Transformation Using Functional Integral Identities

Trigonometric Functions. In modeling processes and in studying control systems, there are many other important time functions, such as the trigonometric functions, cos cor and sin cor, where co is the frequency in radians per unit time. The Laplace transform of cos cor or sin cor can be calculated using integration by parts. An alternative method is to use the Euler identity ... 

The integrand in the numerator of Eq. (32-20) is of the form 4, V, E, where is a scalar function. Using the vector identity of Eq. (37-26), this can be replaced by V, ( E4,) — E V, 4,. The area integral over V, ( Ee,) is transformed into a line integral, using Eq. (37-55), which vanishes for the same reason that Eq. (32-21) vanishes. If we recall the definitions of U and U from the inside the back cover, we finally obtain the alternative form... 

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