MATC46代做、代写Python，c/c++，Java程序语言、代做symmetric case

日期：2019-03-16 11:07

MATC46 Winter 2019

Assignment 5

Due Date: Monday 25 March.

Problems:

1. Prove that 2.

2. Determine the order p of the following Bessel’s equations. Find the general solution for

each of the equation and write down three terms of the Bessel function of the first kind of

p.a) 2 2

x y xy x y ′′ ′ ++ = ( 9) 0 b) 2 2 1 ( )0 4 x y xy x y ′′ ′ ++ =

3. Show that 1 .

4. Verify that y1 = xp

Jp(x) and y2 = xp

Yp(x) are linearly independent solutions of

xy p y xy ′′ ′ + + = (1 2 ) 0, x > 0 .

5. Evaluatea) 4

3 () x J x dx ∫ b) 1 () J x dx ∫ c) 2

3 () x J x dx ∫ d) 3

0 () x J x dx ∫ .

6. Approximate the given function by a Bessel series of the given p.

p = 1 b) f(x) = J0(x); 0 < x < α01, p = 0.

7. Solve the vibrating membrane problem (symmetric case)

a) a = 1, c = 1, f(r) = J0(α1r), g(r) = 0. b) a = 1, c = 1, f(r) = J0(α3r), g(r) = 1 – r2.

8. Using separation pf variables to find the solution of heat boundary value problem

What is the solution if f(r) = 100, 0 < r < a?

9. Solve the vibrating membrane problemcos2θ, g(r, θ) = 0, a = 3, c = 1.

b) F(r, θ) = 0, g(r, θ) = (1 – r2)r2

sin2θ, a = c = 1.