At Grammar School, we were given “Calculus Made Easy” by Silvanus P. Thompson. His prologue states: “Considering how many fools can calculate, it is surprising that it should be thought either a difficult or a tedious task for any other fool to learn how to master the same tricks. Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present to my fellow fools the parts that are not hard. Master these thoroughly, and the rest will follow. What one fool can do, another can.” I thought back then, this is a fellow with sense of humour and it’s a great book.
Man. Barely a minute in and I already know this guy just loves books in general. When you notice details like the texture of the cover and the smell of the book, you're a real bookie.
I spent many an hour (and significant amounts of my limited supply of money) at Woodruff & Thrush Thrice-Read Books in San Jose, long since urban renewed out of existence, alas.
I used that book in high school, and placed out of my entire freshman year of calculus with the AP BC calculus exam. Then I went to a college where they used Holt, and had to help out a number of other guys in the dorm with their calculus homework. What a nightmare it was in comparison. Glad to see that these books are still appreciated. I still have mine (46 years later).
Often this unique quality can be more like an open door to a field a person avoided in the past but only because it wasn't presented correctly. While at Ford on contract and after looking into higher math, I began to understand that the terminology is the bigest hurdle. Like "secret" power words understandable only by the inner favorites of the "club". There was an engineer working in a floor below where I was. He was an ex-special forces guy. A genius at developing algorithms but with an additional quality that is shared by snipers and other special forces guys I've met. They have a gift for describing things in concise terms. Because they typically work under tense circumstances ,.not wordy well suited to deriving algorithms...That's what math is.
My second course in calculus used Advanced Calculus [7/4/1965] R. Creighton Buck. 5 weeks into the course, I had fallen behind on homework and struggled with procrastination. I did all 5 weeks (mostly proofs) one Saturday in about 90 minutes. I have found that I need time to process the information with complex topics. I need an incubation period. So my progress goes in spurts, non-linear progress. Knowing this about my learning process has helped me to avoid being discouraged. During incubation, I work on problems that may be too hard to solve at first.
Your description of this book is awesome! Around the 2:10 mark, you mention that you had a very hard time understanding limits, and it brought back some very painful memories for me. I had aced every math class in high school, and decided to be a math major in college, but I failed miserably at Calculus 1. That was Fall Semester, 1967 so this book hadn't come out yet. Too bad, maybe it would have changed my life!! BTW, I switched majors, got BA in Bus Admin, and later went to grad school for Computer Science, so everything worked out in the end....
Holy cow! I used one edition of Leithold’s book about 1973 for my first exposure to calculus. I remember how elegant and beautiful the contents were. Later i bought a layer edition because my original copy had disintegrated due to damage in storage. Thanks for the trip do memory lane!
You taught me something cool I didn't know and I must have a dozen calculus books - this looks to be one to add to the collection - the typography is superb.
I uses Part 1 and 2 in college and for the first time fell in love with math. I too love these books and still treasure them in my personal book collection. Mine are much more worn than the one in video.
My school principal recommended me that book for learning calculus, it’s insanely good, you should definitely get the 7th edition, that’s the coolest one, they got art work as a cover, and the whole book is really clean. Check it out.
I have bought a second-hand copy of the book today on the basis of your review in this video - particularly the examples of epsilon-delta limit exercises you showed - as that is a technique I have always struggled with. Hopefully the worked examples in the book will give me a better understanding how to tackle basic limit questions.
You are 100% correct on the exposition & treatment of its material. It was the 1st Calc Text I ever bought & by then it was famously known as 'TCWAG' > (I got the complete sing/multi-var version). 40+ years later, it's STILL in my arsenal beside my cherished Anton, Swokowski & Larson collection as secondary faves...LOL
Thanks. I've got 3 or 4 math books going back to WWs I & II, which where used by soldiers on a base (one has a name with barracks number in it). They include Robin's New Plane Geometry, & a math refresher. The math refresher alone is amazing. They actually taught in simple ways that made sense back then! Nothing like what I got in the 70s. I got lucky & went to a private (religious) school for 6th & 7th grades. Outside of being preached at every day, it was quite the education. I addition to the basics, they taught me typing, and computer storage tech (microfiche, etc.). Going back to public school in 8th grade was like getting sent to remedial class. I love science & technology, but I'm old school as to learning! It really can't be overstated how important it is to teach the right things in the right ways, so people can actually learn. tavi.
That book is really beautiful. I like it when books go for a color palette that's black, white, and shades of some other color, but usually they go with a blue that's kind of loudly bright. The green shades in this one are really contemplative and pretty.
I used the 6th edition of The Calculus with Analytic Geometry which we fondly called, TCWAG. The book was so easy to understand, I was doing calculus at 12 years old. His analytic geometry discussion is also so much easier to understand than other standard textbooks used at that time. I learned calculus two years before I entered college, so I was so much ahead of my engineering classmates who were using the same book in our University. Overall, I'd say my favorite math book of all time.
My calc textbook was actually pretty good, that being said, I would have loved something like this that was perfect. My teachers in high school were average but calc and trig can absolutely be self-taught. I did near the top of the school for advanced just by ignoring the teacher working through the book each session, just running through every exercise. That was it. Learn the topic. Do 100 questions on each. Math understanding complete.
Very late in life I found the secret to getting all A's in math ... do ALL the problems, and then do them again. If you have any uncertainty - do them a third time.
The reason calc and trig can be self-taught (for you) is because you have a solid foundation on which to build. Also, you've learned to read math textbooks! Congratulations! I tutor lots of students in math, and the vast majority of them do not have that foundation and cannot read a textbook. It might as well be hieroglyphics.
In 1985 I bought this book when I was a brand new freshman in EE. My older brother used Silverman and my sister used Thomas. So we had all three famus collage calculus books at home. In fact, it was the first book I read mostly cover to cover in English which wasn't written in my mother's tongue. I'm glad that my calculus professor had chosen this book. Aha...I remember there was always a question about limits and delta epsilon in the final :)
A fellow book sniffer! You rock, love everything you put out. Bought The Calculus 7 following this review. Has anyone seen the cover artwork on the 7e? Hardcore man.
