inverse Laplace transforms - well basic algebra actually - Page 1
Forum section: electronics / beginners

author: Simon
author_rank: Unknown
timestamp: October 10, 2020, 08:52:13 am
content: I'm now working on my HND. The quality of materials is no better than before even though they have moved from good old PDF's that you can download, print and use to your hearts content to some horrible online learning system copying across the same crappy material with typo's ta-boot!So I have read the material on inverse Laplace transforms or rather the list of examples on algebraic manipulation on how you get your "thing" into some broken up parts that the standard inverses can be used on. My example is not covered. I am given the below to solve.$$ \frac {3-2s} {s^2-4s+9}$$I have been working on it for a while and I am scratching my head as to how to split the denominator up. I can't factorize it as a quadratic although $$s^2+3^2$$ is some reduction but it is still joined to -4s. This question is in fact nothing to do with laplace transforms but algebra.

author: emece67
author_rank: Frequent Contributor
timestamp: October 10, 2020, 09:29:03 am
content: .

author: pwlps
author_rank: Frequent Contributor
timestamp: October 10, 2020, 09:31:33 am
content: To factor a polynomial first find its roots, then for your case of quadratic function you have P(s)=(s-s1)(s-s2) where s1, s2 are roots (real or complex). Then decompose 1/P(s) in simple fractions.Edit : I wasn't sure for the right term, so apparently it is "partial fraction decomposition" as per Tim's next post.

author: Simon
author_rank: Unknown
timestamp: October 10, 2020, 10:38:00 am
content: The problem is that this seems to involve complex numbers and I am wondering if this was the intention given the overall incompetence and I could be doing days (literally) of work for nothing.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: October 10, 2020, 12:08:51 pm
content: Use complex factorization, or use partial fraction decomposition. Or both I suppose!The latter is thus:Note that, when small rational polynomials (of the form (A + Bx) / (C + Dx), etc.) are added and multiplied together, you get higher order terms (of x^2, x^3, etc. in the numerator/denominator). It stands to reason, we can equate a general rational:(A + Bx + Cx^2 + ...) / (Z + Yx + Xx^2 + ...) = a / (b + x) + (c + dx) / (e + x) + ...There are rules to select appropriate combinations of numerators and denominators in the reduced expressions, so it doesn't need to be impossibly general.Tim

author: pwlps
author_rank: Frequent Contributor
timestamp: October 10, 2020, 12:42:18 pm
content: Just a comment in case you are lost. The procedure I suggested (and equivalent to the one of the last Tim's post) is a sort of ab-initio calculation, of course the table look-up method by emece67 will be much faster. Actually the sin/cos factors showing up in these formulas are coming from the imaginary parts of the roots, you will need to go through the (a bit tedious) calculation to understand why all these approaches are equivalent.

author: Andy Watson
author_rank: Super Contributor
timestamp: October 10, 2020, 01:14:54 pm
content: I think you could use the first shift theorem to take (s-2) out as your first move. Re-write the numerator as \$ -2(s-2) - 1 \$. Now you have:$$L^{-1} \frac {-2(s-2) - 1 } {(s-2)^2 + \sqrt{5}^2 } = e^{2t} L^{-1} \frac {-2s - 1}{s^2 + \sqrt{5}^2 } $$Which you should be able to sort out into the form of \$e^t ( \alpha \cos t + b \sin t ) \$

author: Simon
author_rank: Unknown
timestamp: October 10, 2020, 02:14:50 pm
content: Quote from: Andy Watson on October 10, 2020, 01:14:54 pmI think this is the way they expect me to go. It looks familiar. They have several examples where a quadratic denominator is factorized by adding a constant to "make it work" i have just been racking my brain as to how that works.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: October 10, 2020, 07:34:38 pm
content: Completing the square. Rarely done because you can work backwards from the quadratic formula (which is proved by completing the square in general, i.e., algebraically), so it looks a bit magical seeing it done forward instead. Well, that very proof will show you how to choose the value.Tim

