Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
3) Let ƒ : (0, ∞) → C denote a bounded continuous function. The Laplace transform of f = f(x) is (LĐ)(z) = fe) == da =: F(2) for Rez > 0. The formula for the inverse Laplace transform is 1 (L~¹F)(x) = 2 i fr [F(z)e™z dz where c > 0 and Ã' is the straight line with parameterization z(y) = c+iy, -∞ 0 with Laplace transform F(z) = ½. Fix c> 0 and let Ãc,R denote the straight line with parameterization z(y)=c+iy, -R≤y≤R. Use complex variables to prove that 1 1 x>0 2(x) = = = = = = = ² ² ² = { 1 te ez dz lim 2πi R→∞, x < 0 Tc, R and determine the value of g(x) for x = 0. for for

3) Let ƒ : (0, ∞) → C denote a bounded continuous function. The Laplace transform of f = f(x) is (LĐ)(z) = fe) == da =: F(2) for Rez > 0. The formula for the inverse Laplace transform is 1 (L~¹F)(x) = 2 i fr [F(z)e™z dz where c > 0 and Ã' is the straight line with parameterization z(y) = c+iy, -∞ 0 with Laplace transform F(z) = ½. Fix c> 0 and let Ãc,R denote the straight line with parameterization z(y)=c+iy, -R≤y≤R. Use complex variables to prove that 1 1 x>0 2(x) = = = = = = = ² ² ² = { 1 te ez dz lim 2πi R→∞, x < 0 Tc, R and determine the value of g(x) for x = 0. for for

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

Please please solve

3) Let f (0, ∞) → C denote a bounded continuous function. The Laplace transform of f = f(x) is (Lƒ){(z) = √°°ƒ(a)e¯ª² da =: F(z) for Rez>0. The formula for the inverse Laplace transform is (L¯¹F)(x) = 1 2πί [F(z)e=²z dz where c> 0 and Te is the straight line with parameterization z(y) = c+iy, -∞ <y<∞0. Consider the function ƒ(x) = 1 for x > 0 with Laplace transform F(z) = ¹. Fix c> 0 and let TC,R denote the straight line with parameterization z(y) = c+iy, -R≤y≤R. Use complex variables to prove that 1 1 g(x): = lim Sron ez 2πi Rito - e²² dz ={ 1 x > 0 x < 0 2 c,R and determine the value of g(x) for x = 0. for for
Transcribed Image Text:3) Let f (0, ∞) → C denote a bounded continuous function. The Laplace transform of f = f(x) is (Lƒ){(z) = √°°ƒ(a)e¯ª² da =: F(z) for Rez>0. The formula for the inverse Laplace transform is (L¯¹F)(x) = 1 2πί [F(z)e=²z dz where c> 0 and Te is the straight line with parameterization z(y) = c+iy, -∞ <y<∞0. Consider the function ƒ(x) = 1 for x > 0 with Laplace transform F(z) = ¹. Fix c> 0 and let TC,R denote the straight line with parameterization z(y) = c+iy, -R≤y≤R. Use complex variables to prove that 1 1 g(x): = lim Sron ez 2πi Rito - e²² dz ={ 1 x > 0 x < 0 2 c,R and determine the value of g(x) for x = 0. for for
Expert Solution
steps

Step by step

Solved in 6 steps with 1 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