I'm getting a Degree in Mathematics, currently in my last year, and this is in conjunction with Spivak's Calculus are my go-to books whenever I need to review some Calculus :)
This is The book on this topic. The edition I used in the school has a beautiful art cover showing many numbers in white one after one handmade painting if I'm not wrong. I wondered how in many places mention many other books but never this one. This is the first time I've ever heard mentioning this wonderful book in a math social media. At last someone did it. You definately do know math... XD Good for you, master!
I used the Third edition in both high school and college back in the 90s. I started teaching about ten years ago and it doesn't matter what book I use, I still teach it his way.
My uncle had used this book in college and gave it to me the year before I took calculus in my senior year of high school. I read it and worked a bunch of problems over the summer. It made perfect sense. I breezed through my calculus class and then 3 college level calculus and math theory classes, using this book as reference a few times. Made A in all those classes and came to love calculus!
@@jkshallinheritearth3883 Well... since I'm a straight female, I didn't get any gfs. But I did get a husband -- not because of anything remotely related to calculus! I think it's funny that you assumed I was male. Seems that there are still a lot of stereotypes about gender and higher math.
@@cac8too if women like calculus, then why Newton, Tesla died virg ii nn? 😂 Even today, top mathematicians like Terrance tao isn't popular among females! I mean females don't go crazy over him like they did on convict Jeremy meeks
This book looked familiar right away. I almost certainly used it in college in the 1970s. I think I even noticed the dedication to his son in the book.
this a treat to meet someone who appreciates good math and science books and there are clearly bad and good textbooks and some truly are exceptional and this textbook is. I was lucky enough to open and read a chapter my mathematics professor had in his possession. But I had to promptly give it back within 45 minutes but it gave me a guide to understanding what is a good math and science textbook.
I started studying calculus in 1967, before this book came out. That must be why it was so awful hard. I did pass though and later found partial differential equations a lot easier than "limits".
It was published at the end of “real books” era. From the late sixties, to the early seventies, there was a shift in text book publishing. Text books before that had very similar bindings and were of the same height and depth, with just the width on the shelf varying. The text books from my engineering curriculum, (I graduated in 1980), put on a shelf look totally random. My, Father’s text books put on a shelf, (he graduated in 1949), look like a set of books.
@@jennalee5967 inadvertently. I’m color blind and didn’t pick up on the fact that they had color coded band on the binding hydraulics, hydrology, water works, were blue. Waste water blue with green, structural subjects were red. So, Dad and the rest of the family could get them back in place. But by the time I was old enough to actually read them, I could put them back by topic. A lot of the driving force behind the uniformity was that the Department of Defense, and VA specified them that way. The DoD bought books for the academies, and libraries on bases. The VA furnished books to the Veterans post WWII. Dad said you took your class schedule, and VA ID card to the on campus veteran affairs office, and they cams back with your textbooks, drafting kits, pencils paper, etc. for the semester. When I was a kid, there were seven or eight drafting kits in the folks office, which I was free to use.
@@randallthomas5207 Yeah the post-WWII boom era was an interesting time in American history,even influencing how many textbooks were produced. My late grandmother(b.1919) would always refer to that pre-1945 society as "back back then" with its different chain economy,physical infrastructure,and social construct
I used Leigthold's book in my first year of electronics enginnering. Great book. However, our calculus teachers considered the exercises and problems "easy", so we had to move on to books containing more difficult or demanding exercises to be prepared for the exams. Alas! What great memories.
I tutored Calculus 2 (Integration) for 3 years while in college over a decade ago and to this day I can vividly remember each semester having to tutor the integral of secant cubed multiple times! Every semester it was a challenge to remember the integration by parts trick. It's introduced in a section covering all general forms sec^n*tan^m, with different rules if m & n are odd or even. But the one situation where n is odd and m is even (in this case 0) was always the toughest!!
Speaking of the scent of books: So many going forward will miss out on the smell of all the books in a library or bookstore. A scent that just seemed to make one smarter the moment they smelled it.
I have a book by this author and translated to portughese fron the second edition 1972 - 1976. I totally agree, it's an exellent and complete book .It was my guide during my calculus course in college.
I used Leithold for three calculus courses beginning in 1969 at the University of Missouri but it was the first edition which is significantly different in organization and format--it didn't highlight key equations, for example. I found the material quite difficult but that might partially have been the instruction, typically in massive 100+ person lectures. Or maybe I was stupid. However, I actually did well in the differential equations course I took after calculus, and I apparently learned something as I had a successful career as an engineer, ending up as a technical fellow. I did use calculus at work maybe every other week although typically it was integrating or differentiating polynomials or exponentials so not super complex. For engineers, I thought Leithold emphasized proofs of the underlying assumptions too much and focused too little on practical applications and the types of problems an engineer would need to solve. Calculus was taught by the math department in the College of Arts and Sciences rather than the College of Engineering which was a mistake, I think.
I have a book with the same title, I have always thought calling it "the calculus" is funny. Also very cool that it has epsilon-delta stuff in it, I've never seen that stuff in a book that isn't "analysis level"!
@@MattMcIrvin Hmm perhaps they have phased it out over time? I'm not sure when you took that test, but in 2018 (when I had AP calc) it was not a part of my curriculum. I think there are probably a few good arguments for eliminating that content from the standard calculus sequence, but I am certainly not an education expert.
I love how the comment section is respectful and full of nostalgia for maths videos. This book could have been very useful to me in college. Calculus wasn't as intuitive as I would have hoped.
This book is awesome to learn calculus and analytic geometry, the only observation is , once you learn the topic you should go fast to solve more advanced problems from other books like for example Piskunov, since the exams will come with more difficult problems.
There was a similar book in the UK. It was one of a series in the "Teach Yourself" series and called surprisingly called "Teach Yourself Calculus" by P Abbot first published in 1940, I have the 1967 print. Same idea, lots of worked examples and lots of questions with solutions in the back pages. It is almost a pocket book in size but has 380 pages. So, for UK folks this might be an alternative. Not sure if it's in print today. Doesn't have all that white space that the Leithold book which would be useful for making notes.