author: Nominal Animal
author_rank: Super Contributor
timestamp: October 10, 2020, 09:17:35 pm
content: Just in case this helps those who don't remember/know how to complete a square: You find the binomial square that matches the terms with the variable (here,s), and finally find the additional constant that added to the square, equals the original polynomial. With inverse Laplace transforms, it is useful to write that additive/subtractive constant as a square, too, as emece67 said.In this particular case,s2- 4s+ 9we know that(s- 2)2=s2- 4s+ 4and adding +5 to that gives us the original polynomial:(s- 2)2+ 5 = (s- 2)2+ (√5)2=s2- 4s+ 9If the second-degree term has a multiplier, say2s2- 12s+ 10we divide by that first,2s2- 12s+ 10 = 2(s2- 6s+ 5)and then redo the above, via (s- 3)2=s2- 6s+ 9:2s2- 12s+ 10 = 2(s2- 6s+ 5) = 2(s2- 6s+ 9 - 4) = 2( (s- 3)2- 4 )and therefore2s2- 12s+ 10 = 2( (s- 3)2- 22)

author: Simon
author_rank: Unknown
timestamp: October 10, 2020, 09:32:40 pm
content: Yes but this is new to me. I thought i was learning about Laplace, but instead i have been given the table of standards and been to go off and learn algebra instead

author: Nominal Animal
author_rank: Super Contributor
timestamp: October 10, 2020, 10:49:15 pm
content: Quote from: Simon on October 10, 2020, 09:32:40 pmThat's maths for you.My major problem with physics was always the math; how in maths for physicists they still just examine various maths properties and axioms, instead of maths as a tool for solving problems.The best example is how to solve differential equations. I still haven't found a book that describes how to choose which of the half-dozen methods to try first (for efficiency) when trying to solve various types of differential equations; they all just start talking about special functions and how those can be used to solve differential functions,with the actual how-to-apply-this part left as an exercise. It's like writing a book "how to get rich", and start it by "because I'm rich, you can become rich too. I'll leave that part for you dear readers as an exercise. Now, when you are rich, here are the ways you can use just a few million $ to become filthy rich". For some reason, mathematicians are happy as clams with that; I'm not.I had to write my own ten-or-so-page notes on it, but seem to have lost it on some backup media in the past decade or two...

author: Simon
author_rank: Unknown
timestamp: October 11, 2020, 10:09:49 am
content: The problem here is that I am doing distance learning courses in electrical engineering equivalent to a 1st and 2nd year of university. For some reason it is deemed that I need to know particular maths skills but you can't solve second order differential equations without considerable other foundations in maths. In theory i have studied these with their crap method which seems to keep amounting to "this is how" not "this is why".books which I have I find explain it a bit more but they do expect you to thoroughly understand what comes before in the book which is reasonable enough but I have never been expected to study that stuff thoroughly.

author: pwlps
author_rank: Frequent Contributor
timestamp: October 11, 2020, 01:48:37 pm
content: Quote from: Nominal Animal on October 10, 2020, 10:49:15 pmThis is debatable. I actually had quite a lot of pure maths in my physics courses and also thought all of that would be useless. However some of it eventually happened to be useful years later on many occasions. There are many apparent paradoxes, divergent results of calculations and other subtle erroneous reasonings that come from incorrect math use. There is of course a balance to maintain between theorems and applications but I don't think maths could be reduced to a set of recipes, at some point you will have to understand the roots of these recipes.

author: Simon
author_rank: Unknown
timestamp: October 11, 2020, 03:09:20 pm
content: Yes this is my objection, I am being taught the barest of procedures but how to use it in real life eludes me.

author: coppice
author_rank: Super Contributor
timestamp: October 11, 2020, 03:19:06 pm
content: Quote from: Simon on October 11, 2020, 10:09:49 amMany mathematicians feel it sullies their subject if they address anything practical, like "why". This makes many things they teach appear to be just "that's how it is, said Pooh", when there is real meaning to it. I suspect in many cases they've just learned some of the mathematical processes in a rote manner, and haven't really grasped what's going on themselves.

author: coppice
author_rank: Super Contributor
timestamp: October 11, 2020, 03:28:53 pm
content: Quote from: pwlps on October 11, 2020, 01:48:37 pmThe thing is most engineers are essentially practical people. If the maths lecturers actually pointed out one or two uses for a piece of maths before teaching it, the attention they get from engineering students would go way up. In my electronics degree we were mostly kept on our toes in the maths classes, because the engineering classes tended to use the techniques we were being taught soon after. In a few cases an engineering lecturer had to teach us a piece of maths, because the maths course was out of step, and hadn't quite got there. So, things mostly worked for us. Many science and engineering people complain there was a lack of alignment in their courses, and, as you said, they had to wait a long time to find out the relevance of various chunks of maths. It wouldn't eat into teaching time much to make each chunk of maths appear relevant from the outset.I should point out that the maths courses within our electronics degree course were taught by members of the maths faculty, with their content properly aligned (for the most part) with the engineering faculty. So, they were taught as pure maths courses, but with focussed content. I know that is now always how things work.

