Legendary Calculus Book

[@3koningen]

The most important feature of Apostol’s exposition is that it starts with INTEGRAL calculus BEFORE differential calculus. Courant also did that in his books and I think that is the way to go.

[@spacetimemalleable7718]

Thought this was a great idea. However the engineering & physics depts would object since they would have to adjust their curriculum since they cover Newtonian physics with motion, force first. An engineering student in a calc based physics class would be confused unless the physics class covered differentiation first. Note that a lot of freshmen physics, engineering students take 1st year calc.

[@2002budokan]

@@spacetimemalleable7718 Ideally, all curriculums should start with 2 years intensive math program before they start their actual faculty program. Maybe only Introductory Physics could accompany after the first year. If students fail in this period they should retry and shoul never be allowed to continue unless they finish the required math section. In this period, they should start (if they do not need precalculus) with calculus 1 and 2, LA 1, and Calculus 3, LA 2 (the LA done right way), DE, PDE, Probability and Statistics. After all these any faculty curriculum will be easy to achieve. UPDATE: Before Calculus a precalculus with basic math will be very useful. This should include Logic, Sets, Proofs, Functions, Relations, and special functions Trigonometry, Exp, Log etc...

[@pedroivog.s.6870]

It might be a matter of preference for what I'm used to (currently finishing Calculus 3), but I find it this decision quite strange, derivation is the easiest and most consistent to calculate, after all (besides only involving a division instead of and infinite series). I also missed a section dedicated to limits before either of the operations. I haven't read much of the book yet but do plan on doing so during January, so I'm probably just having a bad first glance

[@palindrame]

I mean that’s the history of calculus pretty much. Ancient dudes came up with the idea of integration, way before people came up with the idea of differentiating stuff and then guys like Euler started exploring different series and it was wasn’t until much later that we formalised the definition of the limit.

[@paulkarch3318]

That is the textbook I had as a freshman and I still have my copy. I came from a rural high school and I thought, at the time, it was a little bit hard.

[@gopalparam6401]

Dear Math Sorcerer, A big thanks to you for getting me re-interested in mathematics. I am over 60 and trying to relearn some of the advanced math that I learned in engineering school more than four decades ago in India. Now I am in eighth grade and hope to ascend to the holy grail of Apostol, Spivak and Rudin someday. These books are expensive if you try to buy them and being a book collector with a limited income it is a huge balancing act. However, Calculus - I & II of Apostol is available for a free on the web. Thank you once again for your work and encouragement.

[@nollix]

Good luck my friend.

[@priyanshukalal1195]

I have wrote to Wiley publishers India to publish a paperback cheap version of it. And the second volume is already here at 700 Rs. on amazon and first volume will be available soon on Amazon.

[@gopalparam6401]

@@priyanshukalal1195 Mr. Kalal, Thank you for your response and good work!

[@gertwallen]

"However, Calculus - I & II of Apostol is available for a free on the web"...really? where?

[@sanatpillai8532]

@@gertwallen you can really just look up "apostol calculus pdf" and a pdf is f definitely one of the first few results. I'm uncertain if volume two is available this way, or of the legal validity of it, but i use it for volume one

[@edhodapp6465]

Apostol’s analysis book was great! I used to hang out with a couple of math grad students while I was undergrad physics. We would sit around all night until the sun came up doing math, and one of them had this book. Because of what I learned from that, some math professors would let me sit in their grad classes. I remember doing proofs on the chalk board, or critiquing a poor proof from one of the other students. Such a long time ago now, after decades of ruining my mind by coding computers. Since I am no longer a poor student, I have Apostol’s calculus books (and hundreds of others that I never have time to read). I like how he starts off like Archimedes with finding areas.

[@emiliobesana2775]

your videos are always relaxing, just you and a math book, no music, no cuts, no bs, perfect

[@konradswart4069]

