Strange Math You've Never Seen

[@algorythmis4805]

At 5:30 it's "and" instead of "or"!

[@TheMathSorcerer]

Oh wow yes can’t believe I did that. Gonna pin this comment. Thank you.

[@Fircasice]

That makes much more sense, thank you!

[@alexfekken7599]

Also, writing something like "P < \infinity" as a way of actually meaning that a limit exists and is finite is a bit sloppy too...

[@SuperYoonHo]

@@TheMathSorcerer Hahaha

[@hOREP245]

@@alexfekken7599 I don't think that's sloppy at all. It's just a shorthand, and when you consider extended real valued functions it means exactly what it says, that it is finite.

[@magnusbruce4051]

Ah, Bessel functions (and spherical harmonics) were part of my second year in my physics degree. The lecturer spent about two full hours talking about spherical harmonics only for me to completely not understand even the vague idea of what we were doing. In the end, a group of us asked him outside of a lecture to show it again but slowly. Being the great guy and great lecturer that he is, he spent a further hour with us in his own time. He also said that the moment anyone gets lost, just stop him and ask him to go over it. I think after that hour we all had a better understanding than most of the rest of the cohort.

[@jimsmith6937]

+1 on the Bessel functions......who new I would rediscover them in RF design?

[@magnusbruce4051]

@@jimsmith6937 As far as I remember, I never used them again but maybe some other students that later specialised in theoretical physics or solar physics or something like that did need the knowledge. I reckon, at least for me, we were taught this stuff as a way of getting at least some practical application of being to handle infinite sums of sinusoidal components, and then that lead into the next module which was largely about Fourier methods. Even then, I didn't have to do any Fourier transforms after the exam for that module. I 'specialised' (for want of a better word) in experimental physics simply because that was the default and I couldn't pick a specialism. I ended up doing a masters and PhD in volcanology but in both of then, my main focus was experimental exploration of material properties.

[@theyhatedHimcuzHetoldtheTruth]

My professors would literally just say "theres this book called nvfjnvjfrnvfr, look it up, I have better things to do now".

[@Liberty2357]

Watch someone poke a water balloon in slow motion.

[@Zalemones1]

@@jimsmith6937 Surprisingly, modified bessel functions of the 1st kind show up in the analysis of strong non-linearities of junction transistor amplifiers

[@BeholderThe1st]

This course would weed out 50% of the engineering majors when I was taking my degree. This for people who had already done Calc 1-3+ courses. I'd often describe it as the math that even mathematicians don't do.

[@BitwiseMobile]

It depends on the discipline really. Not all of these equations are for all disciplines. Maxwell's equations, for example, are probably only going to be used for electrical engineering. Whereas something like numerical integration will be found in physics engines and physics emulators (and maybe even in stock market AI), Differential equations is a wide field and it has applications just about everywhere.

[@mb2776]

@@BitwiseMobile I saw some yt video on QM and maxwell's equations are apperently still used there cause of particle wave duality, describing QED and fields.

[@marcusrosales3344]

@@mb2776 Maxwell's equations pop up in QED, but they are contained in the field tensor. Basically it all surrounds the idea of guage invariance. The jargon is you minimally couple a U(1) guage field to some field theory by introducing a covariant derivative and identify the connection with the vector potential. We can make this vector potential dynamical by introducing a guage invariant term, being the field tensor!

[@marcusrosales3344]

I had to use the confluent geometric functions to solve a Schrodinger eq. Every last one of those functions pops up in physics, most in your undergrad. Many representations of these functions also pop up as integrals when calculating propagators. I've seen them in numerical analysis, and other ones, for interpolation and quadrature.

[@tHaH4x0r]

@@BitwiseMobile Although in general I agree with you, I disagree on numerical integration. Numerical integration is found in a lot of general science/engineering and data processing, and extremely useful knowledge to have.

[@alanmueller4633]

This reminded me of a book in my library. When I worked at NASA JSC in the early 70's they had a technical book store where employees could buy books at discounted rates. I bought "Handbook of Mathematical Functions with Formulas, Graphs, and MathematicalTables" by Abramowtiz and Stegun. It was published by the US Department of Commerce, has a total of 1046 pages and all this before hand calculators. Still has the original price tag at $12.65

[@paulpayton1348]

Ah, yes. AMS 55. I have it in hardcover and softcover. Best thing since Jahnke und Emde. You can get it cheap from Dover Publications. Good choice!

