Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
a. By directly evaluating the integral t ( f * 9) (t) = √² (e^t-e^(-3t))/5 the definition of f * g. e^(w)e^(-3(t-w)) dw = -1 b. By computing ¹ {F(s)G(s)} where F(s) = L {f(t)} and G(s) = L {g(t)}.

a. By directly evaluating the integral t ( f * 9) (t) = √² (e^t-e^(-3t))/5 the definition of f * g. e^(w)e^(-3(t-w)) dw = -1 b. By computing ¹ {F(s)G(s)} where F(s) = L {f(t)} and G(s) = L {g(t)}.

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
See similar textbooks
icon
Related questions
Question

For the functions f(t)=et and g(t)=e−3t, defined on 0≤t<∞, compute f∗g in two different ways: 

a. By directly evaluating the integral in the definition of f * g. (f* g)(t) = (e^t-e^(-3t))/5 t S = e^(w)e^(-3(t-w)) dw b. By computing L-¹ {F(s)G(s)} where F(s) = L {f(t)} and G(s) = L {g(t)}. (f* g)(t) = L−¹ {F(s)G(s)} = L¯¹{ 1/5 1/s(e^t-e^-3t) = help (formulas)
Transcribed Image Text:a. By directly evaluating the integral in the definition of f * g. (f* g)(t) = (e^t-e^(-3t))/5 t S = e^(w)e^(-3(t-w)) dw b. By computing L-¹ {F(s)G(s)} where F(s) = L {f(t)} and G(s) = L {g(t)}. (f* g)(t) = L−¹ {F(s)G(s)} = L¯¹{ 1/5 1/s(e^t-e^-3t) = help (formulas)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS