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5. Write down an explicit formula for a solution of Otu – Autu= 0 in (0,...
Please write neatly Let f(x) be a Cl(R) function and u(t, x) be a solution to...
Please write neatly
Let f(x) be a Cl(R) function and u(t, x) be a solution to the inviscid Burger's IVP Ut + uuz = 0, 4(0,x) = f(x). (a) Use the formula ult, x) = f (x – ut) to derive the following explicit identity for the partial derivative Ou du Ət f($)f'(5) 1+tf'(E) with $ = X – ut. (b) Assume that there exists a number wo E R such that f'(20) < 0 and f(x) > 0. Use...
(2) [15pts] Write the solution of the PDE for 0
Can you help me with this question please?
(2) [15pts] Write the solution of the PDE for 0 <<1 and t>0 u(0,t) 0 u(1,t) = 0 u(x,0)-0 Make sure you simplify as much as possible by using the fact that the source term f depends only on z and not on t. What is the solution at long time lim,-+oo u(x, t) if f()T) [Hint: You can obtain this by solving a single (trivial) ODE]
(2) [15pts] Write the solution...
Find a formula for the solution of the initial value problem for for t>0, -oc < x < oo ut = uzz-u...
Find a formula for the solution of the initial value problem for for t>0, -oc < x < oo ut = uzz-u a(1:0) = g(z) -x < 1 < x where g is continuous and bounded.( Hint: use v(x, t) = et u(z. t).)
Find a formula for the solution of the initial value problem for for t>0, -oc
1. Let u be a solution of the wave equation u 0. Let the points A, B, C, D be the vertices of the...
1. Let u be a solution of the wave equation u 0. Let the points A, B, C, D be the vertices of the paralleogram formed by the two pairs of characteristic lines r-ctC1,x- ct-2,+ ct- di,r +ct- d2 Show that u (A)+u (C)-u (B) + u (D Use this to find u satisfying For which (x, t) can you determine u (x, t) uniquely this way? 2. Suppose u satisfies the wave equation utt -curr0 in the strip 0...
3) consider the heat equation: Find explicit solution by separation of variables for the following cases:...
3) consider the heat equation:
Find explicit solution by separation of variables for the
following cases:
a f(x) = sin x
b f(x)= (sin^3)x
c f(x)= x(pi - x)
** para means 'for' and 'e' means ' and'
3) Considere o problema do Calor Ut x para 0 x<T et > 0 u (0, t)u (T, t) = 0 para t 0 u (x, 0) f (x) para 0 x<T Encontre a solução explicitamente por separação de variáveis, nos seguintes...
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...
1. Consider the insulated heat equation up = cum, 0 <r<L, t > 0 u (0,t)...
1. Consider the insulated heat equation up = cum, 0 <r<L, t > 0 u (0,t) = u (L, t) = 0, t > 0 u(x,0) = f(2). What is the steady-state solution? 2. Solve the two-dimensional wave equation (with c=1/) on the unit square (i.e., [0, 1] x [0,1) with homogeneous Dirichlet boundary conditions and initial conditions: (2, y,0) = sin(x) sin(y) (,y,0) = sin(x). 3. Solve the following PDE: Uzr + Uyy = 0, 0<<1,0 <y < 2...
(5) Do all parts (a) Let f be a function, and let >0. Write explicit forsmulas for the second difference and second central difference operators, Δ, and each of which depend on h (b) For a fun...
(5) Do all parts (a) Let f be a function, and let >0. Write explicit forsmulas for the second difference and second central difference operators, Δ, and each of which depend on h (b) For a function u(x, t) of two variables, consider the second order partial differ- ential equation CER This is the so-called snave equation. Construct a numerical method for approx imating solutions to this equation, by using the second forward difference for the variable t, and the...
a solution to an recursive relation is given by the equation. find the explicit formula for a to the n 0001061000 2...
a solution to an recursive relation is given by the equation.
find the explicit formula for a to the n
0001061000 2 where ao = 2 and a1 = 7, Find the expl u for the number of objects or ways. Leave your answer 2. A solution to an recursive relation is given by the equation: an an-1 + 2an-2 where ao 2 and a17. Find 3. This is a counting problem. All questions in this problem ask you for...
if (r.y) (0,0), 0,f (, y) (0, 0) 2. Consider f : IR2 -R defined by f(r,y)-+ (a) Show by explicit computation that the directional derivative exists at (x, y)- (0,0) for all oi rections u є R2 with 1...
if (r.y) (0,0), 0,f (, y) (0, 0) 2. Consider f : IR2 -R defined by f(r,y)-+ (a) Show by explicit computation that the directional derivative exists at (x, y)- (0,0) for all oi rections u є R2 with 1 11-1, but that its value %(0.0) (Vf(0,0).u), fr at least one sucli u. (b) Show that the partial derivatives of f are not continuous at (0,0)
if (r.y) (0,0), 0,f (, y) (0, 0) 2. Consider f : IR2 -R...