author: pwlps
author_rank: Frequent Contributor
timestamp: October 11, 2020, 03:48:01 pm
content: Quote from: Simon on October 11, 2020, 03:09:20 pmI don't know your degree program but usually, at least in physics or engineering programs I know, these are separate courses : one for pure maths and others (e.g. electromagnetism, electronics etc.) where the applications of maths in real problems are studied. Often there is a problem in synchronization between them (sometimes physics teachers have to improvise when the required math background has not yet been acquired), but even with perfect synchronization it is not easy for students to make connection between these different courses. I'm teaching both physics and electronics and have this problem every day : how to make them understand that the maths they are using are the same maths they have seen in their maths course. I discovered for example that at a beginner level even a change in notation is disturbing: sometimes my students having learned how to solve differential equations with f(x) would be lost when it came to solve the same equations with variables like time, speed, etc. This is also where you see a big difference between good and bad teachers/courses. I you understand the maths but have problems making the connection between the maths and the applications then you're to blame the teacher more than yourself.

author: Simon
author_rank: Unknown
timestamp: October 11, 2020, 04:35:31 pm
content: Vague mentions are made of the use of the math in engineering but that one sentence is it.

author: Nominal Animal
author_rank: Super Contributor
timestamp: October 11, 2020, 07:22:58 pm
content: Quote from: pwlps on October 11, 2020, 01:48:37 pmNo, that's not at all what I was suggesting! Nor did I do anything like that for myself by writing my own notes from scratch. I did not write recipes; I collected the solution approaches I knew, and studied their differences. In particular, I learn very little by rote. (Even after two-three decades of programming in C, I still do not remember standard C library interfaces by rote – things like the order of parameters formemset(), for example. Instead, I know the facilities and types of facilities it provides, and what facilities are provided by other standards like POSIX, and what facilities are available in commonly available libraries. I remember the logic and structure, not details. No recipes!)It is the approach that I am talking about.The paradigm, if you will. Very much in alignment of what coppice wrote above.I am not suggesting that physicists only need to know the form of sayLaplace's spherical harmonics\$Y_{\ell}^{m}\$, which can be used in describing the electron densitities, or "orbitals", at ground state around an atomic nuclei.What I am saying, is that deriving Laplace's spherical harmonics from first principles, but leaving the application (of using them to describe electron orbitals) as an exercise for the reader, is somehow natural to mathematicians, but unsuited for those who wield maths as a tool in anger.(In mathematics, it is typically enough to prove that an answer exists, while the exact value or definition of that answer tends to be regarded as uninteresting. The opposite is true in physics: the first thing one must do when obtaining any sort of an answer, is to check if it makes sense – through dimensional analysis or other methods. Usually, an exact answer is impossible to obtain (like many-body trajectories), but a sufficiently close approximation suffices.)Yes, those principles and axioms are needed and useful, butstarting from themis silly and wasteful for us non-mathematicians. Starting from the application, the algorithms, and expanding naturally into the principles and axioms, produces better results (again, for those who use math, as opposed to those who study math).However, I have not found books and reference material written that way; not for (advanced) differential calculus.The way I have observed others obtaining successful results, is by using exercise books (Schaum's are a common choice), and when trying to solve those, use their text books to find the appropriate solution methods.If you compare to e.g. learning a new language, we have much better approaches and methods than we did a hundred years ago; but in math, we're stuck there. We still place emphasis on knowing the names of the methods (because they're named after the people who discovered them), and learning by rote. Application is left as an exercise. Waste of time!An excellent example of this physics-based approach is to consider summation of parallel velocity vectors. (I.e., you have a spaceship in free fall, moving in a specific direction at a constant velocity, firing a cannon (mass driver) directly forwards, along its velocity vector.)With \$v_s\$ as the ship velocity and \$v_p\$ the velocity of the projectile with respect to the ship, the actual velocity of the projectile is \$v\$,$$v = \frac{(v_s + v_p) c^2}{v_s v_p + c^2}$$If both \$v_s\$ and \$v_p\$ are approximately the escape velocity of the Milky Way galaxy, 525 km/s, \$v = v_s + v_p\$ to six significant digits. And these are velocities humans can only dream of.Why would you start with the relativistic velocity formula, and then prove that \$v = v_s + v_p\$ is its first degree approximation? No, we're notthatstupid: we first use/learn Newtonian mechanics, then about relativity, and how the two match at "relatively low" velocities almost exactly. Yet, we do exactly the stupid approach with most of "higher" calculus.The same applies to Laplace transforms.For me, they key was that it transforms differential equations into algebraic equations, and convolution (of two functions,f*g) into multiplication. It itself isn't interesting; it's just thatits effects are useful. There is no need to have any intuition on "what" the Laplace transform represents, because it is a tool. (Compare to e.g. Fourier transform, which transforms between time domain and frequency domain; the "Laplace domain" itself is not interesting at this stage. Later on, when one gets to measure theory, that domain can be precisely defined and explored.)In other words, Laplace transforms, followed by algebraic operations, followed by inverse Laplace transforms, is an useful way to manipulate differential equations. One does notneedto have an intuitive grasp of what the transform is, only what it does. Tocorrectlyunderstand why it works, one needs a lot of additional maths, measure theory and Lebesgue integrals in particular. (Now, those can be VERY useful, too; but if one only needs Laplace transforms to make otherwise untractable differential equations tractable, it is a waste of time and effort to go into measure theory, just for the "basic knowledge" that provides no applicable tools.)(One of the very poorly approached, but immensely useful mathematical tools for physicists, is calculus of variations.)This here is also the main difference between mathematicians and those who apply maths as a tool in anger: the former need the knowledge, the latter need the tools.For some reason, this observation seems to offend a lot of mathematicians and wannabe-mathematicians. To me, it's just a fact of life, like stupid selfish politicians.

