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For 1D case it will be difficult to use conventional symbols. So I choose 3D case...
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Show that the retarded potentials given by 0(x, t) = 176f d (,4)ret A(x, t) =...
9.251 In a region where μ,-E,-1 and σ 0, the retarded potentials are given are given r(z-ct)Vande...
9.251 In a region where μ,-E,-1 and σ 0, the retarded potentials are given are given r(z-ct)VandeAsTando-)a, byr (a) Show that V . A -μέ--. (b) Find B. H. E. and D. (c) Show that these results satisfy Maxwell's equations if J and ρν are zero. 0t
9.251 In a region where μ,-E,-1 and σ 0, the retarded potentials are given are given r(z-ct)VandeAsTando-)a, byr (a) Show that V . A -μέ--. (b) Find B. H. E. and D. (c)...
2. Consider the following 1-D wave equation with initial condition u (x, 0)- F (x) where F(x) is a given function. a) Show that u (x, t)-F (x - t) is a solution to the given PDE. b) If the function F...
2. Consider the following 1-D wave equation with initial condition u (x, 0)- F (x) where F(x) is a given function. a) Show that u (x, t)-F (x - t) is a solution to the given PDE. b) If the function F is given as 1; x< 10 x > 10 u(x, 0) = F(x) = use part (a) to write the solution u(x, t) c) Sketch u(x,0) and u(x,1) on the same u-versus-x graph d) Explain in your own...
4. Let x E C1 (0,T]; R), T > 0 satisfy _ cos(t)x(t)H(t) + sin(t)2(t) = 0 for all t E (0,T). (a) S...
4. Let x E C1 (0,T]; R), T > 0 satisfy _ cos(t)x(t)H(t) + sin(t)2(t) = 0 for all t E (0,T). (a) Show that this defines a FODE for at least one T>0. 1 mark 2 mark (c) Find the potential and conclude (briefly) what is the solution space for the FODE for (b) Transform (possibly inverting) the DE into an exact DE. T. 2 mark
4. Let x E C1 (0,T]; R), T > 0 satisfy _ cos(t)x(t)H(t)...
Problem 1: We are interested in solving a modified form of diffusion equation given below using Fourier transforms au(x,t) The domain of the problem is-oo < x < oo and is 0 < t < oo . At...
Problem 1: We are interested in solving a modified form of diffusion equation given below using Fourier transforms au(x,t) The domain of the problem is-oo < x < oo and is 0 < t < oo . At time t = 0, the initial condition is given by u (x,0)-0 a) Take the Fourier transform on x and show that the above PDE can be transformed into the following ODE where G() is the Fourier transform of g(x) and U(w,...
Using the reduction potentials given, calculate the equilibrium constant, K, at 20 degrees C for the reaction Using the reduction potentials given, calculate the equilibrium constant, K, at 25°C for...
Using the reduction potentials given, calculate the equilibrium
constant, K, at 20 degrees C for the reaction
Using the reduction potentials given, calculate the equilibrium constant, K, at 25°C for the reaction, 33 3+ Ag (aa) t Fe(a)Ag) Fe (aq) +0.77 V +0.80 V A Ag+(aq) + e- ← a. 1.66 b. 6.4 c. 3.2 d. 6.1 x 10-4 e. 1.6 x 104 Rank the following compounds according to increasing solubility in water. K” is a less than sign) 34...
all a,b,c,d 1. Suppose C is simple closed curve in the plane given by the parametric equation and recall that the outward unit normal vector n to C is given by y(t r'(t) If g is a scalar field on...
all a,b,c,d
1. Suppose C is simple closed curve in the plane given by the parametric equation and recall that the outward unit normal vector n to C is given by y(t r'(t) If g is a scalar field on C with gradient Vg, we define the normal derivative Dng by and we define the Laplacian, V2g, of g by For this problem, assume D and C satisfy the hypotheses of Green's Theorem and the appropriate partial derivatives of f...
Show that for the completely insulated bar (including the ends), ux(0,t) = 0, uz(L,t) 0, and...
Show that for the completely insulated bar (including the ends), ux(0,t) = 0, uz(L,t) 0, and initial condition u(x,0) = f(x), where 1) (use L = 1 and c= 1) f(x) = 1 (5) Can you explain your answer?
Suppose X is a random vector, where X = (X(1), . . . , x(d))T , d with mean 0 and covariance matr...
Suppose X is a random vector, where X = (X(1), . . . , x(d))T , d with mean 0 and covariance matrix vv1 , for some vector v ER 1point possible (graded) Let v = . (i.e., v is the normalized version of v). What is the variance of v X? (If applicable, enter trans(v) for the transpose v of v, and normv) for the norm |vll of a vector v.) Var (V STANDARD NOTATION SubmitYou have used 0...
