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1. Find a relation among the coefficients of the polynomial that makes it satisfy the potential e...
1. Find a relation among the coefficients of the polynomial p(x,y)=a+bx + cy + dx2 + exy +fy2 tha...
Find a relation among the coefficient of polynomial
1. Find a relation among the coefficients of the polynomial p(x,y)=a+bx + cy + dx2 + exy +fy2 that makes it satisfy the potential equation. Choose a specific polynomial that satisfies the equation and show that, if Op/8x and 6p/ ay are both zero at some point, the surface there is saddle shaped
1. Find a relation among the coefficients of the polynomial p(x,y)=a+bx + cy + dx2 + exy +fy2 that...
Suppose the coefficients of the cubic polynomial p(x) = a +bx+cr? + de satisfy the equation...
Suppose the coefficients of the cubic polynomial p(x) = a +bx+cr? + de satisfy the equation )=0 has a root between 0 and 1. Can you generalize this result for an nth-degree Show that the equation p polynomial?
Question 1. A linear homogeneous recurrence relation of degree 2 with constant coefficients is a recurrence...
Question 1. A linear homogeneous recurrence relation of degree 2 with constant coefficients is a recurrence relation of the form an = Cian-1 + c2an-2, for real constants Ci and C2, and all n 2. Show that if an = r" for some constant r, then r must satisfy the characteristic equation, p2 - cir= c = 0. Question 2. Given a linear homogeneous recurrence relation of degree 2 with constant coefficients, the solutions of its characteristic equation are called...
Consider the differential equation, L[y] = y'' + p(t)y' + q(t)y = 0, (1) whose coefficients...
Consider the differential
equation, L[y] = y'' + p(t)y' + q(t)y = 0, (1) whose coefficients p
and q are continuous on some open interval I. Choose some point t0
in I. Let y1 be the solution of equation (1) that also satisfies
the initial conditions y(t0) = 1, y'(t0) = 0, and let y2 be the
solution of equation (1) that satisfies the initial conditions
y(t0) = 0, y'(t0) = 1. Then y1 and y2 form a fundamental set...
(20 pts.) The Laguerre differential equation is ry" + (1 - )y' + Ay = 0....
(20 pts.) The Laguerre differential equation is ry" + (1 - )y' + Ay = 0. (a) Show that x = 0 is a regular singular point. (b) Determine the indicial equation, its roots, and the recurrence relation. (c) Find one solution (x > 0). Show that if = m, a positive integer, this solution reduces to a polynomial. When properly normalized, this polynomial is known as the Laguerre polynomial, L. (2).
1 Solve by using power series: 2)-y = ex. Find the recurrence relation and compute the...
1 Solve by using power series: 2)-y = ex. Find the recurrence relation and compute the first 6 coefficients (a -as). Use the methods of chapter 3 to solve the differential equation and show your chapter 8 solution is equivalent to your chapter 3 solution.
a) By direct substitution determine which of the following functions satisfy the wave equation. 1. g(x,...
a) By direct substitution determine which of the following functions satisfy the wave equation. 1. g(x, t) = Acos(kx − t) where A, k, are positive constants. 2. h(x, t) = Ae where A, k, are positive constants. 3. p(x, t) = Asinh(kx − t) where A, k, are positive constants. 4. q(x, t) = Ae where A, a, are positive constants. 5. An arbitrary function: f(x, t) = f(kx−t) where k and are positive constants. (Hint: Be careful with...
2. For the Berthelot Equation of State (see #5 on Phy 372 home page): (a) Expand...
2. For the Berthelot Equation of State (see #5 on Phy 372 home page): (a) Expand P in terms of v and T, i.e. start with dP and express it in terms of dv and dT. (Here v is the molar specific volume.) Rewrite the expansion with the coefficients evaluated. These coefficients will be functions of v and (b) Ú (c) Write an expression for β. The result will again be a function of v and se the cyclic relation...
3) In a vacuum diode electrons are emitted from a hot grounded cathode (V-0) and they...