[@danielmrosser]

The book by W W Bell is also an excellent reference on tue topic special functions nearly all of these functions generally arise out of a study of well-known differential equations from physics

[@TheMathSorcerer]

👍

[@kdub1242]

Yeah, Bell is available from Dover.

[@Twisted_Logic]

Oh man, some of those chapter titles bring me back to my engineering and physics classes. A lot of them we wouldn't actually calculate ourselves, rather we were encouraged to buy a book of tables (Schaum's Mathematical Handbook of Formulas and Tables, to be specific) with solved general forms and the object would basically be to finagle the problem into something resembling one of the forms and use that to solve things like Bessel functions. ...at least until we got to Math Methods, which I could totally see this being a textbook for.

[@jeffmackey529]

Abromowitz and Stegun or Gradshteyn and Ryzhil!

[@thedeadbatterydepot]

Yes broken question, the final part of the video with the question wrong, with first 1/2 × 3/2 with brackets, goes 3/2,8/3,15/4, he cancelled cross multiply out of the original brackets with the above formula, k= 2/1 + 0/1 is added with no balance in the Infinite formula. K=2/2

[@wealthelife]

This textbook gives me flashbacks of doing applied maths and chemical engineering in the 80s ;) ps. The student/textbook version often only had 'answers' to about 5%-10% of the problems so that students could be assigned Qs that they couldn't look up the answer. If you want all the answers there was often a 'teacher's manual' version of the textbook that provided answers to every exercise Q. Might be hard to find a copy though ;)

[@69erthx1138]

This is a great book. Larry Andrews is an emeritus professor at UCF CREOL. He's very nice guy. I knew one of doctoral students Olga Korotkova.

[@romancandlefight1144]

I appreciate how you kept in every step of the solution. My teachers back in school would always skip a bunch and only the nerds would be able to keep up

[@tejarex]

A reason to only allow positive factors is so that the infinite product is equivalent to an infinite sum of logs of the factors. Allowing negative factors only adds non-essential complications. A corresponding reason to call a limit of 0 divergent is that it corresponds to the log sum diverging to -infinity.

[@josantonioalcantara]

Makes complete sense, since you are able to develop convergence criteria of products by using and reinterpreting those for series.

[@hamc9477]

Of course!

[@josantonioalcantara]

I can’t see no other essential reason why the limit zero is divergent, are there others?

[@RobertMertensPhD]

I have this book and I know Dr. Andrews. And he knows me. When it comes to higher level mathematics he was probably one of the best math teachers I've known. I have three of his books, the other two are Mathematical Techniques for Engineers and Scientists, and Elementary Partial Differential Equations. If you want to see some harder problems, look up the gamma function.... Actually, I used this gamma function to solve a real world problem in diffusion in 2D quantum wires. This particular problem also involved Legendre polynomials, a Heaviside function, a Fourier Series, all buried inside of a differential equation which was buried inside of an integral which came in two parts. It was fun. It took me six months to figure it out, but it was fun.

[@TheMathSorcerer]

Wow that's awesome. Thank you for this comment!

[@sadimanesadimane6746]

Only 6 months? Nyyyyce

[@goddaniel9478]

What the hell are you talking about

[@willk7184]

I'm sometimes amazed humans have attained such levels of higher knowledge. I think we take some of it for granted since it almost seems commonplace. But the people who worked it out and passed it to the next generation are brilliant.

[@jarnoldp]

I actually took this class with him at UCF. I wish I had him sign it. His lectures were like fine wine. That was a general consensus

[@GSDKXV]

UCF?? Small world

[@paroperha]

It makes me so happy to see I recognise all those topics... Proud of how far I've come as a Physics student... And excellent review! Thanks!

[@tc14hd23]

"Strange math you've never seen" aka "what I see when I look at the exam"

[@TheMathSorcerer]

Lol

[@rodneycummings1456]

I went to the University of Central Florida where Dr. Andrews taught. I never had him as a professor, but I did hear that he was an amazing teacher. I heard that he wanted to make sure his students understood what he was doing on the chalk board. I have a copy of his Partial Differential Equations with Boundary Value Problems book. That book is also well written.

[@TheMathSorcerer]

Nice !

[@jerryburke7877]

LETS GO KNIGHTS what did u major in?

