Show the math for getting del^2(del^2 * psi) = 0 to get to the last equation with sin (theta)
Homework Answers
Add Answer to:
Show the math for getting del^2(del^2 * psi) = 0 to get to the
last equation...
7. Consider the differential equation (a) Show that z 0 is a regular singular point of the above differential equation (b) Let y(x) be a solution of the differential equation, where r R and the s...
7. Consider the differential equation (a) Show that z 0 is a regular singular point of the above differential equation (b) Let y(x) be a solution of the differential equation, where r R and the series converges for any E (-8,s), s > 0 Substitute the series solution y in to the differential equation and simplify the terms to obtain an expression of the form 1-1 where f(r) is a polynomial of degree 2. (c) Determine the values of r....
Problem 3. Show that the solution of the partial differential equation (Laplace equation), Wxx(x, y) +...
Problem 3. Show that the solution of the partial differential equation (Laplace equation), Wxx(x, y) + Wyy(x, y) = 0, with the four boundary conditions: w(x,0) = 0, w(x, 1) = 0, w(0, y) = 0 and w(1, y) = 24 sin ny, can be obtained as w(x, y) = 2 sinh nx · sin ny. [Suggested Solution Steps for Problem 3] (1) Apply the method of separation of variables as w(x,y) = X(x) · Y(y); (2) substitute into the...
(1 point) In this problem you will solve the differential equation or @() (1) Since P(a) 0 are not analytic at and 2()...
(1 point) In this problem you will solve the differential equation or @() (1) Since P(a) 0 are not analytic at and 2() is a singular point of the differential equation. Using Frobenius' Theorem, we must check that are both analytic a # 0. Since #P 2 and #2e(z) are analytic a # 0-0 is a regular singular point for the differential equation 28x2y® + 22,23, + 4y 0 From the result ol Frobenius Theorem, we may assume that 2822y"...
Solve the initial value problem honhomogeneous equation: LQ"+RQ+ Q = E. coswt initial Conditions: SQ (0)=Qe,...
Solve the initial value problem honhomogeneous equation: LQ"+RQ+ Q = E. coswt initial Conditions: SQ (0)=Qe, Q (0) = Q! as follows: + First solve the associated homogeneous lequation LQ"+RQ'TEQ =0 by using the characteristic equation Irt art &r=0 to obtain three types of solutions 2 Next show how to find a particular solution Qp to the non homogeneous equation by showing Oplt) = t-Lw²coswt twR sin (wt) ( - Lw²) 4 w²R Eo Show in detail that you can...
(2, Consider the Laplace equation for a ball of radius R described in spherical coordinates (T,0) 2 1 +00n3 2 0 wher...
(2, Consider the Laplace equation for a ball of radius R described in spherical coordinates (T,0) 2 1 +00n3 2 0 where 0 is the zenith angle and assume u is independent on the azirnuth angle d. a) By separation of variables, derive two ordinary differential equations of r and w =cos e given by 12 F" (T) +2r F (r) - n(n + 1 ) Fr (r) = 0, (1 w2)G (w) - 2wG (w) + n(n+ 1)G, (w)...
ㆍ 2 Consider the Laplace equation for a ball of radius R described in spherical coordinates (r,0) 2 urrt r cot ug=0...
ㆍ
2 Consider the Laplace equation for a ball of radius R described in spherical coordinates (r,0) 2 urrt r cot ug=0, uee 7:2 where is the zenith angle and assume u is independent on the azirnuth angle o. a) By separation of variables, derive two ordinary differential equations of r and w=Cos given by r2 F(r)2r F(r)-n(n+ 1)F(r) 0, (1- w2)G (w)- 2wG (w)n(n +1)G(w) 0. (n 0,1,2,.) b) Find Fn (r) and Gn (w) satisfying Gn(1) =1 for...
1 2 NAME Q1. (30pts) Solve the quadratic equation z2-(3+3i)z +6+2i = 0 by realizing the...
