Kategorie: Operational Calculus
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Applications of the shift operator
„And then a step to the right“ In the last post I promised some more examples of using shift operators, so here we are. To begin, consider the simple trigonometric integral equation . We can isolate the function using the shift operator and arrive at , from which the formal solution follows: . To proceed,…
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Fantastic shift operators and where to find them
„It’s just a jump to the left“ Everyone reading this should be familiar with the Taylor expansion of a function . It allows us to write as a series of powers of around some value using only the local information in the neighborhood around , . In particular, by Taylor’s theorem, the coefficients of the…
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What is operational calculus and what should it be?*
Just multiply the differential. Most people who have taken some sort of undergraduate math course in college are probably familiar with the following situation. You are given an ordinary differential equation of type and want to find the function that solves it. What can you do? Well, just multiply both sides by and integrate the…
Pseudo-Riemannian Manifold of Random Ideas 