Teach Yourself is famous for their foreign language self-study books. I like those a lot (especially the old ones). Didn’t even realize they did other topics!
I like Abott's book. There is a spanish translation. " Aprende tú solo cálculo ". I borrowed it a lot of of times from my local library in Zaragoza, Spain. I dit not know it was so old. The spanish translation is from the 80's. Out of print. "Editorial pirámide" if my memory serves.
We didn't use either of these in either high school or college. But my high school calc teacher used Prof E McSquared's to help us understand epsilon-delta proofs as supplementary to the assigned textbook. I still have my copies.
The Silvanus P. Thompson Calculus book from 1910 is definitely aimed at students and attempts to explain calculus without the academic dryness. Definitely worth a look, it’s free on Gutenberg and is very quirky.
I took calc 1 and 2 in 1981 using the Leithold, and it still sits in my personal library. (My edition is the red one with the lamp, and it has sections on multivariate derivatives and integration.)
I was sorry to have missed Leithold at Phoenix College; he left shortly before I was a student. But we still used his The Calculus. And I didn't understand delta-epsilon proofs from his book, either. But I did get to meet him several times at math teacher conventions. Great guy. And a very interesting one; he was part owner of the Portofino and Kiva "adult" theaters in Scottsdale!
Math expertise aside, it's wonderful to see an appreciation for typography, typefaces, and design. And then there's the sensuality (as in appeal to the senses) of a good book…
I read and re-read every page of that book. My professor had a different book but my dad had taken calc with this book so I actually had that older version at home. And this book was SO MUCH BETTER than the book we had in my class. I solved every exercise on this entire book and I even remember the different sections as I speak (write). When my wife was having a hard time with calc I bought her the newer version at the time and the newer versions keep the soul of the original while adding support for modern tools like calculators. The best book of my entire collection in math. Right next to Baldor's for Algebra.
Our calculus text in the Shiraz university in Iran and its famous engineering school was this book too . I loved it so much. In fact it was unic in every aspect such as the size and shape of the book and its beautiful illustrations and of course the brilliant method of approaching the most difficult theories in the calculus.
It's really the best one,can see the method to solve step by step clearly. If following to practice few by few, the skill to solve calculus will be great 😃😃. Thanks to share.
I simply love calculus textbooks and I also love old textbooks. Most of the time, old books are much better written and much easier to understand. Read any book from the 1920s, 30s, etc., you can see that the language used then was much more clear and easier to understand. And I hear you can get these old books for almost nothing but not true if you're not in the US. I am in Germany and the shipping cost is sometimes over $60 for a single book. Thank you for the review!
I took calculus at NTSU which is now University of North Texas. I got consistent D's and so dropped that as a major. Stranger then is later I got into mechanical design with top of the line mech design software. In the 20 years I spent in that I used trig a lot..and I really liked it..I never had a background in math but did well in the trig which is used heavily in tolerance analysis..
Take a Look at "Calculus Made Easy" by Silvanus P. Thompson. Written in 1910 , it's (or at least, was) avaialble as a Penguin Books paperback - now can be had as a pdf download. I't's only an introduction, but so well done, you can do some of the problems in your head as you're reading the book - at least I was, on the NYC subway, and I'm not a math whiz.
In the early 90s, I could only use my calc book for the problem sets - the chapters were useless. Then I learned that a faculty member was the author of the book, and the department had bought his book to help him out. Luckily, the teacher was good.
Different editions of MIT's George B Thomas, Jr's similarly titled book "Calculus and Analytic Geometry," were my respective text books for AP Calculus in high school and Calculus xxx in engineering school at NCE/NJIT in the mid-70s. Apparently, Thomas had gotten the idea of hundreds of exercise problems, exceeding Leithold in their numbers. (Limit as n -> infinity?) LOL
@Eric Kokin -- I had worked with a fellow who had had Thomas at MIT for an Advanced Calculus course, describing the final exam problem GBT had assigned: given a 4-inch cube of ice resting on a hot-plate at a constant 120 degrees F in a room at constant ambient temperature of 72 degrees F, describe the melting patterns of the ice in all dimensions. LOL
Good evening sir, can you please make a video about a solution to a problem which has to do with excercises at the end of a chapter? Sometimes I have this problem where I read a chapter and once I get to the problems I don’t understand how to do them. I think many other people will benefit from this, thanks 🙂👍.
I would recommend math books by Lipman Bers. I remember that while I was taking Calculus, using the standard textbook written by profs at MIT, I noticed that there were many other textbooks, and I browsed a number of them in an effort to improve my perspective on the course material. While I was studying math at the university level, I found a set of notes for a class on Riemann Surfaces by Lipman Bers, and I have since found a collection of notes for a course he gave on Several Complex Variables. After the internet came along, I found a Calculus text by Bers, and looking at it I would say that it is comprehensive. About 1000 pages, with linear algebra, differential equations, and applications for science students. I have seen many tributes to the work of Bers as a mathematician, and I respect the fact that a renowned mathematician went to the trouble to publish such a comprenensive tome to be used by lower division students at the introductory level. Another related book that I would suggest reading would be Advanced Calculus by Loomis. It is probably true that there are more interesting books on quantum mechanics than on calculus, so I would also suggest that the student try to save a few bucks to buy a few of those as a possible preparation for using his hard won knowledge of calculus in the real world.
Calculus by Michael Spivak (4th ed.) is "good." That's for those with interest in Pure Mathematics. For those crazy about Applied Mathematics, Calculus by J. E. Marsden is "excellent" Noel from Nigeria!