1
2
NAME Q1. (30pts) Solve the quadratic equation z2-(3+3i)z +6+2i = 0 by realizing the following plan: (i) find the discriminant A of the equation; (ii) write a program for a scientific calculator to obtain the polar form r(cos 0 + i sin 0) of A and the 'first' root + isin COS 2 of degree two of A; (iii) execute the program, fix the results, find another root A2 of A of degree two (before executing the program,...
12. Consider the unusual eigenvalue problem ux(0) = ur(l) = v(1)-U(0) (a) Show that 2 0 is a double eigenvalue. (b) Get an equation for the positive eigenvalues a>0. 102 CHAPTER 4 BOUNDARY PROBLEM...
12. Consider the unusual eigenvalue problem ux(0) = ur(l) = v(1)-U(0) (a) Show that 2 0 is a double eigenvalue. (b) Get an equation for the positive eigenvalues a>0. 102 CHAPTER 4 BOUNDARY PROBLEMS (c) Letting γ-IVA, reduce the equation in part (b) to the equation γ sin γ cos γ = sin (d) Use part (c) to find half of the eigenvalues explicitly and half of (e) Assuming that all the eigenvalues are nonnegative, make a list of (t)...
Please Help! If possible show every step my biggest issue is understanding how to get rid...
Please Help! If possible show every step my biggest issue is
understanding how to get rid of the Bessel Function. Thank you!
We've seen that the wave equation takes the form 1 af 2 12 = 0, where V2 is the Laplacian, v is the wave velocity, and f is the function describing the wave. In two Cartesian dimensions the Laplacian reduces to V2 f = 0f + 3f, which is a very convenient form for solving systems with rectangular...
Consider the Laplace equation for a ball of radius R described in spherical coordinates (r, 0) 2 1 cot 72 0= n where...
Consider the Laplace equation for a ball of radius R described in spherical coordinates (r, 0) 2 1 cot 72 0= n where is the zenith angle and assume u is independent on the azirnuth angle d. a) By separation of variables, derive two ordinary differential equations of r and w:= cos e given by 2 F" (r) +2rF (r) - n(n + 1) F, (r) = 0, (1 w2)G (w) - 2wG", (w) +n(n +1)G, (w) 0. (n 0,1,2,....
7. Consider the differential equation (a) Show that z 0 is a regular singular point of the above differential equation (b) Let y(x) be a solution of the differential equation, where r R and the series converges for any E (-8,s), s > 0 Substitute the series solution y in to the differential equation and simplify the terms to obtain an expression of the form 1-1 where f(r) is a polynomial of degree 2. (c) Determine the values of r....
Problem 3. Show that the solution of the partial differential equation (Laplace equation), Wxx(x, y) + Wyy(x, y) = 0, with the four boundary conditions: w(x,0) = 0, w(x, 1) = 0, w(0, y) = 0 and w(1, y) = 24 sin ny, can be obtained as w(x, y) = 2 sinh nx · sin ny. [Suggested Solution Steps for Problem 3] (1) Apply the method of separation of variables as w(x,y) = X(x) · Y(y); (2) substitute into the...
(1 point) In this problem you will solve the differential equation or @() (1) Since P(a) 0 are not analytic at and 2() is a singular point of the differential equation. Using Frobenius' Theorem, we must check that are both analytic a # 0. Since #P 2 and #2e(z) are analytic a # 0-0 is a regular singular point for the differential equation 28x2y® + 22,23, + 4y 0 From the result ol Frobenius Theorem, we may assume that 2822y"...
Solve the initial value problem honhomogeneous equation: LQ"+RQ+ Q = E. coswt initial Conditions: SQ (0)=Qe, Q (0) = Q! as follows: + First solve the associated homogeneous lequation LQ"+RQ'TEQ =0 by using the characteristic equation Irt art &r=0 to obtain three types of solutions 2 Next show how to find a particular solution Qp to the non homogeneous equation by showing Oplt) = t-Lw²coswt twR sin (wt) ( - Lw²) 4 w²R Eo Show in detail that you can...
