HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 489

circuits. In most cases one is interested in the system response after time t>0, thus, the definition of the Laplace transform, given above, involves an integration for values of t larger than zero. The inverse Laplace transform maps the function F(s) onto the original function f(t) in the time domain, i.e., L -1{F(s)} = f(t). The convolution integral or convolution product of two functions f(t) and g(t), where g is shifted in time, is defined as t ( f * g )( t ) = ∫ 0 f (u ) ⋅ g (t − u ) ⋅ du . Laplace transform and inverses in the calculator The calculator provides the functions LAP and ILAP to calculate the Laplace transform and the inverse Laplace transform, respectively, of a function f(VX), where VX is the CAS default independent variable, which you should set to 'X'. Thus, the calculator returns the transform or inverse transform as a function of X. The functions LAP and ILAP are available under the CALC/DIFF menu. The examples are worked out in the RPN mode, but translating them to ALG mode is straightforward. For these examples, set the CAS mode to Real and Exact. Example 1 - You can get the definition of the Laplace transform use the following: 'f(X)' ` LAP in RPN mode, or LAP(f(X))in ALG mode. The calculator returns the result (RPN, left; ALG, right): Compare these expressions with the one given earlier in the definition of the Laplace transform, i.e., ∫ L{ f (t)} = F (s) = ∞ f (t) ⋅ e−st dt, 0 and you will notice that the CAS default variable X in the equation writer screen replaces the variable s in this definition. Therefore, when using the Page 16-11