I think i get what you were saying, in another video, about having to 'keep going' even if things don't make sense or you're stuck on a particular problem. it's kind of like, to use an analogy, snowboarding. If you think too much about how snowboarding works, how you are balancing yourself, etc., you will fall. But if you 'go with the flow' , you can move down the hill and reach the bottom (even if you don't understand how it all worked out). This is similar with mathematics, if you spend too much time on a particular problem, or even on say a foundational issue, you will fall into a rabbit hole (that rabbit hole where cantor allegedly spent the last years of his life - ok, a bit too dramatic). And this happens to me a lot. I open a great math advanced maths book (e.g. topology, complex numbers, real analysis, whatever), and i get stuck on something i read in the first chapter, and i can't make serious headway. So I never get to snowboard down the hill, so to speak, mathematically speaking. The ideas of math, the concepts, the big ideas, have their own gravity. That is the trick in math education, or self study in general, to find that gravity. I am also noticing that some authors put all the dont-get-jammed-up-in-this-material in the appendix - that's smart. Note here that I am not saying there is anything wrong with foundational maths, but i believe it is better to gain some momentum before diving into mathematical logics/foundations, zermelo frankel set theory, the difference between proper classes and sets, ur-elements, and all that. I am plenty interested in maths foundations myself, but its a double edged sword. I have mixed feelings about the benefits of it. On the one hand, you can gain more certainty about certain proofs or math concepts, and certainty is usually a good thing in maths. On the other hand you can become more doubtful about maths, e.g. burali forti paradox (russels paradox doesnt bother me that much). But then I start to wonder what is the definition of a paradox - and before i know it i just opened a rabbit hole.
TCWAG!!! I lugged an 8th edition around for almost 3 years in college. It was like a mini-graduation for me that I finished the book. I studied BS Math majoring CS.
@@TheMathSorcerer I wish also to know the criticism of sorcerer. What are the weaknesses? The order of presentation of stuff which is more or less conventional (versus "historic approach" of Apostol)? The absence of graphics or computer algorithms or direct approach with physical applications (versus MIT Gilbert Sprang)? Etc etc The lack of enough demonstrations of theorems (versus Spivak)? Leithold remains wonderful anyway. However, I believe in poetry paideuma concept (as say Ezra Pound book of the archetypal branched head-to-head complementary best poetic verses in history). I believe that Leithold could be part of that calculus paideuma. And the others? Make a classification's criticism and automatically you make guesses. Ricardo Brazil
I spent a couple months looking for the correct book to buy for my own at home when studying Calculus. I always asked my professors, looking for something with more proofs and low-level maths than the usual "apply the formula"; well, by myself I discovered Leithold and bought Calculus with Analytical Geometry 3rd ed., both volumes. It's really a great experience. As you progress, things make sense; but be careful: you'll need to put your mind to work because the author tends to jump steps, logical ones (but that's fine, because you get tougher and start developing skills). Also, the solutions are still there at the end. The ones missing are usually the ones answered by a phrase/text or drawings (except for the first chapter's ones about basic geometry).
OH MY GOSH. Another edition of the book, the Calculus 7 by Leithold is very popular for Math and Engineering majors here in the Philippines especially in the 90's and 00's
My sister had that book, I think 9th Ed. She used it in college and then I used it. I really liked it. It helped me a lot. We had the Spanish translation. When I moved to USA I missed it so much that I had to buy it again.
I always thought it was Thomas' Calculus, 1953. I have a book called "Problems in the Calculus" from 1915. Its a little tiny thing. I used Thomas/Finney 5th ed in high school BC Calc in the early 80's. I use Saxon to teach my high school juniors AB AP Calc. They are a little young to take in Calculus in the manner and sequence of modern calculus books.
I used the 6th edition when I was learning calculus as an undergrad. I later bought the 7th edition ; unfortunately, it went out of print so schools stopped using the book as the main reference.
I used that book in college and I found it to be excellent in many ways. One drawback, which you mentioned, is that the author left out some steps in the process of simplifying the text. As a student using the book for study and learning, the missing steps was a significant roadblock because I didn't realize for awhile that certain steps had been left out of some examples yet other examples were complete. Thus, understanding those examples with missing steps was somewhat challenging. Filling in the missing steps was left to the student - perhaps not a bad idea, but one that was not explained up front.
About that infernal epsilon-delta limit stuff, I'm pretty sure it's not hard so much as poorly explained. In case anyone cares, here's my stab at it. Imagine a function, and there's a point on that function (a, L) where you want to prove that it is continuous: that means that we want to show the limit of f(x) is L as x approaches a. So, imagine a rectangle centered on that point, of a size that the function never touches the top or bottom edges of that rectangle. Can you shrink that rectangle down to nothing and the function still never touches the top or bottom of the rectangle? If so, then the limit exists and it is L. Epsilon-delta is all about establishing that you can indeed construct rectangles that behave as described; the point is sorting out the dimensions of the rectangle, where the height is 2*epsilon and the width is 2*delta. So if you can establish some sort of relationship between epsilon and delta, then you can construct rectangles with those proportions and that means the limit exists. The technique has you start out with the inequality | f(x) - f(a) | < epsilon, and we will ideally want to rework things into a form like | (x - a)*(some expression that doesn't contain x) | < epsilon. So there is a lot of algebra to get to that point, and usually, you have to pull a trick at some point: you can change the contents of the absolute value on the left in some fashion that always makes the expression bigger (or at least no smaller), and then continue your epsilon-delta work against THAT expression. And since that expression is always bigger, squeeze proof logic applies: if you can prove epsilon-delta against that bigger function, it likewise applies to the original smaller function. To pull this off, though, you usually have to constrain yourself to a region of x-values near x=a. Which is fine, because limits are really what happens near a point, not far away from it. One tactic you usually have to apply early on is, you need to combine the "f(x)" and the "f(a)" terms in some fashion that forces an "x - a" to show up. Once you've done that, you can start massaging things so that the "x-a" finally pops out as a factor. that "x-a" will become our delta. Then you have to find some way to dispose of any other x's that are still lingering, and that will usually require some "bigger expression" logic. Example: suppose we want to prove that the limit of e^x is e^a at x=a. So we start with | e^x - e^a | < epsilon. I'd like to arrange an "x - a" in the expression, so I'll make one happen by factoring out an e^a. Then it becomes | e^a*(e^(x-a) - 1) | < epsilon. I'll move that e^a to the other side, so it's | e^(x-a) - 1 | < epsilon / e^a. (Since e^a is always positive, no absolute value issues emerge.) I need to bounce that "1" to the other side. This is tricky because there are actually two conditions, depending on whether x is greater than a. So what we really need to do is expand the absolute value so it becomes: -epsilon / e^a < e^(x-a) - 1 < epsilon / e^a Now we can add 1 to each part: 1 - epsilon / e^a < e^(x-a) < 1 + epsilon / e^a Take the natural log of all three parts -- and we need to make sure that this doesn't break the inequalities (and it doesn't, if we hold that epsilon is less than e^a): ln (1 - epsilon / e^a) < x - a < ln(1 + epsilon / e^a) And now we want to put things back in absolute value form. The problem is, the left and right terms are no longer mirror images, so what we do? Well, |x-a| has got to be smaller than both, so take the one with the smaller magnitude (and absolute value it if necessary). The one with the smaller magnitude is the one on the right, so go with that; and it's already positive so no absolute value is required. | x-a | < ln(1 + epsilon / e^a) Finally, we can say that delta = ln(1 + epsilon / e^a). That gives us proportions for our rectangles, and since we were able to get to this point, it means that the original function must indeed have a limit of e^a at x=a.
