How It Works... |
Evaluating "how it works" requires that you apply a simple sequence of formulae readily understood by any 8-th grade pre-algebra student. Those formulae are presented below; To evaluate, set up the initial matrix by evaluating the first table of formulae in order. Then, for each resulting data point, evaluate using the second table of formulae (again, in order). |
For those without the elemental but requisite math background, a simple layman's explanation can be seen by clicking the link below:: |
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1.1 |
definition of a Laplace transform y(t) | |
1.2 | Y(s) | inversion formula |
1.3 | first derivative | |
1.4 | second derivative | |
1.5 |
nth derivative | |
1.6 |
integration | |
1.7 | F(s)G(s) | convolution integral |
1.8 | ||
1.9 | shifting in the s-plane | |
1.10 |
f(t) has period T, such that f( t + T ) = f (t) | |
1.11 |
g(t) has period T, such that g(t + T ) = - g(t) |
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1 |
unit impulse at t = 0 |
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s |
double impulse at t = 0 |
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unit step u(t) | |
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t | |
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, n=1, 2, 3,…. | |
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, n=1, 2, 3,…. | |
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, k is any real number > 0 |
the Gamma function is given in Appendix A |
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2.11 | , n=1, 2, 3,…. | |
2.12 | ||
2.13 | ||
2.14 | ||
2.15 | |
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2.16a | ||
2.16b | ||
2.17 | ||
2.18 |
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2.19 | ||
2.20 | ||
2.21 | ||
2.22 |
2.23 | ||
2.24 | ||
2.25 | ||
2.26 | ||
2.27 | ||
2.28 | ||
2.29 | ||
2.30 | ||
2.31 | ||
2.32 | ||
2.33 |
2.34 |