author: vodka
author_rank: Frequent Contributor
timestamp: October 11, 2020, 07:44:17 pm
content: Try to learn the Heaviside Method , for me , this method was very useful.Laplace Transforms: Heaviside Methodhttps://youtu.be/S-GoX7dzJ94

author: pwlps
author_rank: Frequent Contributor
timestamp: October 11, 2020, 10:26:08 pm
content: Quote from: Nominal Animal on October 11, 2020, 07:22:58 pmThis reminds me some funny discussions with mathematics students during my studies. Mathematcians were kidding us saying that we have to learn calculating tons of integrals whereas they only need to show whether an integral exists or not. To which we would proudly respond that we physicists have to be able to calculate an integral even when it does not exist. There are indeed situations where suspicious manipulations are used in physics to cope with apparent divergences, e.g. calculating Green functions by incursions to the complex plane, or the quantum electrodynamics which relies on summing apparently divergent series (here even Feynman himself said it is just hiding problems under the carpet). And the Dirac delta function was oficially banned by mathematicians for years (before it was formalized in the distribution theory by Schwartz).Otherwise I agree, actually I remember that I often found easier to learn maths notions when they were introduced in a physics course by a physicist before we got there in our maths course. A good example are the differential operators like div, rot(curl), these definitely should never be taught by mathematicians. Likewise the Dirac function is usually introduced in physics before mathematicians make it more complicated with their distribution theory. But as I said it all relies on the quality of the teachers.

author: coppice
author_rank: Super Contributor
timestamp: October 11, 2020, 10:53:34 pm
content: Quote from: pwlps on October 11, 2020, 10:26:08 pmI seem to remember an engineering lecturer basically teaching us div and curl like we'd never met it before when he needed it, as he realised few people really got it from the maths lectures.Quote from: pwlps on October 11, 2020, 10:26:08 pmThe Dirac function needs something like its use by Shannon to put flesh on the bones.

author: IanB
author_rank: Super Contributor
timestamp: October 11, 2020, 10:54:57 pm
content: Quote from: Simon on October 10, 2020, 09:32:40 pmWhen being taught about inverse Laplace transforms, you should have been given some hints and some examples about how to break things down into smaller pieces that you can find in the table. Things like partial fractions, factorization, variable substitutions and completing the square should at least have been mentioned.