I had a hard time with episilon delta proofs. The problem was that the prof would start with the condition needed for episilon, and get to a function for delta. The problem was that he never went back and showed that the delta function worked. What he had done was always use equivalence relations between the statements rather than implication. With equivalent statements, you can just traverse the proof backwards. He never explained that that was what he was doing. His method did not work for a constant function. He just went directly to any delta will work.
The greatest calculus book off all time was G.H. Hardy's Pure Mathematics. That book set the ball rolling on getting calc taught in colleges. Close to it was Thomas's book.
At Grammar School, we were given “Calculus Made Easy” by Silvanus P. Thompson. His prologue states:
“Considering how many fools can calculate, it is surprising that it should be thought either a difficult or a tedious task for any other fool to learn how to master the same tricks. Being myself a remarkably stupid fellow, I have had to unteach myself the difficulties, and now beg to present to my fellow fools the parts that are not hard. Master these thoroughly, and the rest will follow. What one fool can do, another can.” I thought back then, this is a fellow with sense of humour and it’s a great book.
Man. Barely a minute in and I already know this guy just loves books in general. When you notice details like the texture of the cover and the smell of the book, you're a real bookie.
LOL!
Agreed, especially when he acknowledged the smell. I love the smell of a good book and every other detail he mentioned.
I spent many an hour (and significant amounts of my limited supply of money) at Woodruff & Thrush Thrice-Read Books in San Jose, long since urban renewed out of existence, alas.
I used that book in high school, and placed out of my entire freshman year of calculus with the AP BC calculus exam. Then I went to a college where they used Holt, and had to help out a number of other guys in the dorm with their calculus homework. What a nightmare it was in comparison. Glad to see that these books are still appreciated. I still have mine (46 years later).
Often this unique quality can be more like an open door to a field a person avoided in the past but only because it wasn't presented correctly. While at Ford on contract and after looking into higher math, I began to understand that the terminology is the bigest hurdle. Like "secret" power words understandable only by the inner favorites of the "club". There was an engineer working in a floor below where I was. He was an ex-special forces guy. A genius at developing algorithms but with an additional quality that is shared by snipers and other special forces guys I've met. They have a gift for describing things in concise terms. Because they typically work under tense circumstances ,.not wordy well suited to deriving algorithms...That's what math is.
My second course in calculus used Advanced Calculus [7/4/1965] R. Creighton Buck. 5 weeks into the course, I had fallen behind on homework and struggled with procrastination. I did all 5 weeks (mostly proofs) one Saturday in about 90 minutes. I have found that I need time to process the information with complex topics. I need an incubation period. So my progress goes in spurts, non-linear progress. Knowing this about my learning process has helped me to avoid being discouraged. During incubation, I work on problems that may be too hard to solve at first.
That’s a great book!!!
Your description of this book is awesome! Around the 2:10 mark, you mention that you had a very hard time understanding limits, and it brought back some very painful memories for me. I had aced every math class in high school, and decided to be a math major in college, but I failed miserably at Calculus 1. That was Fall Semester, 1967 so this book hadn't come out yet. Too bad, maybe it would have changed my life!! BTW, I switched majors, got BA in Bus Admin, and later went to grad school for Computer Science, so everything worked out in the end....
Holy cow! I used one edition of Leithold’s book about 1973 for my first exposure to calculus. I remember how elegant and beautiful the contents were. Later i bought a layer edition because my original copy had disintegrated due to damage in storage.
Thanks for the trip do memory lane!
Oh wow that is awesome !!!
Thomas and Finney is the first book I ever went through on my own. It's definitely one of my top ten favorite math experiences of all time.
You taught me something cool I didn't know and I must have a dozen calculus books - this looks to be one to add to the collection - the typography is superb.
I uses Part 1 and 2 in college and for the first time fell in love with math. I too love these books and still treasure them in my personal book collection. Mine are much more worn than the one in video.
My school principal recommended me that book for learning calculus, it’s insanely good, you should definitely get the 7th edition, that’s the coolest one, they got art work as a cover, and the whole book is really clean. Check it out.
Nice!!!
The way that this book really clean,it is very good for eyes too much. The great book always the nice way for studying.
Have u pdf of these editions??
@@usmansaifi363 No, sadly, but you can look for a used book online really cheap online.
@@doomsdaymachiene91 What is the website address for buying used books?
I have bought a second-hand copy of the book today on the basis of your review in this video - particularly the examples of epsilon-delta limit exercises you showed - as that is a technique I have always struggled with. Hopefully the worked examples in the book will give me a better understanding how to tackle basic limit questions.
You are 100% correct on the exposition & treatment of its material. It was the 1st Calc Text I ever bought & by then it was famously known as 'TCWAG' > (I got the complete sing/multi-var version).
40+ years later, it's STILL in my arsenal beside my cherished Anton, Swokowski & Larson collection as secondary faves...LOL
Thanks. I've got 3 or 4 math books going back to WWs I & II, which where used by soldiers on a base (one has a name with barracks number in it). They include Robin's New Plane Geometry, & a math refresher. The math refresher alone is amazing. They actually taught in simple ways that made sense back then! Nothing like what I got in the 70s. I got lucky & went to a private (religious) school for 6th & 7th grades. Outside of being preached at every day, it was quite the education. I addition to the basics, they taught me typing, and computer storage tech (microfiche, etc.). Going back to public school in 8th grade was like getting sent to remedial class. I love science & technology, but I'm old school as to learning! It really can't be overstated how important it is to teach the right things in the right ways, so people can actually learn. tavi.
