第２回 ラプラス変換の基本的性質

第２回　ラプラス変換の基本的性質

 

定理１（ラプラス変換可能の十分条件）

0≧t>∞で連続な関数f(t)、g(t)が、ある２つの定数αとM>0に対して

　　

を満たすならば、s>αであるsに対してf(t)はラプラス変換可能である。

【証明】

仮定より

　　

であり、s>αだから右辺の広義積分は

　　

と収束する。

よって、広義積分は絶対収束する。

（証明終）

 

定義（指数位数）

t≧t₀　　のとき

を満たす定数M、aが存在するとき、関数f(t)は指数位数であるという。

 

 

定理２（線形性）

任意の定数α、βに対して

　　

【証明】

　　

（証明終）

 

問１　次のラプラス変換を求めよ。

　　

【解】

一般に

　　

よって、

　　

（解答終）

 

定理３

s>s₀でならば

　　

【証明】

　　

（証明終）

 

問２　次のラプラス変換を求めよ。

　　

【解】

　　

a=−1とおき、定理２を用いると、

　　

（解答終）

 

問３

　　

と定理３を用いて、次の公式を求めよ。

　　

【解】

　　

とおくと、定理２より

　　

同様に、

　　

とおくと、

　　

（解答終）

 

 

コメント 9

Hello colleagues, how is everything, and what you would like to say regarding this piece of writing, in my view its genuinely remarkable in support of me.| а
by гзд м зеленина т е хохлова 3 класс (2020-03-19 15:12) 

I enjoy reading a post that will make men and women think. Also, thank you for permitting me to comment!| а
by квартиры в дмитровском погосте (2020-03-21 07:05) 

hello there and thank you for your info – I have certainly picked up anything new from right here. I did however expertise several technical points using this website, since I experienced to reload the website lots of times previous to I could get it to load properly. I had been wondering if your web hosting is OK? Not that I'm complaining, but slow loading instances times will often affect your placement in google and can damage your quality score if ads and marketing with Adwords. Well I am adding this RSS to my email and can look out for much more of your respective fascinating content. Ensure that you update this again very soon.| а
by типовой договор социального найма жилого помещения (2020-03-23 12:48) 

Hi there, I found your web site by means of Google whilst searching for a related subject, your website got here up, it appears good. I've bookmarked it in my google bookmarks. а
by counter strike 1.6 server creator 2.2 installation download (2020-03-25 14:41) 

Today, I went to the beach front with my kids. I found a sea shell and gave it to my 4 year old daughter and said "You can hear the ocean if you put this to your ear." She placed the shell to her ear and screamed. There was a hermit crab inside and it pinched her ear. She never wants to go back! LoL I know this is totally off topic but I had to tell someone!| а
by договор купли продажи рассрочка платежа (2020-03-27 12:40) 

Good day! I know this is kind of off topic but I was wondering which blog platform are you using for this website? I'm getting sick and tired of Wordpress because I've had issues with hackers and I'm looking at options for another platform. I would be great if you could point me in the direction of a good platform.| а
by исковое заявление образец по ст 115 ук рф (2020-03-29 07:50) 

Good post however I was wanting to know if you could write a litte more on this subject? I'd be very thankful if you could elaborate a little bit more. Kudos!| а
by гдз по задачнику физики 9-11 рымкевич (2020-03-31 07:01) 

I'm gone to convey my little brother, that he should also go to see this webpage on regular basis to take updated from latest news.| а
by windows xp professional genuine product key free (2020-04-02 13:04) 

Whoa! This blog looks exactly like my old one! It's on a completely different subject but it has pretty much the same layout and design. Outstanding choice of colors!| а
by тетрадь тренажер по географии 7 класс ответы мишняева (2020-04-03 03:34)