I have worked through both volumes of Apostol Calculus two times. There is just _one answer_ at the back of the first book that is wrong! It is integration exercise 6.25.40. The first time I worked through the book, and encountered that problem I couldn't solve it. At least, that is what I thought. The second time I worked through the book, and then succeeded to solve _all_ the exercises, I discovered that this answer was wrong! I also taught my brother calculus from this first volume. He had _a really_ a hard time with them!_ Both volumes of Apostol Calculus are tough. There is a tougher book than this one, though. It is Analysis from Einar Hille. It also comes in two volumes and covers more or less the same subjects, and some Apostol does not cover. But, contrary to Apostol's book, Hille proves _all_ the theorems. Apostol proves _almost all_ of the theorems. The two books of Einar Hille are written not for students, but for university professors who teach calculus from books like those of Apostol. University professors who want to have greater skill than the books of Apostol can give. If you think that Apostol's Calculus books are tough, _which they are!_ just try Analysis from Hille! _These are really tough!_ I tried to do them several times, even right after I had done Apostol's books, both of them, the second time. _I just could not do Hille!_ An additional remark. When I went through Apostol for the second time, I learned a "secret" formula that distinguishes _good_ from _great_ mathematicians. It is a formula that applies not only to mathematics, but to _everything_ which requires the development of your intellect. In the case of this integral I couldn't solve, I _blindly_ thought that the answers at the back of the book were all good. I didn't _check_ my own answers, apart from comparing them with those at the back of the book. But the second time I not only looked at those answers but also _differentiated_ my answers to see whether I could recover the original problem. And when I did this with my answer, and with that of Apostol, I discovered _his_ mistake! The 'secret' is this: _do not restrict yourself to just solving problems! _*_Always CHECK your answers!_* After having solved any problem, ask yourself how you can _test_ your answer! If necessary, _put a lot of thought into this!_ If possible, _design_ methods with which you can check your answers! I learned this from Murray N. Siegel, a high school teacher who succeeded to produce the best students ever! Almost all of his students passed mathematics exams with the highest scores! Later I began to realize, _how terribly important_ this idea of _testing_ is! Testing and checking are the very basis _of science!_ If there is a body of knowledge, but _no method of testing the answers is either given or possible, it is _*_not_*_ science!_ Indeed. it is _the method of testing_ that is the meta-test of any science! It is the method of testing that distinguishes different sciences from each other. Mathematics is a science because its method of testing is _logic!_ If some mathematical proof is not logical, it is wrong. If a certain direction in mathematics does not satisfy logic, it is not mathematics. Axiomatic systems, the _big breakthrough in mathematics_ made by Euclid for the first time in geometry, and later introduced by Emmy Noether and David Hilbert into other branches of mathematics _are rules of testing!_ This, by the way, shows that there is not just _one_ mathematics. Every axiomatic system of mathematics is a complete science in itself! That is why you can have Euclidean and Non-Euclidean mathematics as _different_ (sub) sciences of mathematics. Physics is a science because its method of testing is both logic and the experimental test. Chemistry is a science because its method of testing is the experiment. It is a sub-branch of physics, but has its own testing methods. (Stoichiometry, for exampe.) Astronomy is a science because its method of testing is simply observation. Biology is a science because its method of testing is Darwinian (Neo)Evolution. Any theory claiming to be biological science that violates Darwinian (neo)evolution _is biological nonsense!_ Information theory is a science because the test is simply: 'running programs'. Also, computer programming only began to take off for many people, when compilers were provided with parsers that _tested_ the computer programs on syntactical errors. And branches of mathematics are used to test computer programs semantically. Therefore, computer science really _is_ a science! Economics _is not_ a science, because there is no method of testing in economics. That is why there is no consensus about any economic theory. The greatest nonsense is presented in economics, like Marxian economics, Keynesian economics, and this philosophical direction which even _denies_ that testing is possible: the Austrian vision of economics. Psychology _is not_ a science because you cannot test psychological theories. The same for law, sociology, cultural anthropology, religion, and, I think, many other directions claiming to be science. And, a last remark, just to illustrate how important testing is. Many psychologists who began to use brain scans are baffled by human consciousness. But to my knowledge none have ever thought about why human consciousness exists, and what makes it so unique. Human consciousness is the brain equivalent of _testing!_ The biological function of consciousness is _testing outcomes!_ That is why _becoming conscious_ of any decision always occurs _after_ a decision has been made. This is something that has baffled psychologists using brain scanners, a fact that has led to the most ridiculous theories about human brain functioning. Like: 'none of us know what we are doing, because all decisions are made subconsciously. But the function of consciousness _is not_ to _make_ decisions, but _to test them!_ That is why 'becoming conscious' of decisions happens _after_ having made a decision. Human consciousness is of vital importance for humans, exactly _because_ we, humans, do not come into the world with a primary survival mechanism. We must even learn how to walk, contrary to antelopes, that can run shortly after birth! We come _helpless_ into the world. Our brains are such, that we not only _can_ but even _must provide ourselves_ with a primary survival mechanism. No other life form has put this demand on it. And to do this in the correct way, nature has provided us with _consciousness_ as a way of _testing_ whether we are doing and learning the right things. This is why learning mathematics, and _doing and testing exercises_ is a very thorough method to develop our consciousness!