Please write neatly
Let f(x) be a Cl(R) function and u(t, x) be a solution to the inviscid Burger's IVP Ut + uuz = 0, 4(0,x) = f(x). (a) Use the formula ult, x) = f (x – ut) to derive the following explicit identity for the partial derivative Ou du Ət f($)f'(5) 1+tf'(E) with $ = X – ut. (b) Assume that there exists a number wo E R such that f'(20) < 0 and f(x) > 0. Use...
Can you help me with this question please?
(2) [15pts] Write the solution of the PDE for 0 <<1 and t>0 u(0,t) 0 u(1,t) = 0 u(x,0)-0 Make sure you simplify as much as possible by using the fact that the source term f depends only on z and not on t. What is the solution at long time lim,-+oo u(x, t) if f()T) [Hint: You can obtain this by solving a single (trivial) ODE]
(2) [15pts] Write the solution...
Find a formula for the solution of the initial value problem for for t>0, -oc < x < oo ut = uzz-u a(1:0) = g(z) -x < 1 < x where g is continuous and bounded.( Hint: use v(x, t) = et u(z. t).)
Find a formula for the solution of the initial value problem for for t>0, -oc
1. Let u be a solution of the wave equation u 0. Let the points A, B, C, D be the vertices of the paralleogram formed by the two pairs of characteristic lines r-ctC1,x- ct-2,+ ct- di,r +ct- d2 Show that u (A)+u (C)-u (B) + u (D Use this to find u satisfying For which (x, t) can you determine u (x, t) uniquely this way? 2. Suppose u satisfies the wave equation utt -curr0 in the strip 0...
3) consider the heat equation:
Find explicit solution by separation of variables for the
following cases:
a f(x) = sin x
b f(x)= (sin^3)x
c f(x)= x(pi - x)
** para means 'for' and 'e' means ' and'
3) Considere o problema do Calor Ut x para 0 x<T et > 0 u (0, t)u (T, t) = 0 para t 0 u (x, 0) f (x) para 0 x<T Encontre a solução explicitamente por separação de variáveis, nos seguintes...
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...
1. Consider the insulated heat equation up = cum, 0 <r<L, t > 0 u (0,t) = u (L, t) = 0, t > 0 u(x,0) = f(2). What is the steady-state solution? 2. Solve the two-dimensional wave equation (with c=1/) on the unit square (i.e., [0, 1] x [0,1) with homogeneous Dirichlet boundary conditions and initial conditions: (2, y,0) = sin(x) sin(y) (,y,0) = sin(x). 3. Solve the following PDE: Uzr + Uyy = 0, 0<<1,0 <y < 2...
(5) Do all parts (a) Let f be a function, and let >0. Write explicit forsmulas for the second difference and second central difference operators, Δ, and each of which depend on h (b) For a function u(x, t) of two variables, consider the second order partial differ- ential equation CER This is the so-called snave equation. Construct a numerical method for approx imating solutions to this equation, by using the second forward difference for the variable t, and the...
a solution to an recursive relation is given by the equation.
find the explicit formula for a to the n
0001061000 2 where ao = 2 and a1 = 7, Find the expl u for the number of objects or ways. Leave your answer 2. A solution to an recursive relation is given by the equation: an an-1 + 2an-2 where ao 2 and a17. Find 3. This is a counting problem. All questions in this problem ask you for...
if (r.y) (0,0), 0,f (, y) (0, 0) 2. Consider f : IR2 -R defined by f(r,y)-+ (a) Show by explicit computation that the directional derivative exists at (x, y)- (0,0) for all oi rections u є R2 with 1 11-1, but that its value %(0.0) (Vf(0,0).u), fr at least one sucli u. (b) Show that the partial derivatives of f are not continuous at (0,0)
if (r.y) (0,0), 0,f (, y) (0, 0) 2. Consider f : IR2 -R...
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