author: Nominal Animal
author_rank: Super Contributor
timestamp: October 11, 2020, 11:58:42 pm
content: Quote from: pwlps on October 11, 2020, 10:26:08 pmSome of the mathematicians I know of and respect are very good at teaching other mathematicians, but not so good at teaching physicists. It is a matter of approach.Also, I am not disparaging mathematicians here (other than the odd ones that seem to think everyone should be a mathematician); I often find myself needing the expertise of one. Besides, similar divide exists between physics and engineering: physicists find, investigate, and model; engineers apply and build. (You only need to take a look at the test apparatuses physicists build if no proper engineer is available to help..)Wrt. this thread, it means that just because something seems illogically hard, does not mean you're out of your depth or studying the wrong thing; it just means that you aren't using reference manuals and learning methods that work best for yourself.I was a programmer before I started studying physics at the university. JPEG image format had been introduced a couple of years before, and MP3 audio compression the previous year, and I was immensely interested in them. I understood their idea, but not the math behind it. When Fourier series (and cosine transform) was introduced in one of the 101 courses, everything just clicked into place, and it was enjoyably easy for me. (Discrete cosine transform being at the core of JPEG and MP3 compression; converting from spatial or temporal domain to frequency domain, discarding unneeded components and quantizing only the "important" frequency components, roughly speaking.)Similarly, whenever I have the time to delve into the subject, trying to understand the subject by doing related exercises and trying to solve actual problems, I get much, MUCH more out of lectures and discussions with subject matter experts. It is not theiropinionsthat matter to me, but the reasons for their opinions, their own point of view, and experience and tales of common pitfalls, that often unlock the parts of the subject I could not unlock on my own. This fully applies to practical experience, too.I don't know if Simon or anybody reading this thread learns best the way I do, but it is definitely worth your time to find out how you do learn best. Perhaps some of my suggestions above will help, perhaps not, but the important thing is to realize that there are many, MANY ways to approach each subject, and only a subset of them work for any given person.

author: Simon
author_rank: Unknown
timestamp: October 12, 2020, 06:52:00 am
content: I learn best by understanding the application of it. Yes calculus made no sense to me at school, but when the electronics teacher finished off the math for us so that he could explain Fourier it made more sense.attached is all that I have from my course on inverse Laplace transforms.

author: rstofer
author_rank: Super Contributor
timestamp: October 13, 2020, 02:02:19 pm
content: Quote from: Simon on October 12, 2020, 06:52:00 amThe meat of it is in Worked Examples 10..13. In fact, WE 13 has a bit of everything. Before my grandson even started his Differential Equations course last semester, I told him to spend time on partial fraction expansion. It's covered in Algebra II but not like it's covered in DEs. We were laughing about it the other day. Well, I was laughing, he was groaning.MATLAB, the only way to do this work:Script file InverseLaplace:Code:syms a sF = 1/(s-a)^2;ilaplace(F)Command line:Code:>> InverseLaplaceans =t*exp(a*t)Where my grandson attends university, they doallof their work with MATLAB. There is a mandatory 1 semester course on using MATLAB the very first semester.

author: Simon
author_rank: Unknown
timestamp: October 13, 2020, 02:05:31 pm
content: This is why university education is no longer that useful. Yes ideally I should be taught to use these tools. So I have a math module that now has turned into two plus if only i just know how to use what I gather is non trivial software. I am supposed to be doing this around a day job but they don't care, take the money and run.

author: rstofer
author_rank: Super Contributor
timestamp: October 13, 2020, 02:21:41 pm
content: It is exponentially more difficult to do a degree program while working. I did it, I hated it but I gutted it out, I do NOT recommend it. College is supposed to be fun. This Covid thing has taken out all of the social interaction and has really ruined the experience.

author: Simon
author_rank: Unknown
timestamp: October 13, 2020, 02:24:04 pm
content: The problem is that it is not until I get to the assignment that I find that the poorly written crap they charged £500 for has very little to do with what I am doing and that having struggled through it with the aid of books I am now starting again to do the actual learning.

author: rstofer
author_rank: Super Contributor
timestamp: October 13, 2020, 02:38:51 pm
content: Your program sounds less than optimal and it may be a result of having so few options. No doubt you would pick a different program if it were available.Thanks to Covid, colleges and universities are opening up their courses to online learning and this requires a huge shift in thinking by the staff. When the class sizes are small (like a dozen students), Zoom is one way to interact. I think it gets out of hand when there are 100 students or more. I don't know how the bigger schools are doing it.I think distance learning is going to be with us forever.