[@kuroisan2698]

please, Can you recommend a textbook about linear algebra that is similar to Apostol's Calculus

[@konradswart4069]

@@kuroisan2698 I don't know what book is similar. However, I _do have_ a recommendation if you want to learn many subjects in mathematics with the least amount of trouble. Have you ever looked at the Schaum series? I have passed many exams without even _doing_ exercises. What I did was just read a Schaum book, follow all the worked-out exercises, and put effort into them just to understand them. I didn't even do the supplementary exercises! No need! Linear Algebra by Seymour Lipschutz is such a book. It gives a very good understanding of linear algebra. I try to post a link. But KZbin often deletes posts with links. So, I try to do it in a separate answer.

[@albertovaldez1444]

awesome comment, totally agree

[@gertwallen]

Apostol's book belongs to a very small league of books that teach Calculus stressing understanding and thinking by showing proofs of theorems so you know where all comes from, but at the same time keeping a balance of pragmatism without making the subject extremely rigorous and abstract like a pure math major requires.On the other extreme you have Calculus books like Stewart's that converts you into just a formula factory aimed at engineers. Needless to say, Tommy's Bible as it was referred at Caltech is the way to go.

[@Bloodyslayer73]

Apostol’s book was also very popular in calculus courses for engineering in Latin American universities. It was very well known to be very complete and complex.

[@TheMathSorcerer]

Very nice!!!

[@martinrevoiralynch4460]

Still usted for math undergraduate in calc 1, at least in my country.

[@dont-want-no-wrench]

only mildly interested in calculus, etc. no application in the kind of work i do, but i do love the passion you have for math- only person i ever saw who collects these books with such enthusiasm, that's why i follow your channel!

[@stevemenegaz9824]

Find an area that grabs your interest. Set theory? Discrete Math?

[@user-uq5mn1ih9d]

I am Norwegian and courses in under graduate math at University of Oslo in 1976-77, There we used these books. It was a chock to learn math in english, but it was no problem. I loved these books. I found these in Perlego.

[@wargreymon2024]

This is a very well-written, well-made, organized, comprehensive book WITH ANSWERS. I see the reason ppl ask you to review such a good book.

[@markulit3120]

Great book, I hope I'll be able to find one here in the Philippines. Great video too!

[@TheMathSorcerer]

thank you!

[@davidandrade5572]

The volume 2 is a fantastic book. Definitely the best if you are taking a vector calculus course. It is tough (that is how vector calculus is) but it does not cheat you. It is an absolute gem.

[@themooseyoyos]

Love the new intro!

[@70mavgr]

Tom M. Apostol held a chemical engineering degree before going into mathematics. He was a very smart individual.

[@tmendoza6]

Yes love the smell I just found an old perfect copy of "Set Theory" Hausdorff with library card taken out six times 1958, 60,69,70,88

[@TheMathSorcerer]

wow!!!!

[@user-yw9ek7nd8i]

Both Calculus and Analysis by Apostol are all perfectly written. They are so good.

[@sicko_the_ew]

I've heard that L'Hôpital was written L'Hospital (but pronounced as it is now) in the version of French before some spelling reform that got rid of things like silent "s" letters. The circumflex on the "o" was to indicate it went with a missing letter.

[@bourne3106]

What a book to bed down for winter, log fire, a glass of port and many notebooks

[@iQmliAwyrMRyPWfV]

PLEASE do book review on more 'generalized' math books, such as "expression making" or "equation making". How to express ideas thru maths, proportions, and how to accustom one's self to thinking like a mathematician. I know you reviewed George Polya HOW TO SOLVE IT, but i mean something more mathy and not vaguely problem solving, please. Thank you!

[@Pteromandias]

Hey so I've been following a lot of your videos. I have been interested in getting into mathematics, even if it's just completely self study. It's something I feel like I missed out on, since I had an aptitude for it in school. So here I am. I have to say of the calculus texts you've recommended - of which I have purchased three: Spivak, the violin one, and Apsotol - I have to say Apostol is my absolute hands-down favorite. It is just indescribably beautiful.

