l*****n
发帖数: 1679 | 1 求高人用留数理论给解个积分？？？！！！谢多谢多谢
积分限是-∞到+∞，被积式是 1/(7*x^2-29/210),对x积分。
要求用留数理论做，我用methmatica算的，提示出错，原式在（-∞到+∞）内不收敛。
很费解！！！
请高人指点！！！ 还有请问，methmatica算出来的结果精确度跟用留数理论方法算出
来的结果一样吗？ 能精确到小数点后几位？
多谢！多谢了！明天就是DEADLINE，请大家帮个忙 |
t**g
发帖数: 522 | 2 of course this integral diverges. Check your integrand to see if it is
correct. |
s*n
发帖数: 245 | 3 这不就是柳树定理？把pole 挖掉？教课书的原例吗。
【在 l*****n 的大作中提到】
: 求高人用留数理论给解个积分？？？！！！谢多谢多谢
: 积分限是-∞到+∞，被积式是 1/(7*x^2-29/210),对x积分。
: 要求用留数理论做，我用methmatica算的，提示出错，原式在（-∞到+∞）内不收敛。
: 很费解！！！
: 请高人指点！！！ 还有请问，methmatica算出来的结果精确度跟用留数理论方法算出
: 来的结果一样吗？ 能精确到小数点后几位？
: 多谢！多谢了！明天就是DEADLINE，请大家帮个忙
|
p****e
发帖数: 3548 | 4 虽然忘了怎么用留数了，但是应该是收敛的,主值收敛
mathematica 用
Integrate[1/(7*x^2 - 29/210), {x, -\[Infinity], \[Infinity]},
PrincipalValue -> True]
【在 t**g 的大作中提到】
: of course this integral diverges. Check your integrand to see if it is
: correct.
|
t**g
发帖数: 522 | 5 If you use Cauchy Principal value, it may or may not be convergent. But usually when we evaluate integral, we do not use principal value unless it is specified.
The evaluation of this integral does not need Residual Theorem! It is a simple integral.
【在 p****e 的大作中提到】
: 虽然忘了怎么用留数了，但是应该是收敛的,主值收敛
: mathematica 用
: Integrate[1/(7*x^2 - 29/210), {x, -\[Infinity], \[Infinity]},
: PrincipalValue -> True]
|
d*b
发帖数: 21830 | 6 看你们这帮人的数学水平，真是无语啊。都是北大清华毕业的吧？磕打的一般都不会这
么烂
【在 l*****n 的大作中提到】
: 求高人用留数理论给解个积分？？？！！！谢多谢多谢
: 积分限是-∞到+∞，被积式是 1/(7*x^2-29/210),对x积分。
: 要求用留数理论做，我用methmatica算的，提示出错，原式在（-∞到+∞）内不收敛。
: 很费解！！！
: 请高人指点！！！ 还有请问，methmatica算出来的结果精确度跟用留数理论方法算出
: 来的结果一样吗？ 能精确到小数点后几位？
: 多谢！多谢了！明天就是DEADLINE，请大家帮个忙
|
p****e
发帖数: 3548 | 7 是可以分式分解然后积出个对数的形式，但还是要主值，要不发散
如果是物理问题，用主值一般是正确的
usually when we evaluate integral, we do not use principal value unless it
is specified.
simple integral.
【在 t**g 的大作中提到】
: If you use Cauchy Principal value, it may or may not be convergent. But usually when we evaluate integral, we do not use principal value unless it is specified.
: The evaluation of this integral does not need Residual Theorem! It is a simple integral.
|
b****s
发帖数: 1300 | 8 同意前半句，后半句你这不是纯属挖坑，制造人民内部矛盾吗？
【在 d*b 的大作中提到】
: 看你们这帮人的数学水平，真是无语啊。都是北大清华毕业的吧？磕打的一般都不会这
: 么烂
|
s*n
发帖数: 245 | 9 It is just a textbook example of using residue theorem. Just move the poles
on the real axis slightly above or below the real axis and apply residue
theorem.
usually when we evaluate integral, we do not use principal value unless it
is specified.
simple integral.
【在 t**g 的大作中提到】
: If you use Cauchy Principal value, it may or may not be convergent. But usually when we evaluate integral, we do not use principal value unless it is specified.
