(a)
To establish: The commutative law of the convolution integral.
(a)
Explanation of Solution
Theorem used:
If
Where
The function h is known as the convolution of f and g; the integrals in equation (2) are called convolution integrals.
Calculation:
Consider left hand side
Let
Hence, the commutative law is proved.
(b)
To establish: The distributive law of the convolution integral.
(b)
Explanation of Solution
Consider left hand side
Hence, the distributive law is proved.
(c)
To establish: The associative law of the convolution integral.
(c)
Explanation of Solution
Consider left hand side
Let
Hence, the associative law is proved.
Want to see more full solutions like this?
Chapter 6 Solutions
Elementary Differential Equations
- Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat...Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEY
- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,