[@geraldwellborn5047]

Very nice. I appreciate you working out the problem as an example. I have not worked these types types of problems since 1977 when I was in a DE class. It brought memories. Thank you

[@TheMathSorcerer]

You are welcome!

[@gheffz]

Thanks for the infinitive product example and simplification approach you used. By the way, the GAMMA function is one of my favourites. Thank you for showing this book. _(And yes, it is very well made... and I can see the layout is very readable, clear and uncluttered.)_

[@HansBezemer]

It's nice to see some familiar faces in these books! I did floating point implementations of Beta, incomplete Beta and Error functions for the Forth Scientific Library. But for my own compiler I did a lot more. I especially like Gamma functions - especially the "weird" ones, like Ramanujan and Cristinel Mortici approximations.

[@evanurena8868]

I also like Gamma functions and thet have some very interesting properties as mellin transforms, which is rarely taught in topics of special functions. For some time, ive also been pondering about combinatorial idenities being expressed as gamma functions with the use of the gamma factorial.

[@mlguy8376]

When you do a PhD in theoretical physics and use maple to solve some model equations it usually spits out all those functions at once. ;)

[@PaulPassarelli]

To condition a high quality bound volume, you need to condition the spine! Stand the book on the spine and open the two covers. Then holding the pages up vertically, begin from the outer pages on both sides and begin paying them flat a few pages at a time. Press the pages down at the binding, and repeat, working a few pages at a time from the outside to the center. Repeat this process until the binding becomes supple. Hopefully you've not broken the spine already.

[@chaotickreg7024]

We're lucky we don't need the paper knives anymore

[@Oceloctopus]

Haven't watched the video yet but for a second I thought you were correcting some of the weird math in the book. "ah yes, bound volume, some sort of amplifier function *nods sagely*"

[@pianoman47]

A dying art form!

[@Hazzar595]

@@Oceloctopus Lol I thought that too until the second sentence

[@user-xv9fe4eo1b]

Had old Soviet book written by another author but named exactly like this (though in Russian). Needless to say the content is the same and even the sequence is somehow similar (but hyperheometric function was explained at first place and used further on e.g. in Gamma function explanations). Good old times of studentship...

[@kdub1242]

Was it the one by N N Lebedev? The contents looked very similar. I worked through much of it in school and found it very useful.

[@user-xv9fe4eo1b]

@@kdub1242 as far as I remember - yes, it was Nikolay Lebedev's book, issue of 1962.

[@kdub1242]

@@user-xv9fe4eo1b An American math professor named Richard Silverman translated a whole bunch of great Russian language books into English and that was one of them. Fond memories. I studied physics rather than math, but many of the books were extremely useful for applications.

[@user-xv9fe4eo1b]

@@kdub1242 oh wow, never thought they were appreciated as highly! Funny enough, one of my handbooks was written by a guy with a name you'd expect to be Russian or Ukrainian, and it came as a surprise for me that the book was translated from English and was first published in New York. The book is called "Vibration problems in Engineering" and it's main author Stepan Timoshenko (who was actually born near Chernigov and graduated in Saint Petersburg) was also one of the key early contributors to ASME code development.

[@kdub1242]

@@user-xv9fe4eo1b Oh yeah, there were a whole bunch of applied mathematics books that became classics in the US. And for undergrad physics, the very famous "Problems in General Physics" by I.E.Irodov has, despite its boring title, entertained and challenged young physics students worldwide for decades. And for grad level physics, I need only mention Lev Landau. When it comes to math and physics (and probably a lot of other subjects too), you just can't beat the Russians and Ukrainians.

[@harshaphukan5091]

Spherical harmonics have a lot of important applications in computational materials science. Thank you for sharing your take on this book!

[@TemplarOnHigh]

That table of contents takes me back to graduate school. Bessel functions - the horror.

[@phasma6669]

I think I still have this textbook !! My favorite was the Bessel and Gamma Functions and integrals, and I believe they did some Fourier Analysis in this text [ though I had a separate text just for Fourier ] .... Strange...I actually enjoyed those topics 🙂

[@TheMathSorcerer]

❤️

[@starguy2718]

I am using Bessel functions of the second kind, in a research study that I'm conducting.