That book is really beautiful. I like it when books go for a color palette that's black, white, and shades of some other color, but usually they go with a blue that's kind of loudly bright. The green shades in this one are really contemplative and pretty.
I used the 6th edition of The Calculus with Analytic Geometry which we fondly called, TCWAG. The book was so easy to understand, I was doing calculus at 12 years old. His analytic geometry discussion is also so much easier to understand than other standard textbooks used at that time. I learned calculus two years before I entered college, so I was so much ahead of my engineering classmates who were using the same book in our University. Overall, I'd say my favorite math book of all time.
Awesome !
My calc textbook was actually pretty good, that being said, I would have loved something like this that was perfect. My teachers in high school were average but calc and trig can absolutely be self-taught.
I did near the top of the school for advanced just by ignoring the teacher working through the book each session, just running through every exercise. That was it. Learn the topic. Do 100 questions on each. Math understanding complete.
Very late in life I found the secret to getting all A's in math ... do ALL the problems, and then do them again. If you have any uncertainty - do them a third time.
The reason calc and trig can be self-taught (for you) is because you have a solid foundation on which to build. Also, you've learned to read math textbooks! Congratulations! I tutor lots of students in math, and the vast majority of them do not have that foundation and cannot read a textbook. It might as well be hieroglyphics.
In 1985 I bought this book when I was a brand new freshman in EE. My older brother used Silverman and my sister used Thomas. So we had all three famus collage calculus books at home. In fact, it was the first book I read mostly cover to cover in English which wasn't written in my mother's tongue. I'm glad that my calculus professor had chosen this book. Aha...I remember there was always a question about limits and delta epsilon in the final :)
i think u have enjoyed learning very much
@@theabuzerbharuchi yes. You should never stop learning, specially Math.
@@bayareapianist I'll definitely implement this in my life cause I also love mathematics
I love this book, used it during my first semester at engineering along with Earl Swokowski's Calculus. Great review, thanks.
👍👍
A fellow book sniffer! You rock, love everything you put out. Bought The Calculus 7 following this review. Has anyone seen the cover artwork on the 7e? Hardcore man.
I haven't seen the cover yet, but a few people have mentioned that it's awesome!
The Calculus 7 following this review? What does it cover up?
Does the 7th edition (TC7?) cover analytic geometry?
That tony watches... That guy smells me book
Hahahaha
Butafal book very good and plase we ned mor reivew in old mathematic book great thank you from egypt
I'm getting a Degree in Mathematics, currently in my last year, and this is in conjunction with Spivak's Calculus are my go-to books whenever I need to review some Calculus :)
Interesting. What is the name of your college?
@@KRYPTOS_K5 I study in the Simón Bolívar University in Caracas, Venezuela
I've always been a Sherman K. Stein fan myself, but I'm glad you got along with this one.
I used Stein in college.
This is The book on this topic. The edition I used in the school has a beautiful art cover showing many numbers in white one after one handmade painting if I'm not wrong. I wondered how in many places mention many other books but never this one. This is the first time I've ever heard mentioning this wonderful book in a math social media. At last someone did it. You definately do know math... XD Good for you, master!
❤️❤️
I used the Third edition in both high school and college back in the 90s. I started teaching about ten years ago and it doesn't matter what book I use, I still teach it his way.
That’s awesome !!
Have this book, had it since 1972, it is great, fun reading. Loved calculus, used to dream calculus. Easily my favourite text book.
Wow that’s awesome 😎
My uncle had used this book in college and gave it to me the year before I took calculus in my senior year of high school. I read it and worked a bunch of problems over the summer. It made perfect sense. I breezed through my calculus class and then 3 college level calculus and math theory classes, using this book as reference a few times. Made A in all those classes and came to love calculus!
So how many gfs you made with the help of this book? 😂
@@jkshallinheritearth3883 Well... since I'm a straight female, I didn't get any gfs. But I did get a husband -- not because of anything remotely related to calculus! I think it's funny that you assumed I was male. Seems that there are still a lot of stereotypes about gender and higher math.
@@cac8too if women like calculus, then why Newton, Tesla died virg ii nn? 😂
Even today, top mathematicians like Terrance tao isn't popular among females! I mean females don't go crazy over him like they did on convict Jeremy meeks
@@cac8too Right on! 👏👍
This book looked familiar right away. I almost certainly used it in college in the 1970s. I think I even noticed the dedication to his son in the book.
this a treat to meet someone who appreciates good math and science books and there are clearly bad and good textbooks and some truly are exceptional and this textbook is. I was lucky enough to open and read a chapter my mathematics professor had in his possession. But I had to promptly give it back within 45 minutes but it gave me a guide to understanding what is a good math and science textbook.
I started studying calculus in 1967, before this book came out. That must be why it was so awful hard. I did pass though and later found partial differential equations a lot easier than "limits".
It was published at the end of “real books” era. From the late sixties, to the early seventies, there was a shift in text book publishing. Text books before that had very similar bindings and were of the same height and depth, with just the width on the shelf varying. The text books from my engineering curriculum, (I graduated in 1980), put on a shelf look totally random. My, Father’s text books put on a shelf, (he graduated in 1949), look like a set of books.
Fascinating,did you ever shuffle your dad's books?
@@jennalee5967 inadvertently. I’m color blind and didn’t pick up on the fact that they had color coded band on the binding hydraulics, hydrology, water works, were blue. Waste water blue with green, structural subjects were red. So, Dad and the rest of the family could get them back in place. But by the time I was old enough to actually read them, I could put them back by topic. A lot of the driving force behind the uniformity was that the Department of Defense, and VA specified them that way. The DoD bought books for the academies, and libraries on bases. The VA furnished books to the Veterans post WWII. Dad said you took your class schedule, and VA ID card to the on campus veteran affairs office, and they cams back with your textbooks, drafting kits, pencils paper, etc. for the semester. When I was a kid, there were seven or eight drafting kits in the folks office, which I was free to use.
