr(r,0)- (r) _oo < x < oo. a. Sketch the domain of dependence of the point (,t) (4, 1) in the (x, t)-plane in 1. case c = 2, Do the same in the case c b. State the general solution forrnula for this problem! in terms of the data f, φ, ψ. c. Now suppose ψ = 0...
For the equation 2x2 + 2y2 - 12x + 8y - 24 = 0, do the...
For the equation 2x2 + 2y2 - 12x + 8y - 24 = 0, do the following. (a) Find the center (h,k) and radius r of the circle. (b) Graph the circle. (c) Find the intercepts, if any. (a) The center is (Simplify your answer. Type an ordered pair.) The radius is ra (Simplify your answer.) (b) Use the graphing tool to graph the circle. Click to enlarge graph X (c) Find the intercepts, if any. Select the correct choice...
(10') Consider the equation Cut #cut = 1, 2 & R. (a) Find the characteristic curves. Sketch two curves on the t-x plane. (b) Define the characteristic coordinates. (c) Solve the equation with initial condition u(x,0) = x2 + 1.
Use the 1D diffusion equation to find T(x,t):
2. A bar of length L has an initial temperature distribution T(x,0) = a + br ( x = L are the ends of the bar). The ends are insulated. Find T(x,t) for t > 0. 0 and си oFlu сх
please provide me with full working solution. Any help is
appreciated. thank you in advance
Consider the diffusion equation, au(x,t u(x,t) Here u(x,t) > 0 is the concentration of some diffusing substance, the spatial variable is x, time is t and D is a constant called the diffusivity with dimensions [LT-11. We will consider the diffusion equation on a finite spatial domain (0<x< 1) and an infinite time horizon (t > 0). To solve the diffusion equation we must include...
Consider the plane autonomous system 4) 2 X'=AX with A (a) Find two linearly independent real solutions of the system (b) Classify the stability (stable or unstable) and the type (center, node, saddle, or spiral) of the critical point (0,0). (c) Plot the phase portrait of the system containing a trajectory with direction as t-oo whose initial value is X(0) (0,6)7 and any other trajectory with direc- tion. (You do not need to draw solution curves explicitly.)
Consider the plane...
Show if y y(x) is a solution to an autonomous differential equation y' - f(y), then so is any "horizontal translation" of y. That is, show for any real number C, the function yc(x) - y(x C) is also a solution to y'-f . y). Of course, y and yc may have possibly different initial conditions
Show if y y(x) is a solution to an autonomous differential equation y' - f(y), then so is any "horizontal translation" of y. That...
(i) Show that if X, 9X then aX+b aX + b for any real a and b. (ii) If X has zero mean and variance op, show that P(X 2 t) 2, fort > 0 (iii) Show that X, 0 if and only if EG .) +0, as n +. (iv) Let X1 X2, ... be independent and identically distributed random variables whose com- mon characteristic function satisfies '0) = in. Show that x;".
02 Comsider the linca ecomd order partia i (a) [2 marks] determine the class of the equation (b) [2 marks] Find the characteristics of the equation. 12 Marks] Sketch the characteristics in the (x, y) plane (c) (d) [2 Marks] determine the characteristic coordinates (e) [9 marks] Reduce the equation to standard form (f) [3 marks] find its general solution.
02 Comsider the linca ecomd order partia i (a) [2 marks] determine the class of the equation (b) [2 marks]...
Question 4
heoWoing pradlen are so be homed on on Werbsenday: p 17. Show all wark ant insdicate any lememary roe opsrations ased in sofation of syseses, caleuloion of ieweres.ete. m written in PENCIL i our own hand Skow esough work to jumty your asuners Write th reporate shevts of psper which you alach do nov wowk she probiens on th age. No peinted horwork or homewowk copved fom a solulons mamal or onine source wii be graded wnt so...
5. (2+2+3 Points) Consider the linear wave equation for-oo <エ<oo,-oo < t <oo for - oo<<oo for utt-c2uzz = f(x, t) tr(r,0)- (r) _oo < x < oo. a. Sketch the domain of dependence of the point (,t) (4, 1) in the (x, t)-plane in 1. case c = 2, Do the same in the case c b. State the general solution forrnula for this problem! in terms of the data f, φ, ψ. c. Now suppose ψ = 0...
For the equation 2x2 + 2y2 - 12x + 8y - 24 = 0, do the following. (a) Find the center (h,k) and radius r of the circle. (b) Graph the circle. (c) Find the intercepts, if any. (a) The center is (Simplify your answer. Type an ordered pair.) The radius is ra (Simplify your answer.) (b) Use the graphing tool to graph the circle. Click to enlarge graph X (c) Find the intercepts, if any. Select the correct choice...
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