[@ChuffingNorah]

My first sight of the Higher Transcendental Functions was glimpsed in Part II of the textbook: "A Course of Modern Analysis" by Whittaker & Watson, published by the Cambridge University Press. It's title is somewhat cryptic now considering it was first published way back in 1902; it can appear rather archaic now using "Shew" instead of "Show", but it is a veritable treasure trove of all the advanced functions. I believe it is still in print, on Amazon as a paperback, as it was/is a real Classic! I gather both Profs were contemporaries of the superstar G.H.Hardy, whose own book "A Course of Pure Mathematics" is another abiding classic, still in print. As some bore once opined: "Don't read the Books about the Books; instead, read the Books!"

[@SandyRiverBlue]

There is a certain joy in successfully working a problem.

[@LT72884]

I just purchased a "Engineering controls and control systems" from 1957. Im in my controls class now and its weird. Root lucust plots are crazy

[@DavesMathVideos]

I have this book. Takes me back to my engineering days in the mid 2000's

[@TheMathSorcerer]

Cool

[@Fazz321]

Well, it's pretty standard collection for applied mathematicians - we learned all those functions in university. I couldn't comprehend them at the time but I still remember the names.

[@daviddavid-up1jc]

Вы в советском Союзе как мой отец занимались более продвинутой математикой. Американцы до этого не дотягивается.

[@daviddavid-up1jc]

Я немножко сожалею потому что сам по математике не понимаю но хочу заниматься Инженером по электричестве. Если у вас есть какая-то рекомендация или совет по книгам пожалуйста дайте знать.

[@Fazz321]

​@@daviddavid-up1jc Да нет, обычный ВУЗ в Сибири. В 2016-ом закончил. Лучшая книга это та, которую вы можете понять.

[@ahelguerrero]

perfect example of the meme: “i know some of these words”

[@jesusfuckingchrist01]

WOW you saw the math from a book called “Functions for… applied mathematicians” when you were studying applied mathematics at university!? Whoever would have guessed? Phenomenal! With top minds like yours, this Ukraine thing should be wrapped up in no time.

[@JxH]

11:40 "You just have to..." Open MS-Excel, fill in the index column (2, 3, 4...), type in the formula, add another column for the result-so-far, then pull it down the screen (duplicating rows) until it converges, examine it and then state, "Looks like about one-half." Pull it down some more, "Yep, converging to 0.5." Very likely competitive in time to the analytical approach. 🙂

[@dominiclipari]

This video is attracting two groups of people that share only a modest overlap: advanced mathematicians, and people into book binding.

[@raptornein2422]

Awesome video! I subbed forever ago when I was in Calc 3, and since then the number of videos I watch has dropped, but this one has peaked my interest yet again. I forgot how cool Calc 2 was!!

[@onradioactivewaves]

3 seconds in and I knew this would be one of those "making sense of any and every thing in the book is left as a trivial exercise to the reader"

[@malcolmhays2726]

I haven't done calculus in decades. I didn't do so well in calculus when I took it in college. Yet I was able to follow along quite easily...Very well explained!

[@BArkadeepDas]

Modern Analysis by Whittaker and Watson is also a book which includes several special functions and in general it can be called a legendary book as it way more information than a standard analysis book.

[@carlhopkinson]

That partial product demo was super-cool !!!!!!

[@l.w.paradis2108]

Cool little example . . . I love the ones anyone can follow, 30 years after their diff eq class. ;)

[@l.w.paradis2108]

Also, how surprising that an applied math/engineering math book lacks comprehensive solutions. Wow. :)

[@frankharr9466]

That is a cool book. And yeah, I've heard of those, but that's because I watch some other math channels here, not (strictly) because of my education. Thank you for sharing!

[@mark4asp]

There are two editions to this book: 1st - 1986, and 2nd - 1992. The 2nd edition also has a reprint by a different publisher. The 1st edition is discussed above.

[@joshlovesfood]

The problem at the end reminds me of a beginner’s Real Analysis problem. I found Real Analysis to be overwhelming and difficult

[@kristianhauservillegas3343]

Physics major here. I enjoyed solving the exercises of Whittaker & Watson's "Course of Modern Analysis" when I was a student. :)

[@bogdanoff1723]

Quantum mechanics textbook: Hold my beer 🍺

[@starguy2718]

General relativity textbook: Hold MY beer.