3) In a vacuum diode electrons are emitted from a hot grounded cathode (V-0) and they are accelerated towards the anode at potential Vo (see Griffiths, prob.2.48). The clouds of emitted electrons build up until they reduce the electric field at the cathode to zero. From then on a steady current I flows between the plates. Let the anode and cathode be much larger than the distance d between them, so that the potential φ, electron density ρ and electron...
(1 point) a. Find the most general real-valued solution to the linear system of differential equations...
(1 point) a. Find the most general real-valued solution to the linear system of differential equations x -8 -10 x. xi(t) = C1 + C2 x2(t) b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle center point / ellipses spiral source spiral sink none of these ОООООО (1 point) Calculate the eigenvalues of this matrix: [Note-- you'll probably want to use a calculator or computer to estimate the...
Find a relation among the coefficient of polynomial
1. Find a relation among the coefficients of the polynomial p(x,y)=a+bx + cy + dx2 + exy +fy2 that makes it satisfy the potential equation. Choose a specific polynomial that satisfies the equation and show that, if Op/8x and 6p/ ay are both zero at some point, the surface there is saddle shaped
1. Find a relation among the coefficients of the polynomial p(x,y)=a+bx + cy + dx2 + exy +fy2 that...
Suppose the coefficients of the cubic polynomial p(x) = a +bx+cr? + de satisfy the equation )=0 has a root between 0 and 1. Can you generalize this result for an nth-degree Show that the equation p polynomial?
Question 1. A linear homogeneous recurrence relation of degree 2 with constant coefficients is a recurrence relation of the form an = Cian-1 + c2an-2, for real constants Ci and C2, and all n 2. Show that if an = r" for some constant r, then r must satisfy the characteristic equation, p2 - cir= c = 0. Question 2. Given a linear homogeneous recurrence relation of degree 2 with constant coefficients, the solutions of its characteristic equation are called...
Consider the differential
equation, L[y] = y'' + p(t)y' + q(t)y = 0, (1) whose coefficients p
and q are continuous on some open interval I. Choose some point t0
in I. Let y1 be the solution of equation (1) that also satisfies
the initial conditions y(t0) = 1, y'(t0) = 0, and let y2 be the
solution of equation (1) that satisfies the initial conditions
y(t0) = 0, y'(t0) = 1. Then y1 and y2 form a fundamental set...
(20 pts.) The Laguerre differential equation is ry" + (1 - )y' + Ay = 0. (a) Show that x = 0 is a regular singular point. (b) Determine the indicial equation, its roots, and the recurrence relation. (c) Find one solution (x > 0). Show that if = m, a positive integer, this solution reduces to a polynomial. When properly normalized, this polynomial is known as the Laguerre polynomial, L. (2).
1 Solve by using power series: 2)-y = ex. Find the recurrence relation and compute the first 6 coefficients (a -as). Use the methods of chapter 3 to solve the differential equation and show your chapter 8 solution is equivalent to your chapter 3 solution.
2. For the Berthelot Equation of State (see #5 on Phy 372 home page): (a) Expand P in terms of v and T, i.e. start with dP and express it in terms of dv and dT. (Here v is the molar specific volume.) Rewrite the expansion with the coefficients evaluated. These coefficients will be functions of v and (b) Ú (c) Write an expression for β. The result will again be a function of v and se the cyclic relation...
3) In a vacuum diode electrons are emitted from a hot grounded cathode (V-0) and they are accelerated towards the anode at potential Vo (see Griffiths, prob.2.48). The clouds of emitted electrons build up until they reduce the electric field at the cathode to zero. From then on a steady current I flows between the plates. Let the anode and cathode be much larger than the distance d between them, so that the potential φ, electron density ρ and electron...
(1 point) a. Find the most general real-valued solution to the linear system of differential equations x -8 -10 x. xi(t) = C1 + C2 x2(t) b. In the phase plane, this system is best described as a source / unstable node sink / stable node saddle center point / ellipses spiral source spiral sink none of these ОООООО (1 point) Calculate the eigenvalues of this matrix: [Note-- you'll probably want to use a calculator or computer to estimate the...
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