author: Simon
author_rank: Unknown
timestamp: October 13, 2020, 03:11:19 pm
content: It is less than optimal. It's a sideline of a university that like all universities has to be a business. I don't know how it compares to on campus learning but it certainly does not deliver. It can take me days to get an answer from the tutor who can't even be bothered to include in her out of office email when she will be back. The material often is deficient in English never mind math.It is the only university that offers online HNC and HND courses in electrical engineering (years one and two of uni for people who won't do a degree). Everyone else seems to be in love with mechanical engineering. Even the well respected and now crap open university has stopped doing electrical.

author: rstofer
author_rank: Super Contributor
timestamp: October 13, 2020, 04:12:21 pm
content: Last week, in another thread, I posted links to the Bureau of Labor Statistics (www.bls.gov) and they point out that growth in Electrical Engineering employment doesn't come close to the growth in Computer Science. I didn't link Mechanical Engineering but it is marginally better at 12,000 new jobs over the next 10 years versus 10,000 for EEs. Those aren't very promising numbers when you divide by 10 for the annual number.Software Developers have fantastic job growth (300k+) versus Computer Programmers with a loss of 20,000 jobs over the next 10 years.https://www.bls.gov/ooh/computer-and-information-technology/software-developers.htmMy grandson changed his major from ME to Applied Mathematics. Job growth is abysmal but that may be a side effect of the way the job is categorized. Large data is the growth area. Machine learning, AI, all that stuff is driving industry. The job pays better than engineers (Computer and Information Research Scientists) but 10 year growth is pegged at just 5000 new jobs.In the meantime, Applied Math applies everywhere so his job prospects should be pretty decent. We'll see...I pursued EE as a hobby, never intending to work in the field. I don't think I would recommend it today. It's easy to get one of 300k+ Software Developer jobs, not so easy to get 1 of 10,000 EE jobs. Remember, those numbers are over 10 years. You can expect just 1,000 new jobs in EE per year - pretty slim.Of course those are all US numbers. I have no idea what is going on in the UK.

author: coppice
author_rank: Super Contributor
timestamp: October 13, 2020, 04:24:48 pm
content: Quote from: rstofer on October 13, 2020, 04:12:21 pmThe Bureau of Labor Statistics of labour statistics haven't a clue what the demand for labour will be more than a year or two into the future. Nobody has. In 10 years most advanced companies will be making a large percentage of their income from products which don't exist right now. Historically this has been the case for the last 100 years, and the need to keep moving to the next big thing doesn't seem to be slowing down.

author: rstofer
author_rank: Super Contributor
timestamp: October 13, 2020, 04:34:01 pm
content: Quote from: coppice on October 13, 2020, 04:24:48 pmMuch of their information comes from industry. What does the industry project?Everybody is just guessing but some guesses are better than others. The worst guessers are those signing up for classes. They have no clue!I was working on a project when I worked for a major chip manufacturer. We were going to build a plant in southern California to build mainframes. Somebody asked about internal heat gain and I suggested that it would remain what it was today. To which a VP of manufacturing told me "never bet against technology!". Boy, was he right! The PCs of today are orders of magnitude more powerful than even the largest mainframe of the late '70s and uses 3 or 4 orders of magnitude less power.If you choose not to believe the absolute value of the numbers, it might still be reasonable to accept the ratios. CS > ME > EE Even with this scheme, EE doesn't look too impressive.We may not have a decent crystal ball but, one way or another, CS is going to play a huge role.

author: IanB
author_rank: Super Contributor
timestamp: October 13, 2020, 05:58:20 pm
content: With regards to EE today, wouldn't much of the high value area come under "systems engineering"?For example, who designs smartphones? Is that EE, or software development, or is it a highly complex system of interacting parts containing hardware, firmware and software?