: The evaluation of this integral does not need Residual Theorem! It is a simple integral.
|
t**g
发帖数: 522 | 10 I have seen lots of people just talk the talk. When ask them to solve the
probelm, then they can't. They just say some faqncy words but cannot solve
real problems. I have seen too many of this kind of people. I really look
down on those. But it seems people like this fair relatively well. What a
superficial world.
I bet you have a very superficila understanding of residual theorem.
Please give the answer, not just say using the residual theorem you can this
and that, blah
poles
【在 s*n 的大作中提到】
: It is just a textbook example of using residue theorem. Just move the poles
: on the real axis slightly above or below the real axis and apply residue
: theorem.
:
: usually when we evaluate integral, we do not use principal value unless it
: is specified.
: simple integral.
|
|
|
m***c
发帖数: 1177 | 11 楼主是工程的PHD
【在 l*****n 的大作中提到】
: 求高人用留数理论给解个积分？？？！！！谢多谢多谢
: 积分限是-∞到+∞，被积式是 1/(7*x^2-29/210),对x积分。
: 要求用留数理论做，我用methmatica算的，提示出错，原式在（-∞到+∞）内不收敛。
: 很费解！！！
: 请高人指点！！！ 还有请问，methmatica算出来的结果精确度跟用留数理论方法算出
: 来的结果一样吗？ 能精确到小数点后几位？
: 多谢！多谢了！明天就是DEADLINE，请大家帮个忙
|
s*n
发帖数: 245 | 12 0
what is your saying?
this
【在 t**g 的大作中提到】
: I have seen lots of people just talk the talk. When ask them to solve the
: probelm, then they can't. They just say some faqncy words but cannot solve
: real problems. I have seen too many of this kind of people. I really look
: down on those. But it seems people like this fair relatively well. What a
: superficial world.
: I bet you have a very superficila understanding of residual theorem.
: Please give the answer, not just say using the residual theorem you can this
: and that, blah
:
: poles
|
x*a
发帖数: 48 | 13 expand to 1/(x+a) and 1/(x-a) then both integrate to 0 due to symmetry
though one can argue about the convergence issue at their poles (a/-a) |
x***t
发帖数: 263 | 14 闲着没事，
V.P. + Int(upper semi sphere) + Int(path around -a) + Int(path around +a) =0
==>
V.P. = - Int(path around -a) - Int(path around +a)
// Int(upper semi sphere) = 0 XX lemma
so V.P. = i*Pi + i*Pi = 2*i*Pi
【在 l*****n 的大作中提到】
: 求高人用留数理论给解个积分？？？！！！谢多谢多谢
: 积分限是-∞到+∞，被积式是 1/(7*x^2-29/210),对x积分。
: 要求用留数理论做，我用methmatica算的，提示出错，原式在（-∞到+∞）内不收敛。
: 很费解！！！
: 请高人指点！！！ 还有请问，methmatica算出来的结果精确度跟用留数理论方法算出
: 来的结果一样吗？ 能精确到小数点后几位？
: 多谢！多谢了！明天就是DEADLINE，请大家帮个忙
|
c****e
发帖数: 2097 | 15 楼主每次都把作业题给别人作?
【在 l*****n 的大作中提到】
: 求高人用留数理论给解个积分？？？！！！谢多谢多谢
: 积分限是-∞到+∞，被积式是 1/(7*x^2-29/210),对x积分。
: 要求用留数理论做，我用methmatica算的，提示出错，原式在（-∞到+∞）内不收敛。
: 很费解！！！
: 请高人指点！！！ 还有请问，methmatica算出来的结果精确度跟用留数理论方法算出
: 来的结果一样吗？ 能精确到小数点后几位？
: 多谢！多谢了！明天就是DEADLINE，请大家帮个忙
|
c****e
发帖数: 2097 | 16
=0
ONE OF YOUR RESIDUES DOESN'T HAVE THE RIGHT SIGN, IT SEEMS
【在 x***t 的大作中提到】
: 闲着没事，
: V.P. + Int(upper semi sphere) + Int(path around -a) + Int(path around +a) =0
: ==>
: V.P. = - Int(path around -a) - Int(path around +a)
: // Int(upper semi sphere) = 0 XX lemma
: so V.P. = i*Pi + i*Pi = 2*i*Pi
|