[@Andrumen01]

Ah yes, that was one of the Calculus book I used when I was an undergrad: Apostol, Spivak and J. Stewart (Early Transcendentals).

[@35USCode]

I was waiting for this one, thank you.

[@sophiaisabelle01]

Seems like the content on this channel has been gradually getting better over time. We hope to see more videos like this. May God bless you.

[@spivak4342]

How about doing a comparison with spivak ?

[@movdqa]

I have a copy of this book that I bought mail-order from a bookseller though Abe Books back in the 1990s. It cost $10. The price of this book exploded to ridiculous amounts later on. A few years later, I spotted Volume II at our corporate library and I found the owner of the book (he was an English major) and I asked him if I could have it and he said, "Sure". So I have volumes I and II. They are both in the blue cloth binding. I have never seen that white book cover before. At any rate, it's a fairly terse book compared to modern undergraduate texts.

[@brandonbennett4970]

Wow im loving the new intro!

[@abstractnonsense3253]

These two books are excellent and it's really a shame they're not cheaper because they could have been the standard introduction to Calc1, Calc2, Calc3, Linear Algebra, and Differential Equations all in two coherent volumes. I hope Dover Publications republishes these at some point.

[@adorp]

Will Wiley let that happen? Is it public domain yet?

[@Singularitarian]

Awesome video, I love all this commentary on these books.

[@neilreynolds3858]

I've never seen a copy of Apostol. It was legendary even when I was in high school but nobody had a copy. For $110.70 for a first edition, I'll get a copy.

[@adorp]

I found an used $10 copy of this and self-learned calculus after school. School only taught me to fear calculus. This book cleared it up. I did not find it hard, but maybe that's because I had already grown to fear calculus as some complex ancient sorcery. When going through Apostol, calculus felt much simpler than what I had remembered it as.

[@Calcprof]

I had calculus from this book. 3 people in the class got math PHDs.. at least 2 (including me) became math professors at research universities. (I don't know about the 3rd PhD).

[@WitchidWitchid]

I was lucky. I got these books on the cheap at a library sale. I like the smell of old math books. It's hard to describe, slightly damp, earthy, and maybe a slight hint of.moldiness. I alsi have a couple.of math books that have a very smoky smell. They were in a building that had a fire 🔥 many decades ago. Fortunately they weren't damaged but they picked up a strong burned smoky odor. Although it has faded away quite a bit they still carry a noticeable smoky odor particularly when opened.

[@PythonDad]

I recently lambasted the Courant/John calculus book on another video of yours. Apostol's book basically does what Courant claims he set out to do in his book. Despite the book's age, its notation is modern and it is free of bizarre idiosyncrasies. It is also structured much better instead of being a stream-of-consciousness rant. There is no ambiguity with any of Apostol's definitions, and hence it is easier to learn to write proofs with this book than it is with most. Apostol suspected that most people using this book for a first calculus course would probably not have learned about proof writing previously, and I think it is appropriately accessible. I think Apostol's second volume and Lang's Calculus of Several Variables are the only books worth using as a first exposure to multivariable calculus. It would be nice if there were more options, but if you pick either of those you're in good hands. I think Lang's is a little bit better for applications of linear algebra to calculus. Apostol has more problems, and if you do all of the chapters about differential equations you will have learned almost as much as you would in a first course dedicated to the topic. He also has short chapters about calculus for functions of complex variables and for probabilities, at least in the second edition.

[@MurshidIslam]

I'm interested to know your views on Courant's book.

[@PythonDad]

