
(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.
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Chapter 6 Solutions
Elementary Differential Equations
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