[@aravartomian1]

Also you can use induction if you prefer. Base case: 3/4=1/2(1+1/2). Induction: 1/2(1+1/k-1)(1-1/k^2). Which is equal to 1/2(1+1/k) after some algebra.

[@thecrazyukrainian1335]

Physics major here (Junior currently). I took a Mathematical Physics course and a large section of the class was special functions. It does come up a lot but the sad part is we didn't have a book for the class. Hard to study and practice when there isn't a textbook to skim through. I was a sophomore learning this, so it was a shock when you mentioned that high undergrads and/or beginner grads learn this stuff (Save me :( ) Definitely interesting.

[@GaryGrumble]

If you like this book you would like Courant & Hilbert, Methods of Mathematical Physics. My teacher for an applied math course was a Dr. Brown who was a grad student of Courant who was a grad student of Hilbert. History matters.

[@devd_rx]

Special people will always tend to special people after all

[@kellygarcia6588]

Great video! To hold your book open I recommend using a binder clip if you havent tried it!! I use a big binder clip to hold my textbook pages open when I put them on my stand :)

[@compphysgeek]

1:13 Legendare? you are legendary, buddy ;)

[@johnleclair663]

I feel like one final statement is missing after solving the limit. I truly believe my math professor would have taken a point away 24 years ago for not stating something like: “since P = 1/2 and P < infinity AND P != 0, we can say that the infinite product converges to 1/2”

[@lightyagami1752]

Unless your math professor was also a comp sci professor he should've taken marks away from himself for using P != 0 rather than P ≠ 0.

[@johnleclair663]

@@lightyagami1752 I think even then marks would have been taking off. I was just typing quickly ! But yes, one should not Solve a mathematical problem with a programming language :-)

[@lawrencedoliveiro9104]

We have Unicode now. Why shouldn’t modern programming languages accept “≠” as an operator?

[@johnleclair663]

@@lawrencedoliveiro9104 the C and C++ standards do not define the that symbol as an operator.

[@lawrencedoliveiro9104]

@@johnleclair663 I did say “modern”, did I not ...

[@EddieVBlueIsland]

Large rubber bands can hold the pages. The lack of worked out answers is deliberate so the professor can "earn" his way - after all that who the book is marketed to.

[@Sakurao]

That pencil is iconic

[@crazyfly5505]

Excellent! This should be a thing for all your book reviews. You should pick an interesting problem from each book and work through it with us!

[@TheMathSorcerer]

Ok!

[@TheMathSorcerer]

👍

[@anandsinghrajput7236]

@@TheMathSorcerer yes please..very nice suggestion....make your minds prepared for future ..will wait for this 🙏

[@TheMathSorcerer]

Yes I really enjoy doing these videos. I feel like people learn something after watching them and it’s worth it👍

[@ericdunn9001]

You have the exact same handwriting as me and it's freaking me out lmao. I have a math degree personally so this literally looks like my old homework.

[@TheMathSorcerer]

LOL that is cool

[@shawnscientifica7784]

I never realized how much math I know as an engineer until other people start talking about math 😭😭

[@karol_p]

It's a good coincidence KZbin showed me this video. I have a case with Legendre polynominals involved.

[@werhnerwangra]

I feel so much better after watching this video because I struggled like a dog with these problems in my undergraduate studies

[@jwf3148]

What a clear, useful and welcoming video....Thank you !!!

[@TheMathSorcerer]

You are welcome!

[@jaimeduncan6167]

Excellent video. A detail: Missing is the justification of why you can't say an infinite product converges if it approaches zero.

[@mencken8]

This is the favorite book I’ve never owned. There is an empty spot in my bookcase where I sometimes go to appreciate the fact that I do not now and shall never own it.

[@satyavivekanandbattula1091]

Sir Make videos on Geometry . And also give some tips regarding Geometry.

[@sam12345768]

let ,set,define,consider,compute and finally solutions i have touched learnt all kinds of mathematics from simple to complex from high school tech to physics to ME.i miss that time.

[@IN-pr3lw]

I stopped doing Maths after highschool and I did the foundation paper but I'm almost finished watching this video 😂

[@DDDhoch2]

You skipped though the pages and there was a graph. My brain instantly: "Oh! The gamma function! Nice!"

[@mikej9062]

I especially enjoyed the page smell review part.

[@TheMathSorcerer]

👍👍👍

[@MrCarburettor]

Darn, I wish to be able to watch you when I was in college...