@@MurshidIslam Here is the comment I left on The Math Sorcerer's video about it: "I'm writing a mini blog in the comments here because I have very strong and very low opinions of this book. Anytime I just hate a book I try to find reviews of it by people who know more about what they're talking about than I do to make sure I'm not overreacting. In this case, there are at least two people with much more credibility than I have who agree. Upon the original release in 1965, Robert Rankin noted in a review (in The Mathematical Gazette 1967-May Vol. 51 Iss. 376) that the book is sloppy about definitions. This is something I found myself and is what made it so hard to follow the author's logic when compounded with the weird terminology and notation. Ralph Boas (in his review in Math Reviews) was pretty critical of the fact that Springer bothered reprinting these two books in 1989, referring to them as "museum pieces" which ignored changes in standard notation, terminology, and presentation that have mostly made calculus easier to learn and to teach. He also noted that there are dodgy proofs in the 1989 edition that go all the way back to Courant's original 1927 work Vorlesungen über Differential- und Integralrechnug that were never fixed. Pretty scummy if you ask me. I also feel like there is some serious arrogance from the author that spills right onto the page. Both reviewers note a claim in the preface that Courant's 1927 book was the first to approach differential and integral calculus as a unified subject rather than treating them separately. Rankin said "Incidentally, the excellence of this earlier work can be acknowledged without subscribing to the claim made in the preface to the work under review that it presented the first unified treatment of the differential and integral calculus." Boas was less forgiving and provided counterexamples outright. There is a claim in the preface that this book was meant as an update to the 1927 book that would better benefit American university students learning calculus. It isn't entirely clear to me what they're referring to. The tables of contents in the two show very minimal changes. The first chapter of volume one about the real numbers is probably the most incoherent 100-ish pages of mathematical exposition I have ever read. To me it comes off as a stream-of-consciousness rant. Straight from the horse's mouth, Courant states that it is critical that calculus not be completely divorced from its applications to physics or the ways it can be understood intuitively, but his development and motivation of everything in chapter 1 are the least intuitive I have ever seen." Furthermore, I have several friends who were math majors who say that Courant uses terminology they have never heard of. Many people bring this book up as one that is much better than the mainstream offerings, but I don't think it deserves to be mentioned in the same breath as Spivak, Apostol, and Hardy's books, which it often is.

[@pakeka6175]

Wow, I have heard his name (my professors mention him often) BUT it is the first time I see his book.

[@colt4667]

11:31 "Hopefully you'll have all of your books forever." My wife just does not understand why I have so many books. I haven't counted them but I think I have fewer than one thousand.

[@83jbbentley]

Holy Smokes! You wouldn’t joking about that price. $450 clams..it’s a gorgeous book though.

[@RyanReadsGreek]

Thanks for the video, Have you already done one on any classics like Euler's Elements of Algebra, Euclid, Descartes, the Disquisitiones Arithmeticae of Gauss, etc.?

[@lkern6238]

I just bought Apostol's Mathematical Analysis A Modern Approach to Advvanced Calculus (2nd printing) at the local Goodwill warehouse for 20 cents.

[@rich_in_paradise]

Calculating curvature gets really important when you're working with parametric curves like Bezier's or b-splines. Got to equalize the derivatives where they join if you want it to look smooth.

[@ChrisJones-nk8ti]

Thanks for busting my budget again Math Sorcerer!! LOL!!!

[@EmpyreanLightASMR]

I'm always impressed by (12:08 for example) people who just "do the math" in the margins of the pages. My dad's calc book is full of his work, all clean, just like in your example. Meanwhile, here's me using reams of scratch paper I find and just scratch and scribble and cross-out my way through these problems. It makes me wonder if either teaching methods have gotten worse, or if more calc is being crammed into our 15 weeks than in the past, or if I'm just more dumb 😂

[@johngreen3543]

At UNLV in the late 60's the Math professors got together and replaced Thomas (a standard text which was popular with a wide variety of interested majors). They knew this book was written primarily for Math majors as it contains proofs of all major theorems. But the complaints finally arrived at the department from physics and engineering that the book was too theoretical and not suitable for their tastes. I fought it as a grader at the time but it did no good. It was gone after 2 years. I still have my old copy in my library.

[@Adventurin_hobbit]

Sir I believe that old books are much more better than modern books because I think it concerns with theorical mathematics alot whereas the new noes I think they have made easy books like Stewart precalculus,Blitzer, Sullivan... So I suggest you if you share me the same opinion to make a one full video about mathematics from zero to advanced level but with old books recommendations Alot of love from middle east ❤️❤️

[@Adventurin_hobbit]

@@memeentomorr No I am not I am just a student

[@Adventurin_hobbit]

@@memeentomorr I wished If I met your hopes about me ❤️❤️😂

[@chickenstrangler3826]

I agree. When I flip through older books they have a lot more words explaining what's going on, why and the thought process. These school textbooks are just giant work books only good for practicing math skills, not learning the fundamentals of why and where it all comes from.

[@Adventurin_hobbit]

Through out my experience I recommend you Michael spivak calculus I hope I have written it right .