2. Let So and Si be the prices of a stock at t = 0. 1...
2. Let So and Si be the prices of a stock at t = 0. 1 in the one-period binomial model. Assume the no-arbitrage condition 0 〈 d 〈 1 + r < u, and assume P(H)-p. We define θ-up + d(1-p)-1. Show that the expected value at t 0 of is 1S 1+θ Si 1+θ Eo =So-
Given that H is a set and that x is an interior point of the set R∖H, prove that x is not close t...
Given that H is a set and that x is an interior point of the set R∖H, prove that x is not close to H. So, I have an example where they are opposite of the question, I just don't know how to spin it around. Suppose that S is a set of real numbers and that x is a given number. Then the following two conditions are equivalent to one another: 1.The number x is close to the set...
9.251 In a region where μ,-E,-1 and σ 0, the retarded potentials are given are given r(z-ct)VandeAsTando-)a, byr (a) Show that V . A -μέ--. (b) Find B. H. E. and D. (c) Show that these results satisfy Maxwell's equations if J and ρν are zero. 0t
9.251 In a region where μ,-E,-1 and σ 0, the retarded potentials are given are given r(z-ct)VandeAsTando-)a, byr (a) Show that V . A -μέ--. (b) Find B. H. E. and D. (c)...
2. Consider the following 1-D wave equation with initial condition u (x, 0)- F (x) where F(x) is a given function. a) Show that u (x, t)-F (x - t) is a solution to the given PDE. b) If the function F is given as 1; x< 10 x > 10 u(x, 0) = F(x) = use part (a) to write the solution u(x, t) c) Sketch u(x,0) and u(x,1) on the same u-versus-x graph d) Explain in your own...
4. Let x E C1 (0,T]; R), T > 0 satisfy _ cos(t)x(t)H(t) + sin(t)2(t) = 0 for all t E (0,T). (a) Show that this defines a FODE for at least one T>0. 1 mark 2 mark (c) Find the potential and conclude (briefly) what is the solution space for the FODE for (b) Transform (possibly inverting) the DE into an exact DE. T. 2 mark
4. Let x E C1 (0,T]; R), T > 0 satisfy _ cos(t)x(t)H(t)...
Problem 1: We are interested in solving a modified form of diffusion equation given below using Fourier transforms au(x,t) The domain of the problem is-oo < x < oo and is 0 < t < oo . At time t = 0, the initial condition is given by u (x,0)-0 a) Take the Fourier transform on x and show that the above PDE can be transformed into the following ODE where G() is the Fourier transform of g(x) and U(w,...
Using the reduction potentials given, calculate the equilibrium
constant, K, at 20 degrees C for the reaction
Using the reduction potentials given, calculate the equilibrium constant, K, at 25°C for the reaction, 33 3+ Ag (aa) t Fe(a)Ag) Fe (aq) +0.77 V +0.80 V A Ag+(aq) + e- ← a. 1.66 b. 6.4 c. 3.2 d. 6.1 x 10-4 e. 1.6 x 104 Rank the following compounds according to increasing solubility in water. K” is a less than sign) 34...
all a,b,c,d
1. Suppose C is simple closed curve in the plane given by the parametric equation and recall that the outward unit normal vector n to C is given by y(t r'(t) If g is a scalar field on C with gradient Vg, we define the normal derivative Dng by and we define the Laplacian, V2g, of g by For this problem, assume D and C satisfy the hypotheses of Green's Theorem and the appropriate partial derivatives of f...
Show that for the completely insulated bar (including the ends), ux(0,t) = 0, uz(L,t) 0, and initial condition u(x,0) = f(x), where 1) (use L = 1 and c= 1) f(x) = 1 (5) Can you explain your answer?
Suppose X is a random vector, where X = (X(1), . . . , x(d))T , d with mean 0 and covariance matrix vv1 , for some vector v ER 1point possible (graded) Let v = . (i.e., v is the normalized version of v). What is the variance of v X? (If applicable, enter trans(v) for the transpose v of v, and normv) for the norm |vll of a vector v.) Var (V STANDARD NOTATION SubmitYou have used 0...
2. Let So and Si be the prices of a stock at t = 0. 1 in the one-period binomial model. Assume the no-arbitrage condition 0 〈 d 〈 1 + r < u, and assume P(H)-p. We define θ-up + d(1-p)-1. Show that the expected value at t 0 of is 1S 1+θ Si 1+θ Eo =So-
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