author: Mechatrommer
author_rank: Super Contributor
timestamp: October 13, 2020, 06:09:57 pm
content: Quote from: rstofer on October 13, 2020, 02:02:19 pmbecause differential equations are not easily solvable by hand of engineering level people. people higher up in the intellectual hirarchy have to developed numerical method (close approximation) for it to be implemented practically using computer, that is your grandson's MATLAB. and then there are boundary conditions whether we aware of it or behind the screen, that are nonsense from reality perspective. there is place where MATLAB is banned, is when you attend pure mathematics course where you need to understand the inverted triangle and those convoluted sort of musical notes signs and do some abstract mental manipulations is a must.Quote from: Simon on October 13, 2020, 02:05:31 pmits funny why i have to hear this from time to time? maybe its just for you, why you attend this Laplace course anyway? if you ask a farmer, they will tell you all those diodes and transistors and what you are working on your bench are all nonsense, they are all not needed, crops is what makes you not hungry, money is what matters. are you attending just to get engineering grade salary? the people you are paying £500 to are a bunch of people that need to feed just trying to get the community top notched and "mentally fit". there are areas where Laplace Transform is super important, ie that involves controls and stable feedback loop. most of us dont really appreciate it because we are not in the business, we just use opamp for granted, happy to use our car everyday and enjoy watching rocket science and exhibition jet fighter flying around without knowing behind those are heavy Laplace transform. if its not our business, there is no need for us to dig into it, just as farmers dont need any electrical parts nonsense, they just enjoying to use their cropping machineries. imho your statement is more dangerous than anyone promoting slopiness while working with mains. your statement is like telling kids they dont have to go to higher schools, its ok just to become a farmer, its ok just to aim as a janitor, you wont be hungry.btw i myself feeling "crippled" when dealing with these weird transform, when all they can give me is a table for limited number of Inverse Transforms. sometime we derived a weird equation from our designed system that is not in the table (like you experienced in OP). i think i have to go back to first principle, there must be reason why they dont teach first principle very well.. well.. this is the first principle of LT for your hate pet...https://en.wikipedia.org/wiki/Laplace_transformand this for inverse...now we can start from there... is it not needed? is like saying all those people working on this since industrial age back to Al-Jabar is for nothing... i bought and downloaded some more advanced Controls books because i want to build a hobby plane, man my brain got dizzy, eyeballs spin and got sleepy very quick when trying to follow them, luckily my hobby plane project is postponed indefinitely, but i know i will have to one day, when i get more serious, when it involves life or death matter. if it tastes bitter then i need to make it tastes better whether i like it or not. if we are not doing it, there is no need for higher education, i agree, its just for us. its ok to be here on low side admit that, let the man up there do their things. but dont say they are not needed or not that useful. fwiw ymmv.

author: rstofer
author_rank: Super Contributor
timestamp: October 13, 2020, 07:52:14 pm
content: Some universities, like the University of Florida, have separate math tracks for math majors and engineering majors. The math majors are going to enjoy the elegance of the math itself; engineers want to know how to apply it. Completely different focus.In the end, engineering is nothing by Applied Mathematics. Once you have the math skills, the rest of the program (EE, ME, CE, etc) is pretty easy. A few principles, a bunch of math and you're there.I have the (dis) advantage of graduating in the early '70s when slide rules were king. We did a lot of stuff by approximation, it was all we had. We certainly didn't have the MATLAB meshgrid or surf functionality. We had to work through the plot by hand and then analyze it with a Spirule and the Root Locus method. Control Systems was a difficult course. I remember very little...https://www.nzeldes.com/HOC/Spirule.htm

author: Nominal Animal
author_rank: Super Contributor
timestamp: October 13, 2020, 09:51:30 pm
content: Not just Matlab, but Octave (free), Maxima (free), SageMath (free), too.In particular, if you install Maxima on your machine (it's available for all OSes), you can verify if your inverse Laplace transform of (3-2s)/(s2-4s+9) is correct by telling itilt( (3-2*s)/(s^2-4*s+9), s, t);expand(ratsimp(%));That second line first tries to simplify the expression, then expands the result. It says-e2tsin(t√5) / √5 - 2 e2tcos(t√5)To check that that answer makes sense, we can do the forward Laplace transform to that (and simplify it):ratsimp(laplace(%, t, s));It is useful as an exploration tool, but only if you control yourself so you don't use it to skip the exercises. See more (and a better inverse Laplace transform) atthe maximalist. In particular, if you write your own notes, it can be useful to verify you don't make silly typos or such errors.

author: rstofer
author_rank: Super Contributor
timestamp: October 14, 2020, 08:43:07 am
content: Quote from: Nominal Animal on October 13, 2020, 09:51:30 pmI have Octave and would have used it for the example above but, for some reason, the 'symbolic' package wasn't working. It's an error on my part, I'm sure. I often port my MATLAB scripts to Octave just to verify that they are (or aren't) portable.I have used wxMaxima (Maxima with a GUI frontend) and I like it a lot. It seems to be about 1 step up from Fortran and I really like Fortran.I'll have to take a look at SageMath.I use symbolab.com for solving and desmos.com for graphing. Both are excellent.