(2, Consider the Laplace equation for a ball of radius R described in spherical coordinates (T,0) 2 1 +00n3 2 0 where 0 is the zenith angle and assume u is independent on the azirnuth angle d. a) By separation of variables, derive two ordinary differential equations of r and w =cos e given by 12 F" (T) +2r F (r) - n(n + 1 ) Fr (r) = 0, (1 w2)G (w) - 2wG (w) + n(n+ 1)G, (w)...
ㆍ
2 Consider the Laplace equation for a ball of radius R described in spherical coordinates (r,0) 2 urrt r cot ug=0, uee 7:2 where is the zenith angle and assume u is independent on the azirnuth angle o. a) By separation of variables, derive two ordinary differential equations of r and w=Cos given by r2 F(r)2r F(r)-n(n+ 1)F(r) 0, (1- w2)G (w)- 2wG (w)n(n +1)G(w) 0. (n 0,1,2,.) b) Find Fn (r) and Gn (w) satisfying Gn(1) =1 for...
1
2
NAME Q1. (30pts) Solve the quadratic equation z2-(3+3i)z +6+2i = 0 by realizing the following plan: (i) find the discriminant A of the equation; (ii) write a program for a scientific calculator to obtain the polar form r(cos 0 + i sin 0) of A and the 'first' root + isin COS 2 of degree two of A; (iii) execute the program, fix the results, find another root A2 of A of degree two (before executing the program,...
12. Consider the unusual eigenvalue problem ux(0) = ur(l) = v(1)-U(0) (a) Show that 2 0 is a double eigenvalue. (b) Get an equation for the positive eigenvalues a>0. 102 CHAPTER 4 BOUNDARY PROBLEMS (c) Letting γ-IVA, reduce the equation in part (b) to the equation γ sin γ cos γ = sin (d) Use part (c) to find half of the eigenvalues explicitly and half of (e) Assuming that all the eigenvalues are nonnegative, make a list of (t)...
Please Help! If possible show every step my biggest issue is
understanding how to get rid of the Bessel Function. Thank you!
We've seen that the wave equation takes the form 1 af 2 12 = 0, where V2 is the Laplacian, v is the wave velocity, and f is the function describing the wave. In two Cartesian dimensions the Laplacian reduces to V2 f = 0f + 3f, which is a very convenient form for solving systems with rectangular...
Consider the Laplace equation for a ball of radius R described in spherical coordinates (r, 0) 2 1 cot 72 0= n where is the zenith angle and assume u is independent on the azirnuth angle d. a) By separation of variables, derive two ordinary differential equations of r and w:= cos e given by 2 F" (r) +2rF (r) - n(n + 1) F, (r) = 0, (1 w2)G (w) - 2wG", (w) +n(n +1)G, (w) 0. (n 0,1,2,....
Most questions answered within 3 hours.
-
Foreman company obtained a $20,000, 6% loan on May 1, 2018.
Principal and interest will be...
asked 1 minute ago -
5. Problem 11.05 (Discounted Payback)
eBook
Project L costs $60,000, its expected cash inflows are $14,000
per...
asked 29 minutes ago -
1. Which of the following is true about politics and health
organizations?
A. Health organizations are...
asked 54 minutes ago -
A space vehicle is coasting at a constant velocity of 18.1 m/s
in the +y direction...
asked 1 hour ago -
5) Use the following balanced equation to answer questions
(a)-(i).
3 Cu(s) + 8 HNO3(aq) →...
asked 1 hour ago -
A three-year maturity bond with a 12% annual coupon rate is
currently traded at par $1000...
asked 1 hour ago -
1.
What is the minimum volume to use in the Spec 20 cuvette in order
to...
asked 2 hours ago -
A builder wants to install wall-to-wall carpeting in a living
room of length 8.87 m and...
asked 2 hours ago -
Organizational change can produce anxiety in those affected by
the change. In what ways can change...
asked 2 hours ago -
Ozone in the atmosphere may react with nitric oxide.
From the following data, calculate the DG...
asked 2 hours ago -
Steven Long, a bond analyst, is analyzing a convertible bond.
The characteristics of the bond are...
asked 2 hours ago -
Michael Bordellet is
the owner/pilot of Stellar Air Service. The company flies a daily
round trip...
asked 2 hours ago