所有你必須會的拉普拉斯轉換Laplace Transform

工程數學之拉普拉斯轉換 (i.e.拉普拉斯變換 Laplace Transform) ! 這裡包含了所有你該熟練的一般函數的拉式轉換 L{e^(at)}, L{t^n}, L{sin(bt)}, L{cos(bt)}, L{U(t-a)}, L{δ(t-a)}, ... 和你該知道的拉普拉斯轉換特性 L{e^(at)f(t)}, L{tf(t)}, L{f'(t)}, L{integral of f(u)}, L{f(t)*g(t)},...., 還有一些例子. 這會對你微分方程的課 或是 訊號學的課有幫助. 喜歡數學請訂閱 @bprptw 加入會員可得到我設計的Laplace transform for you pdf: 👉 https://www.youtube.com/channel/UCrONDbyO94HIrJyfhS6qfjA/join -----感謝會員們的贊助----- 吉掰米 Dino Lin 水源ミヤゴ chuan liu jacket paul Strasbourg Chung 鄭雷丘 Kin Man Wong 李疾風 Rust鏽 柳師 黃郁茜 --------------------------------------- 題目: https://www.blackpenredpen.com/_files/ugd/287ba5_bb285a61a06745e6a7452c4c379a7de0.pdf --------------------------------------- 0:00, 24題拉普拉斯轉換 (i.e. 拉普拉斯變換 or 拉氏轉拉氏轉換) Q1, 3:23, L{e^(at)}, Q2, 6:49, L{t^n} (用級數) Q3, Q4, 17:40, L{sin(bt)}, L{cos(bt)} Q5, 25:04, L{sinh(bt)}, hyperbolic sine Q6, 27:34, L{cosh(bt)}, hyperbolic cosine Q7, 30:50, L{U(t-a)}, unit-step function Q8, 36:38, L{Πa,b(t)}, the window function Q9, 41:30, L{δ(t-a)}, Dirac Delta function Q10, 46:58, L{f(t-a)U(t-a)}, shifting theorem in the t-domain part 2, 53:33, L{f(t)U(t-a)} Q11, 59:03, L{(t-2)^2*U(t-2)} vs. L{t^2 U(t-2)}, 拉普拉斯轉換例子 Q12, 1:05:11, L{f(at)} 1:10:04, 例子 L{sin(t)} vs L{sin(bt)} Q13, 1:13:28, L{e^(at) f(t)}, shifting theorem in the s-domain Q14, 1:17:14, L{t^3 e^(2t)} Q14*, 1:19:18, L{e^(3t)cos(2t)} Q15, 1:22:26, L{tf(t)} = -d/ds(F(s)) Q16, 1:29:23, L{tsin(bt)} 1:31:29 的分母應該是(s^2+b^2)^2 Honorable metions: L{t^nf(t)}=(-1)^n d^n/ds^n(F(s)) Q17, 1:37:22, L{f(t)/t} Q18, 1:50:28, L{sin(t)/t}=pi/2-tan^-1(s) 1:54:30 積分sin(t)/t, 積分sin(t)/(te^t), 積分sin(e^t)? Q19, 2:01:43, L{f'(t)} Q20, 2:08:31, L{f''(t)} Q21, 2:13:00, L{integral of f(u)} Q22, 2:19:55, L{f(t)*g(t)}, the convolution theorem Honorable mentions: L{sin(t)cos(t)} vs. L{sin(t)*cos(t)} Q23, 2:39:24, L{sqrt(t)}, ft. Gamma function (1/2)階乘 https://youtu.be/EE3Y0-j9tRE, 高斯積分 https://youtu.be/QdYsbx0SVKA Q24, 2:47:34, 壓軸 L{ln(t)} 做完啦, 好爽!! ---------我是分隔線--------- 點這訂閱: 👉 https://bit.ly/3r4bEfo 贊助老師: 👉 https://www.patreon.com/blackpenredpen 加入會員: 👉 https://www.youtube.com/channel/UCrONDbyO94HIrJyfhS6qfjA/join 衣服商品: 🛍 https://bit.ly/bprp_merch ------------------------------------ 祝你幸福 #黑筆紅筆 不是為了考試的數學頻道