@@randallthomas5207 Yeah the post-WWII boom era was an interesting time in American history,even influencing how many textbooks were produced. My late grandmother(b.1919) would always refer to that pre-1945 society as "back back then" with its different chain economy,physical infrastructure,and social construct
I used Leigthold's book in my first year of electronics enginnering. Great book. However, our calculus teachers considered the exercises and problems "easy", so we had to move on to books containing more difficult or demanding exercises to be prepared for the exams. Alas! What great memories.
I tutored Calculus 2 (Integration) for 3 years while in college over a decade ago and to this day I can vividly remember each semester having to tutor the integral of secant cubed multiple times! Every semester it was a challenge to remember the integration by parts trick. It's introduced in a section covering all general forms sec^n*tan^m, with different rules if m & n are odd or even. But the one situation where n is odd and m is even (in this case 0) was always the toughest!!
I recommend you to study Islam with open mind..and without prejudice
❤️
@@منوبيالفلسطي Non sequitur.
so it's sin^(m-n)/cos^m?
I was never taught secants, so I don't remember what it is...
Thank you!
love these textbook videos! super useful for my continued selfstudy/review
👍
Thoroughly enjoy these book reviews! The smell test makes me want them more
why can't they make a cologne to make me smell like old textbooks? Life isn't fair!!!
Speaking of the scent of books: So many going forward will miss out on the smell of all the books in a library or bookstore. A scent that just seemed to make one smarter the moment they smelled it.
Thank You Math Sorcerer, You inspire me a Lot
I have a book by this author and translated to portughese fron the second edition 1972 - 1976.
I totally agree, it's an exellent and complete book .It was my guide during my
calculus course in college.
Ha! We had the full 3-part book for my college calculus courses. And my professor said, "if you take a light hold on Leithold, you'll drop it."
I used Leithold for three calculus courses beginning in 1969 at the University of Missouri but it was the first edition which is significantly different in organization and format--it didn't highlight key equations, for example. I found the material quite difficult but that might partially have been the instruction, typically in massive 100+ person lectures. Or maybe I was stupid. However, I actually did well in the differential equations course I took after calculus, and I apparently learned something as I had a successful career as an engineer, ending up as a technical fellow. I did use calculus at work maybe every other week although typically it was integrating or differentiating polynomials or exponentials so not super complex. For engineers, I thought Leithold emphasized proofs of the underlying assumptions too much and focused too little on practical applications and the types of problems an engineer would need to solve. Calculus was taught by the math department in the College of Arts and Sciences rather than the College of Engineering which was a mistake, I think.
Wow interesting thank you!!
I have a book with the same title, I have always thought calling it "the calculus" is funny. Also very cool that it has epsilon-delta stuff in it, I've never seen that stuff in a book that isn't "analysis level"!
I'm pretty sure my AP Calculus text in high school had that stuff--we went through it at the beginning of the "B" semester.
@@MattMcIrvin Hmm perhaps they have phased it out over time? I'm not sure when you took that test, but in 2018 (when I had AP calc) it was not a part of my curriculum. I think there are probably a few good arguments for eliminating that content from the standard calculus sequence, but I am certainly not an education expert.
I love how the comment section is respectful and full of nostalgia for maths videos. This book could have been very useful to me in college. Calculus wasn't as intuitive as I would have hoped.
The typesetting for this book is an art all its own.
I know it's ridiculously cool lol!!
This book is awesome to learn calculus and analytic geometry, the only observation is , once you learn the topic you should go fast to solve more advanced problems from other books like for example Piskunov, since the exams will come with more difficult problems.
Piskunov is a funny book not for everyone
Piskunov is a marvelous book!
There was a similar book in the UK. It was one of a series in the "Teach Yourself" series and called surprisingly called "Teach Yourself Calculus" by P Abbot first published in 1940, I have the 1967 print. Same idea, lots of worked examples and lots of questions with solutions in the back pages. It is almost a pocket book in size but has 380 pages. So, for UK folks this might be an alternative. Not sure if it's in print today. Doesn't have all that white space that the Leithold book which would be useful for making notes.
Teach Yourself is famous for their foreign language self-study books. I like those a lot (especially the old ones). Didn’t even realize they did other topics!
I like Abott's book. There is a spanish translation. " Aprende tú solo cálculo ".
I borrowed it a lot of of times from my local library in Zaragoza, Spain. I dit not know it was so old. The spanish translation is from the 80's. Out of print. "Editorial pirámide" if my memory serves.
We didn't use either of these in either high school or college. But my high school calc teacher used Prof E McSquared's to help us understand epsilon-delta proofs as supplementary to the assigned textbook. I still have my copies.
The Silvanus P. Thompson Calculus book from 1910 is definitely aimed at students and attempts to explain calculus without the academic dryness. Definitely worth a look, it’s free on Gutenberg and is very quirky.
I took calc 1 and 2 in 1981 using the Leithold, and it still sits in my personal library. (My edition is the red one with the lamp, and it has sections on multivariate derivatives and integration.)
A good math teacher is a divine gift.
I used Leithold for Calculus. Its the best book for Calculus ever written.
My favorite calculus book! Greatings from brazil!
Great vid! I learned Calculus in HS using Howard Anton book. Still got it.
Nice!
I was sorry to have missed Leithold at Phoenix College; he left shortly before I was a student. But we still used his The Calculus. And I didn't understand delta-epsilon proofs from his book, either. But I did get to meet him several times at math teacher conventions. Great guy. And a very interesting one; he was part owner of the Portofino and Kiva "adult" theaters in Scottsdale!
Wow !
We had epsilon-delta proofs in Denmark - and nobody really considered them hard. Why do Americans routinely find them hard?
Math expertise aside, it's wonderful to see an appreciation for typography, typefaces, and design. And then there's the sensuality (as in appeal to the senses) of a good book…
I read and re-read every page of that book. My professor had a different book but my dad had taken calc with this book so I actually had that older version at home. And this book was SO MUCH BETTER than the book we had in my class. I solved every exercise on this entire book and I even remember the different sections as I speak (write).