[@Foosion]

Im just starting college this year, can’t wait

[@matthewchapman2248]

I have books like these; gifted to me by dear friend. Now I'm so thankful. For anyone who needs to have comprehensive knowledge and written works for E.E this will help if you're in college or university or even if you're on the job learning

[@azimuth4850]

Enjoying these combo book review and problem solving vids.

[@TheMathSorcerer]

😀

[@markromine5103]

I've seen it, at 7:30am MWF in the 90s, on the opposite side of campus from all my other classes, my apartment, and any available parking. 🙃

[@starguy2718]

Didn't you just LOVE those classes! Ah, fond memories.

[@SPVLaboratories]

I used to do research on generalizations of Bessel functions. You should check out Watson, a 700 page behemoth all about Bessel functions.

[@livedandletdie]

I prefer that Π with the index beginning at 1... it's a lot easier to deal with. Less math needed...

[@frankied.2828]

Really nice. Thank you for making this video

[@austinbutts3000]

Great video! One thing to note on the practice problem if you the viewer want insight that applies to other problems: one way to do the cancellation is to split the fractions between two partial products, re-index one of the products to start at, say, n=1, and then identifying what cancels when comparing terms with the same index. Visual pattern recognition is great with simple problems, but refining techniques of manipulating partial sums or products to get terms to cancel will eventually take you a lot further.

[@instaremergence]

Love your videos professor 😍 I joined your channel membership today itself and i got many perks

[@TheMathSorcerer]

Thank you!!

[@ashharkausar413]

Great video. Would love to see you do some of the more complicated stuff in that book.

[@samdog_1]

Okay, granted the problem you did was not that difficult, but it still felt great being able to follow along step-by-step. Especially considering I haven’t taken a math class since the late-1970s.

[@TheMathSorcerer]

that's awesome! I picked it so people who had some background might understand, I am glad you could:)

[@zacharyibarra1838]

“Legend-der functions” 😭 All physicists crying at the butchering of a great man’s name.

[@BuckingHorse-Bull]

yes finally the mathematic formulas I needed to organize my sock drawer

[@sonic5d]

I loved the example! Thank you^^

[@markhugo8270]

Proper way to do this is to do an integral about a pole in the complex mapping of a function. As you circle around and calculate the residuals you will find the convergence and the terms. See Churchhill Complex variables.

[@AlongtheRiverLife]

Love all this! Why I am relearning after taking it all 40 years ago!

[@nabeelsherazi8860]

Like 80% of this book plus 40% more stuff is covered -- better IMO -- in Arfken and Weber. We used that textbook for my undergrad mathematical methods course and I still use it as a reference.

[@starguy2718]

The Wright Bros invented the airplane using high school algebra and a little bit of trig. Higher math can be overkill, for real-world applications.

[@Google_Does_Evil_Now]

4:15 Pi? Why are you using Pi? Something to do with a circle? You're multiplying a series of values so why is Pi involved? Are you measuring a circular curve, radius, pieces within the circle, area inside the circle? The values are being multiplied? What's the formula for, describing? Perhaps tell us this instead of that the book is nice quality? :-) Applied Maths - So what does this apply to? Please bring me along by letting my brain make the connections of what we're doing and why. If that's possible. So far I know you like this book, it doesn't have enough answers, and you've decided to start writing a formula but I've no idea why, what you're trying to solve, what you're trying to describe with it. Hope you take this as positively, well meaning, feedback. You're enthusiastic, nice to listen to, probably a good teacher by your enthusiasm and talking while writing. Please just bring me along by telling me what the maths is going to apply to - applied math :-)

[@hooberdoober576]

Unless, of course, you're an engineer. Signed.. Registered Professional Electrical Engineer

[@LouisEmery]

At 0:18 I was able to tell this book was discarded from a library (sticker on spine). Good find. I do the same. ;)

[@computer-training-for-seniors]

This world does not reward those who are smart, but those who are practical.

[@starguy2718]

"A" students work for "C" students; "B" students work for the government. -- Robert Kiyosaki

[@walterbrown8694]

The symbol you were calling "Pi" is NOT "Pi" - It is the Product symbol ( which may have another name, but it is not Pi ) I am an 87 y.o. retired electrical engineer who has never heard that symbol called Pi.

[@TheMathSorcerer]

It’s called pi also👍 Lowercase pi is the one we often see. The one for the product symbol is capital pi.