author: coppice
author_rank: Super Contributor
timestamp: October 14, 2020, 02:20:26 pm
content: Quote from: rstofer on October 14, 2020, 08:43:07 amIts frustrating how often something written for MATLAB doesn't work properly with Octave. In most cases the code runs, but gives the wrong answer. So, you need MATLAB installed anyway, so you can run some test cases on both platforms and compare the results.

author: rstofer
author_rank: Super Contributor
timestamp: October 14, 2020, 04:41:05 pm
content: I just pay for the MATLAB Home license and call it good. It costs me a couple of hundred dollars per year (I have several optional packages) but that's the way it goes. I whine and snivel at renewal time but I get over it pretty quick.

author: coppice
author_rank: Super Contributor
timestamp: October 14, 2020, 05:20:35 pm
content: Quote from: rstofer on October 14, 2020, 04:41:05 pmIf its just for occasional testing, just find the students in your family.

author: Nominal Animal
author_rank: Super Contributor
timestamp: October 15, 2020, 02:38:54 am
content: Me, I'm seriously addicted to Maple. It does a much better job at simplifying complex algebraic expressions than Maxima or SageMath.I have a license through my Uni till the end of this year, but after that, I may need to buy my own (for Linux).I very often examine classical atomic potential models (as used in molecular-level material physics with lots of atoms, and in chemistry and biology in examining biomolecules and their interactions via force-field and similar potential models). Not only does one need the forces, F(r) = -dV(r)/dr, for simulations – so even reading a paper I like to ask Maple what the derivative of the potential looks like, as that is what really matters from simulation point of view –; but models like embedded atom models can have their potential defined via numerical models, and then using a distance function f(r) instead of the distance r (especially f(r)=r2or f(r)=r-2in particular, so one can avoid the slow square root operation completely), and examining the theoretical forms, helps understand the corner cases one will encounter when implementing one in a simulator.So, on average, each week my subconscious tends to bubble up a reformatting/convolution/idea that is interesting enough to experiment on, to see if it might help with these potential models and VERY large distributed simulations (as in millions to billions of atoms)... And this is not "for work", this is basically what my mind does to me. Call it a hobby, I guess?What I can tell, is that by doing this, no equation or mathematical problem really scares me anymore. Indeed, answering maths questions whose answers I don't know before I find out, has become a nice hobby; much like playing with physical puzzle toys. (I like those too.) And I really have started to value theorems and transforms; not for their internal detail, but their power of manipulation.

author: rstofer
author_rank: Super Contributor
timestamp: October 15, 2020, 05:36:49 pm
content: I have developed a fascination with analog computing and I have 3 computers, 2 of which are ComDyna 6's These things are fun to play with.I can do the same thing with MATLAB's Simulink. I can plop down integrators, wire them through some attenuators, adders and even multipliers, perhaps add in some adjustment knobs and I'm off to the races.Here's a more or less silent video on the Predator Prey problem:I attached a Simulink design for the Predator Prey along with the outputThe problem gives a wide open territory where, were it not for foxes, rabbits would grow without bound. But the more foxes there are, the more fox/rabbit interactions occur and fox population increases but rabbit population decreases until the fox population starts to die off and the rabbit population recovers.

author: rstofer
author_rank: Super Contributor
timestamp: October 15, 2020, 06:14:51 pm
content: Quote from: coppice on October 14, 2020, 05:20:35 pmMy grandson has the Student license for MATLAB but he uses it every single day. Moving the license from his machine to mine doesn't seem to be workable.At first I didn't see the Individual license for Maple but I finally found it: $239 That's entirely reasonable if it isn't a subscription and it doesn't seem to be.OTOH, MATLAB itself is just the base software. It's the packages that build on top that are important. It's a really complete product if you keep adding packages. Simulink is a great add-on.

author: coppice
author_rank: Super Contributor
timestamp: October 15, 2020, 06:41:24 pm
content: Quote from: rstofer on October 15, 2020, 06:14:51 pmStudents are usually able to install MATLAB on multiple machines using the academic licences. Quite a few seem to have it on both a desktop PC and a laptop.