Initial value theorem
Encyclopedia
In mathematical analysis
, the initial value theorem is a theorem used to relate frequency domain
expressions to the time domain
behavior as time approaches zero.
Let
be the (one-sided) Laplace transform of ƒ(t). The initial value theorem then says
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
, the initial value theorem is a theorem used to relate frequency domain
Frequency domain
In electronics, control systems engineering, and statistics, frequency domain is a term used to describe the domain for analysis of mathematical functions or signals with respect to frequency, rather than time....
expressions to the time domain
Time domain
Time domain is a term used to describe the analysis of mathematical functions, physical signals or time series of economic or environmental data, with respect to time. In the time domain, the signal or function's value is known for all real numbers, for the case of continuous time, or at various...
behavior as time approaches zero.
Let
be the (one-sided) Laplace transform of ƒ(t). The initial value theorem then says
