Find Laplace Transform using Convolution Property | 13 Practice Problems | Exam Review | Method 8

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In this video we study the convolution method of finding Laplace transforms of certain functions.

Topics lineup
---------------------------------------------
00:00 Intro
02:34 Find convolutions
02:45 Pb a: 1* t
05:54 Pb b: t * t
07:25 Pb c: t * eᵗ
15:26 Pb d: eᵗ * sin t
21:53 Pb e: eᵐᵗ * eⁿᵗ, m ≠ n
24:59 Pb f: sin 3t * cos 2t
30:14 Convolution property (CP)
30:36 Pb g: ℒ{∫₀ᵗ τeᵗ⁻^τ dτ}
32:10 Pb h: ℒ{∫₀ᵗ (2τ −1)eᵗ⁻^τ dτ}
33:47 Pb i: ℒ{∫₀ᵗ eᵗ⁻^τ dτ}
35:07 Pb j: ℒ{∫₀ᵗ e²ᵗ⁻^τ dτ}
38:10 Pb k: ℒ{∫₀ᵗ τe⁻^τdτ}
41:25 Pb l: ℒ{∫₀ᵗ e⁻²^τsin 3(t−τ)dτ}
42:31 Pb m: ℒ{∫₀ᵗ sin τ sinh (t−τ)dτ}
43:25 Pb n: ℒ{∫₀ᵗ sin t sinh (t−τ)dτ}
44:20 Practice problems

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#differential_equations #exam_review #laplace_transforms

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Math challenge: See whether you know the convolution of e⁻²ᵗ * U(t−3) and how to find the Laplace transform ℒ{∫₀ᵗ sin t sinh (t−τ)dτ}. If you know the answer please comment below. They may be a bit challenging.

MathTutor

Topics lineup

00:00 Intro
02:34 Find convolutions
02:45 Pb a: 1* t
05:54 Pb b: t * t
07:25 Pb c: t * eᵗ
15:26 Pb d: eᵗ * sin t
21:53 Pb e: eᵐᵗ * eⁿᵗ, m ≠ n
24:59 Pb f: sin 3t * cos 2t
30:14 Convolution property (CP)
30:36 Pb g: ℒ{∫₀ᵗ τeᵗ⁻^τ dτ}
32:10 Pb h: ℒ{∫₀ᵗ (2τ −1)eᵗ⁻^τ dτ}
33:47 Pb i: ℒ{∫₀ᵗ eᵗ⁻^τ dτ}
35:07 Pb j: ℒ{∫₀ᵗ e²ᵗ⁻^τ dτ}
38:10 Pb k: ℒ{∫₀ᵗ τe⁻^τdτ}
41:25 Pb l: ℒ{∫₀ᵗ e⁻²^τsin 3(t−τ)dτ}
42:31 Pb m: ℒ{∫₀ᵗ sin τ sinh (t−τ)dτ}
43:25 Pb n: ℒ{∫₀ᵗ sin t sinh (t−τ)dτ}
44:20 Practice problems

Thank you for watching.

MathTutor

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