Computers And Technology College

Find the product solution of

Dr(r, θ) =

∂2u

∂r2

+

1

r

∂u

∂r

+

1

r

2

∂2u

∂θ2

= 0​

Answers

Answer 1
This is the product solution of the two independent solutions of the form:

R(r)Θ(θ)

where R(r) is the radial component and Θ(θ) is the angular component.

We can assume that the second term of the equation is separable, meaning that we can rewrite it as:

∂2u

∂θ2

= -λu

where λ is a separation constant.

Substituting this into the original equation, we get:

∂2u

∂r2

1

r

∂u

∂r

λ

r

2

u

= 0

Multiplying both sides by r^2, we get:

r^2

∂2u

∂r2

r

∂u

∂r

λu

= 0

This is a form of the Bessel differential equation, which has solutions of the form:

u(r) = AJv(√λr) + BYv(√λr)

where Jv and Yv are Bessel functions of the first and second kind, respectively, and A and B are constants determined by the boundary conditions.

Substituting this back into the product solution, we get:

Dr(r, θ) = (d^2/dt^2 + λ) [R(r)Θ(θ)]

This shows that the product solution is a linear combination of functions that satisfy the partial differential equation.

Related Questions

H. W 2: A class includes 20 female students and 30 male students, including 15 female students and 20 male students with black hair. If a person is randomly chosen from the class, what is the probability that the chosen person is a female student with black hair? Hint: (Female student with black hair ) = P(AU B)​

Answers

Answer:

The probability that the chosen person is a female student with black hair is 15/50, or 3/10.

Using An assembly code
Read a 3 digit number from one row, then a 1 digit number from the second row. Subtract the 1 digit number from the 3 digit number, and display the result. Make sure you print your name first, then your output.
Sample Input
123
1
Output
Name Last name
122
Sample Input
100
1
Output
Name Last name
099 (or you can display 99 without the 0, either one is fine)

Sample Input
001
1

Output

Name Last name
0 (or you can display 000, either one is fine by me)

Answers

An example implementation of the algorithm you described in x86 assembly language using NASM syntax:

The Assembly Language Program

section .data

   ; Define your data here if needed

section .text

   global _start

_start:

   ; Print your name here

   

   ; Read the 3-digit number

   mov eax, 3       ; number of characters to read

   mov ebx, 0       ; file descriptor (stdin)

   mov ecx, buf     ; buffer to store the input

   mov edx, eax     ; maximum number of characters to read

   int 0x80         ; invoke the read system call

   

   ; Convert the input to a number

   mov eax, buf

   sub eax, '0'     ; convert the hundreds digit

   mov ebx, 10

   imul ebx

   mov ecx, buf+1

   sub ecx, '0'     ; convert the tens digit

   add eax, ecx

   imul ebx

   mov ecx, buf+2

   sub ecx, '0'     ; convert the units digit

   add eax, ecx

   

   ; Read the 1-digit number

   mov eax, 1       ; number of characters to read

   mov ebx, 0       ; file descriptor (stdin)

   mov ecx, buf     ; buffer to store the input

   mov edx, eax     ; maximum number of characters to read

   int 0x80         ; invoke the read system call

   

   ; Convert the input to a number

   mov ebx, 10

   mov ecx, buf

   sub ecx, '0'     ; convert the digit

   mul ebx

   

   ; Subtract the 1-digit number from the 3-digit number

   sub eax, ecx

   

   ; Convert the result to a string

   mov ebx, 10

   div ebx

   add edx, '0'     ; convert the units digit

   mov [result+2], dl

   div ebx

   add edx, '0'     ; convert the tens digit

   mov [result+1], dl

   add eax, '0'     ; convert the hundreds digit

   mov [result], al

   

   ; Print the result

   mov eax, 4       ; system call for write

   mov ebx, 1       ; file descriptor (stdout)

   mov ecx, result  ; address of the string to print

   mov edx, 3       ; number of characters to print

   int 0x80         ; invoke the write system call

   

   ; Exit the program

   mov eax, 1       ; system call for exit

   xor ebx, ebx     ; exit status

   int 0x80

section .bss

   buf resb 4       ; buffer for input (3 digits + newline)

   result resb 4    ; buffer for output (3 digits + null terminator)

Note that this implementation uses system calls for input/output and assumes that the input is terminated by a newline character. You may need to modify it to suit your specific requirements or platform.

Read more about assembly language here:

https://brainly.com/question/30299633

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