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1. Find the convolution of (a) 2tu(t) and t³u(t) (b) e¹u(t) and tu(t) (c) e¯²tu(t) and e¯tu(t). In each case reverse the order to check that (f * g)(t) = (g* f)(t). Answers 1. (a) 11/05 (b) -t-1+et (c) e−t — e−2

1. Find the convolution of (a) 2tu(t) and t³u(t) (b) e¹u(t) and tu(t) (c) e¯²tu(t) and e¯tu(t). In each case reverse the order to check that (f * g)(t) = (g* f)(t). Answers 1. (a) 11/05 (b) -t-1+et (c) e−t — e−2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Find the convolution of (a) 2tu(t) and t³u(t) (b) etu(t) and tu(t) (c) e−2u(t) and e¯tu(t). In each case reverse the order to check that (ƒ * g)(t) = (g* f)(t). Answers 1. (a) 1/1 +5 (b)-t-1+et (b)-t-1+et (c) e-te-2
Transcribed Image Text:1. Find the convolution of (a) 2tu(t) and t³u(t) (b) etu(t) and tu(t) (c) e−2u(t) and e¯tu(t). In each case reverse the order to check that (ƒ * g)(t) = (g* f)(t). Answers 1. (a) 1/1 +5 (b)-t-1+et (b)-t-1+et (c) e-te-2
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