[@walterbrown8694]

@@TheMathSorcerer All these years of applied math in engineering and I never called the product symbol by its correct name - even this "Old Dog" can still learn - Thanks for the input ( Retired from engineering, but I may still be able to win a couple of "Bar Bets" with this !)

[@TheMathSorcerer]

❤️❤️❤️

[@robertl.crawford4369]

Giant Pi?

[@josantonioalcantara]

Capital sigma for the sum sign, because that’s the name of the Greek letter. You might have found weird to call it pi, because it’s more frequent to hear it to refer to the number, but that’s the generic name of the Greek letter. For the number it’s to abbreviate perimeter p=π while in this scenario is to abbreviate product. Recall that Σ correspond to the capital S to abbreviate sum.

[@bsharpmajorscale]

I've heard of most of those things, but only because at one point I skimmed a lot of reference books at the library for cool functions to use in Four 4s. I'll have to check if my library has that book!

[@happyd6145]

There is still hidden Mathematics in the Jungle of Academics that can be used to fly and summon Ghosts.

[@jaketan5172]

There is another resource that allows calculus to be learned easily by hand, literally. Level N of Kumon Math (no, not marketing for Kumon) has worksheets that allows one to learn by working from simple to complex differential equations in incremental steps over 200 worksheets organised in 20 sets of 10 worksheets for each level of difficulty. Hand-eye-mind connection is attained with little sweat and much achievement for learners as young as 15 years old.

[@MitzvosGolem1]

All that to drive a train? Dr Feynman loved mathematicians ..

[@edysinsimon8646]

Back in the day, (statical engineering) several function/ regression modeling was quite the directive in terms of demo of the star-wars tech back in the early 1980s! This saved my bacon more than one time!

[@matheuseliaspereira9566]

Some good books on special functions are the ones by Olver (Nist handbook), Butkov (Mathematical Physics), Watson's Treatise on Bessel Functions, Prudnikov (table of functions and integrals) all five volumes, Gradshteyn (table of funtions and integrals)

[@jacobharris5894]

I’m self studying Bessel functions right now in my free time so that whenever I encounter them again in physics they don’t feel like their coming out of nowhere and I’m familiar with all their properties. I’ve only made it through the first chapter but so far Introduction to Bessel Functions by Frank Bowman is pretty good. I’m reading it more for the applications but I’ve surprisingly been able to understand all the proofs so far. They probably could be more rigorous but they work for me.

[@Number6_]

You should be seeing most of these things by year 3 of a decent math degree. Any math grad should have seen all this.

[@RazzleberryHaze]

I tried to follow along and now there's a flaming hole in my living room floor and it smells of sulphur and burning meat HELP

[@daniellindner826]

Very interesting book!! I’ll be arriving at infinite series soon in my self study of math.

[@TheMathSorcerer]

Awesome !

[@romancandlefight1144]

I haven't studied math in over 14 years and was average at best in high school but somehow got the feeling it was converging to 1/2 a few mins before you finished :0

[@kummer45]

This math SHOULD be mandatory in every math school. Special functions is the door for higher math in applied science. Laguerre, Bessel, Legendre, Hypergeometric, Hermite polynomials and differential equations is a fundamental topic in mathematical physics. The book is a standard in the subject. There very good ones out there. Elliptic functions should be studied again in Math Majors and Physics Majors IN DETAIL, extreme detail. These subject should not be looked sideways.

[@sqwndw6430]

Sure they're great topics but hopefully you're not confusing mathematics with applied science. For example take a look at group theory, number theory, and mathematical logic, which indeed are mandatory in many math programs. Do you see the difference?

[@noobyfromhell]

> This math SHOULD be mandatory in every math school Please no. Why would someone who's interested in algebraic geometry, or numerical simulation, or probability and statistics, or really anything but proving things about equations of physics want to spend time on hypergeometric functions?

[@Bluuplanet]

What to do with a (like) new book to make the binding flexible without breaking it: Stand the book with binding against the desk. Open both covers so they lay on the desk and run your finger down the insides of the hinge line with pressure. Open about 10 pages at the beginning and end of the book and repeat the finger creasing maneuver with pressure. Repeat this, opening about 10 more pages, front and back. Continue this process until you are at the center of the book. This makes the binding more flexible without cracking it.