5 ms·
This is tangential, and veering very much into the off-topic .. but the Laplace transform has a special place in my heart, because after banging my head against
by rusk 7y ago
This is tangential, and veering very much into the off-topic .. but the Laplace transform has a special place in my heart, because after banging my head against the wall of advanced calculus and other engineering mathematics topics for 4 years, with varying degrees of success, when presented with laplace I could "just do it".
From what I recall, the transformations were so well defined and the solution space so self contained that I could solve the assignments with little difficulty.
I remember in one of the other modules using laplace to solve a problem and the lecturer remarking that it was "an interesting approach". I had no idea what it meant, (though had some slight intuition about how it worked, based on previous exposure to Fourier transforms), but to this day I can't understand how I could take to it so fluently, while floundering at everything else.
Could just have been that in 4th year I gave up part time work and drinking to focus on my finals, and this improved my abilities.
- ta0xdeadbeef 7y agoThe whole point of Laplace is to make problems easier to solve by mapping linear differential equations to algebraic equations. To quote my dynamical systems professor, "you learned how to solve this in high school." There is a bit of hand holding in engineering courses with it however. A lot of looking at transform tables, and maybe a few problems where you need to exploit the properties of the transform or remember its definition to solve a problem. That can trip people up, and it happens in the real world more often than you'd like.
- lonelappde 7y agoIt's the multivariate calculus version of drawing a graph at logarithmic scale?
- zozbot234 7y agoThe LaPlace transform is also isomorphic to the net present value problem in finance. The Wiki article on net present value even links to a paper pointing this out from a finance POV. (The problem of how the net present value of a flow varies with changes in the discount rate is also of some theoretical interest in finance, since it clarifies the conditions under which the so-called 'roundaboutness' of e.g. an investment is well defined.)
- pgt 7y agoCan you expound on this? I recently applied some classic signal processing techniques to help reconcile my personal tax accounting by tracking coherence. This sorta works if you consider double-entry accounting as reverb in a linear time-invariant chamber (or echoes with unknown delay). I would love hear about any non-traditional applications of DSP.
- dreamcompiler 7y agoThis was my experience too. I learned LTs after my differential equations course, and I was a little mad at my DE instructor for forcing us to solve the things the hard way. In retrospect that was probably the right approach. Students should learn manual transmission before automatic.