[@stevemenegaz9824]

Apostol's Calculus Vol1 2nd ed. is available free as a pdf as is his mathematical analysis. I would read Salas,Hille, Eitgen first, and then Apostol, then.go onto a good Real Analysis book like Apostol or Tao. For advanced calculus, go look up pdfs for Hans Kagan, and Steen Pedersen. If Apostol and Salas are too hard, there a lot of easier books to build your ability, but you need to read and breathe Salas, IMO.

[@Simon-lb2iu]

I have Mathematical Analysis by Apostol from my Uni days. I'm glad I kept it as it's going for AUD $200 on Amazon at the moment!

[@Anonymous-qw]

I've still got that one from uni in the 1980s. My copy looks a bit tatty I wonder if I could get $200 for it.

[@osvaldocristo]

I have that title. I used it at the graduation on 1980 and 1981 when had Calculus I, II, III and IV. I had a paperback edition but it cost me a lot, even second hand. It was complemented by Advanced Calculus from Wilfred Kaplan, a must to go to Advanced Electromagnetic classes. Thanks to motivate me to go to it and enjoy its odd smells!

[@Andrew-qc8jh]

O man, I have to get this book.

[@rauckr09]

PDF Solution manuals for both volumes are also available.

[@surrealistidealist]

A SPANISH EDITION exists, but it's over $870 on Amazon just for one of the volumes! 😯🤯

[@vrixphillips]

vanillin! it's a substance that is produced when certain wood pulps begin to decay! :) That's why most old books begin to have that vanilla and old wood smell :)

[@TheWayofAPilgrim]

Math Sorcerer it's probably a lot to ask, but could you make a walkthrough series of these two book. I've picked them both up I'm working on Volume two now, but there are some things I just couldn't understand and wasn't able to find an explanation on the internet!

[@WitchidWitchid]

I have both of the Apostal Calculus/Analysis books. I like them because they are mathematically rigorous with plenty of theory and proofs. I used his book extensively when I was reviewing Multivariable Analysis and in particular the proofs of the theorems.of Gauss, Green, and Stokes.

[@metildajoseph5265]

Greetings Mr.Professor, Comprehensive Textbook for Calculus with brief details. Thanks for the Valuable Insights. Take Care, Professor.. With regards, RanjithJoseph (R.J)

[@johnishikawa2200]

This book, and the one by George B. Thomas - these are must haves - I have decided this. At some point, I will dive back into this material with a vengeance. Given the vacation that I have taken from it - years - it will come back to me quickly and easily, for it will all be review.

[@nareksargsyan183]

Your book reviews are amazing.

[@stephenrhodes6660]

Taking the Apostol series is what decided me to major in mathematics.

[@TheMathSorcerer]

very nice:)

[@stephenrhodes6660]

@@TheMathSorcerer I should add that I took in the first editions. It is a bit disorienting to see the second edition of vol one. :-) On the other hand I have to say the look of the later edition is not so great---all the bold face and different typefaces (sic?). It brings to mind those physics and engineering texts that go hog-wild with bold-face vectors and (un-bolded) scalars. Math texts tend to distinguish by using Greek characters for vectors. . . [Am struck by Apostol second edition's mention of Edmund Landau's Foundations of Analysis. My fellow freshman friend liked it too, but then he exempted the (otherwise) required calculus coarse]

[@J_H2961]

I thought i was the only one who smelled books! LOL😂

[@robrobbins]

Somebody should write a math book for generative art. Generative art NFTs are becoming very popular and some interesting designs are based on math formulas.

[@John_Smith__]

Amazing Book no doubt ! Finally you talk about the Tom Apostol Calculus book ... I have one of those (both Volumes) and it is not in English 😀

[@issammaine1349]

Differential And Integral Calculus - N Piskunov

[@callmedeno]

Actually I never thought of having a book of graphs as a reference. I mean I guess if you know all the functions you can just plug it into geograba but you've made me realise it might be something good to have lying around

[@dd-uf9nw]

I read this book from introduction to chapter which talks about sequence and series of functions.if you want to study analysis you should first read and solve exercises from this book instead of directly going for analysis. This book also motivated me to read analysis from Tom apostol's book instead of other books. My aim is to finish the analysis part in a year or two.

[@briang.valentine4311]

The author is of Greek descent, and he pronounces his name "aposTOL" - with the accent on the last syllable

[@xavierwainwright8799]

Maybe you should check out "Calculus Set Free: Infinitesimals to the Rescue" by C. Bryan Dawson. It uses infinitesimals to evaluate limits..., it's got solutions to odd-numbered problems, it's got a lot of notes in the margins, a lot of nice pictures and it has subchapters entirely on how you might want to approach something like doing integrals or showing series convergence/divergence.

[@johnbutler2437]

Enjoyable video. Where can I get a copy of this book, please?

[@zgennaro]

Both volumes available online for free in pdf.

[@HiltonFernandes]

People from USA probably haven't heard about the great book of calculus by the Soviet author named Piskunov.

[@guidichris]

I was able to get the Mathematical Analysis book, used, 2nd printing for about $35 from Amazon, Unfortunately, a reasonable price on this text does not seem to exist.

[@TheMathSorcerer]

Yeah it doesn't exist lol. That's really good for 35 dollars.

[@haroldfoutz5317]

Hey I really liked your video it's very informative. I GOT VOLUME 2 Calculus Tom m apostol.

[@Rael563]

Sorcerer, What edition is your copy published by Blaisdell, Random House? The Vol 1 that you show is titled "Intro, vectors and analytic Geometry." Your links are to "Vol 1, Calculus with Intro to Linear Algebra" which is the same as my paperback Wiley International 2nd Edition.

[@chyngyzismailov5821]

Can you please make a review of Calculus: An Intuitive and Physical Approach by Morris Kline? Thank you.

[@Blazej1983]

...I like very much these videos, I think I also have this book :-) At 10:20 we see the determinant with a first row consisting of vectors... Have you ever stopped for a while and think about this "symbol"? I mean a determinant with one row consisting of vectors and the other rows the elements of the field? Is it really correct in this form? How is determinant defined? Is it possible to have a "mix" of elements (vectors and elements of a field) in one determinant? No doubt, this symbol of determinant is very helpful in several cases...

[@pseudolullus]

Technically he was called Guillaume (marquis) de L'Hôpital but the fact is that many 18th century editions of his books actually spelt his name as "L'Hospital". So many mathematicians used that name. Anyway, the circumflex ^ denotes that an "s" formerly followed that specific vowel, as in être (estre) so it doesn't matter that much.

[@12degreesnowman11]

So L’Hôpital is pronounced ‘Hospital’?

[@pseudolullus]

@@12degreesnowman11 It was pronounced that way long ago

[@lorax121323]

@@pseudolullus Yes, back in the Middle Ages, literally hundreds of years before Guillaume de l'Hôpital was born.

[@pseudolullus]

@@lorax121323 Yes. Did I say otherwise? The main convo is about spelling as far as I can tell.

[@spacetimemalleable7718]

My favorite Calculus books, the two volumes of Apostol. Its comprehensive, motivating, and rigorous. Believe it should be THE Standard calc. books. It's so thorough. You are correct however: the only negative is its outrageous price. Last I looked on Amazon, the USED vol 1, 2 were $125, 121 respectively. Totally immoral!

[@gwenroberts8649]

Visual Calculus by Apostol and Mamikon!

[@thomascousins9150]

I loved this book for Calculus, dealing with the integral calculus before differentiation. Any comments about Richard Dean's book "Elements of Abstract Algebra". I really liked the sections on Galois Theory.

[@MurshidIslam]

Wow! A calculus book that starts with integration! I've never seen that before. Is that a thing that old calculus books did? Or is it a unique feature of Apostol's book?

[@Fekuchand_]

In the field of mathematics there are two school of thoughts 💭 1)some mathematicians think that it's always good to start with integration so you learn the calculus in a better way 2)second school of thoughts argue that no you should learn calculus by first learning limits,continuity, differentiation and then integration. Well in olden days in 1960 and before few schools used to teach integration then differentiation. Now it's pretty much norm in most schools to teach first limits continuity differential calculus then integration 😃

[@shishirkulkarni9685]

Thank you sir for your videos. 🙏 can you suggest books on purely theoratical calculus and analysis which cover latest developments on the subject .

[@ishikagarg1903]

Sir could beginners start with this book ? As I am very much curious to know about calculus apart from my academic books . Would be highly obliged if you reply .

[@juyifan7933]

This book is legendary, but is not for the beginner, it is generaly only used in Honors classes. You already need to be familiar with proof based mathematics, much like Spivaks Calculus book.

[@maxgarcia1153]

I love these longer reviews where we actually get to see the contents a little more in -depth Btw, I have two books I’m not sure you’ve reviewed before. The first one is Applied complex Analysis with Partial Differential Equations by Nakhle H. Asmar And the other is Differential Equations, Dynamical Systems and an Introduction to Chaos by Hirsch et al Are you familiar with any of these? The latter is the hardest book I’ve personally come across so I’d like to know your thoughts on it (or the former) if they ever cross your path :) Thanks!!

[@EmpyreanLightASMR]

19:18 iirc, the cirumflex over the o denotes there used to be an s in the name. Hôpital used to be Hospital

[@EmpyreanLightASMR]

circumflex or circonflex in French I think, it's been a while. my typo though.

[@feraudyh]

I remember being told Apostol was very rich because of the book sales.

[@callmedeno]

Basic Maths, Apostol and (unfortunately for my slowing maturing mathematical mind) shilov, these were the books some legend gave me to go from nothing, couldn't pass a high school test to competent. I've had health issues that have slowed me down significantly but all I know is is why the fuck don't we teach everyone from the bottom up. Why not start at the axioms for everyone. Why not just try and start with groups, if you are going to teach algebra there are a lot of kids who will always be begging the question 'but where does all this come from' in the back of their mind. At the very least, first day of secondary school / junior high school get people onto proving things. 'We've got to just churn out people who can use math because not everyone is capable', yea right. If I can do it at all then any sod can do it and they will have a better understanding, hell they may even enjoy it

[@lorax121323]

Group theory was invented after people had been solving algebra problems for thousands of years. The epsilon-delta definition of a limit and both Riemann and Lebesgue integrals were formally stated almost 2 centuries after Leibniz and Newton's original formulations of calculus. The late 19th century/early 20th century math foundations disputes revealed that it's extremely difficult to tell what counts as an axiom and what counts as a theorem, since what is obvious to some might seem like a deduction to others, and even an arbitrary rule to some others. Once you see the entire forest, you might not have much trouble tracing a path between the trees, but while going through a mess of weeds, shrubs, and trees, stumps, creeks, and rivers, it'll be very easy to get lost and have no idea where you're going and how to survive without getting eaten by snakes or alligators or dying of some strange river parasite infection caused by drinking unfiltered river water. Even though learning everything as derived from sets of axioms might seem more orderly and well-fitting, it might not necessarily feel more intuitive or easier to comprehend. For many people, it might make more sense to approach math in a playful way, seeing different types of results, operations, shapes, and types of structures as coming about from fiddling with numbers, gluing stuff together by adding or multiplying until it brings about something in particular. I believe it would be more stimulating for many learners to see books with questions in the form of "What happens if you do...?" and "What would you get by applying .... onto ....?" rather than "Prove [insert well-known result of a mathematical problem that requires a specific trick]" or "Prove that [insert trivial statement directly derived from the set of definitions provided earlier in the same chapter]".

[@EyeoftheAbyss]

It's incredibly shameful of Wiley publishing for charging so much.

[@Anonymous-qw]

I collected marvel comics as well when I was a kid. But when I went away to university my mother cleaned my bedroom out and through them all away. What is the the difference between Calculus and Analysis? My uni lecturer said Analysis was Posh Calculus?

[@dimitrioskalfakis]

two volumes of magnificence!

[@_______alone_____lover]

very nice video🔥🔥🔥🔥

[@slacker4206]

What’s the easiest calculus book to understand?

[@nomatman8352]

nice video. could you comment on why this book starts with integral calculus? did the author consider this to be a better starting point to learning calculus? maybe the author mentioned something in the preface or introduction ? thanks.

[@anthonypetrozzelli5429]

Thank you for the video. I am 65, and I want to overcome my gear of advanced mathematics. What do you recommend f

[@RanBlakePiano]

This deserves an answer !

[@user-zi2ld3dq4b]

Thank you for your great reviews. Just one question: In which books can I learn methods of evaluating non-elementary integrals? They seem to appear a lot in physics and I cannot find a good source to study them. Thanks.

[@cameronvincent]

If I want to learn the black-scholes model where do I start

[@rahulgupta-jw3jv]

Very good book 👍

[@reda3305]

I love math but i don't know how to be good with it

[@phamgiaminh1025]

Im wondering whether should i use this or spivak, especially for the exercises, which book is more difficult?

[@theprofile4676]

spivak's in my opinion

[@bbtutorial7737]

Sir at what age You fall in Love With Mathematics.

[@talitoplays3120]

Are you gonna do lectures on calc2 and 3 on Udemy ?

[@paulmcmillen5925]

What book would you recommend on Analytic Geometry?