When my wife was having a hard time with calc I bought her the newer version at the time and the newer versions keep the soul of the original while adding support for modern tools like calculators.
The best book of my entire collection in math. Right next to Baldor's for Algebra.
just searched up the previous owner and the dude really is successful
Thanks for the information on the Calculus book....i love calculus indeed
Yaaay, that's the book I used to learn Calculus for the first time! I still have it!!
Gonna need a crash course in calculus and trig. Looks like a good reference. Just ordered a 3rd edition from Amazon. Good luck.
Awesome !
Absolutely the best math books reviewer ... thank you sir .
Our calculus text in the Shiraz university in Iran and its famous engineering school was this book too . I loved it so much. In fact it was unic in every aspect such as the size and shape of the book and its beautiful illustrations and of course the brilliant method of approaching the most difficult theories in the calculus.
It's really the best one,can see the method to solve step by step clearly. If following to practice few by few, the skill to solve calculus will be great 😃😃. Thanks to share.
I simply love calculus textbooks and I also love old textbooks. Most of the time, old books are much better written and much easier to understand. Read any book from the 1920s, 30s, etc., you can see that the language used then was much more clear and easier to understand. And I hear you can get these old books for almost nothing but not true if you're not in the US. I am in Germany and the shipping cost is sometimes over $60 for a single book. Thank you for the review!
I’ve always heard it pronounced “light hold”. It’s a German name and “ei” is pronounced like a long i as in “light” or “right”.
Thank you!!!
Same book I learned Calculus from in 1976-77 at Tennessee Tech, but we used the third edition. I still have it.
I took calculus at NTSU which is now University of North Texas. I got consistent D's and so dropped that as a major. Stranger then is later I got into mechanical design with top of the line mech design software. In the 20 years I spent in that I used trig a lot..and I really liked it..I never had a background in math but did well in the trig which is used heavily in tolerance analysis..
Very nice review :)
I’m gonna buy it! Thanks 🙏
I used the 6th edition of this book in high school. The memories of dragging that thing around came flooding back 😂
Take a Look at "Calculus Made Easy" by Silvanus P. Thompson. Written in 1910 , it's (or at least, was) avaialble as a Penguin Books paperback - now can be had as a pdf download. I't's only an introduction, but so well done, you can do some of the problems in your head as you're reading the book - at least I was, on the NYC subway, and I'm not a math whiz.
Beautiful collector’s reference book.
In the early 90s, I could only use my calc book for the problem sets - the chapters were useless. Then I learned that a faculty member was the author of the book, and the department had bought his book to help him out. Luckily, the teacher was good.
Thank you so much, teacher for all works
I love your passion for this fascinating subject.
Love these kind of videos
Thanks
Different editions of MIT's George B Thomas, Jr's similarly titled book "Calculus and Analytic Geometry," were my respective text books for AP Calculus in high school and Calculus xxx in engineering school at NCE/NJIT in the mid-70s. Apparently, Thomas had gotten the idea of hundreds of exercise problems, exceeding Leithold in their numbers. (Limit as n -> infinity?) LOL
@Eric Kokin -- I had worked with a fellow who had had Thomas at MIT for an Advanced Calculus course, describing the final exam problem GBT had assigned: given a 4-inch cube of ice resting on a hot-plate at a constant 120 degrees F in a room at constant ambient temperature of 72 degrees F, describe the melting patterns of the ice in all dimensions. LOL
Good evening sir, can you please make a video about a solution to a problem which has to do with excercises at the end of a chapter?
Sometimes I have this problem where I read a chapter and once I get to the problems I don’t understand how to do them. I think many other people will benefit from this, thanks 🙂👍.
That’s a good idea, thank you!!!!!
@@TheMathSorcerer Thanks for listening to my suggestion :)
Great review!!
The right tools for the job. Teaching and Learning.
I would recommend math books by Lipman Bers. I remember that while I was taking Calculus, using the standard textbook written by profs at MIT, I noticed that there were many other textbooks, and I browsed a number of them in an effort to improve my perspective on the course material. While I was studying math at the university level, I found a set of notes for a class on Riemann Surfaces by Lipman Bers, and I have since found a collection of notes for a course he gave on Several Complex Variables. After the internet came along, I found a Calculus text by Bers, and looking at it I would say that it is comprehensive. About 1000 pages, with linear algebra, differential equations, and applications for science students. I have seen many tributes to the work of Bers as a mathematician, and I respect the fact that a renowned mathematician went to the trouble to publish such a comprenensive tome to be used by lower division students at the introductory level. Another related book that I would suggest reading would be Advanced Calculus by Loomis. It is probably true that there are more interesting books on quantum mechanics than on calculus, so I would also suggest that the student try to save a few bucks to buy a few of those as a possible preparation for using his hard won knowledge of calculus in the real world.
Calculus by Michael Spivak (4th ed.) is "good." That's for those with interest in Pure Mathematics. For those crazy about Applied Mathematics, Calculus by J. E. Marsden is "excellent"
Noel from Nigeria!
I think i get what you were saying, in another video, about having to 'keep going' even if things don't make sense or you're stuck on a particular problem.
it's kind of like, to use an analogy, snowboarding. If you think too much about how snowboarding works, how you are balancing yourself, etc., you will fall. But if you 'go with the flow' , you can move down the hill and reach the bottom (even if you don't understand how it all worked out).
This is similar with mathematics, if you spend too much time on a particular problem, or even on say a foundational issue, you will fall into a rabbit hole (that rabbit hole where cantor allegedly spent the last years of his life - ok, a bit too dramatic).
And this happens to me a lot. I open a great math advanced maths book (e.g. topology, complex numbers, real analysis, whatever), and i get stuck on something i read in the first chapter, and i can't make serious headway. So I never get to snowboard down the hill, so to speak, mathematically speaking. The ideas of math, the concepts, the big ideas, have their own gravity. That is the trick in math education, or self study in general, to find that gravity.
I am also noticing that some authors put all the dont-get-jammed-up-in-this-material in the appendix - that's smart.
Note here that I am not saying there is anything wrong with foundational maths, but i believe it is better to gain some momentum before diving into mathematical logics/foundations, zermelo frankel set theory, the difference between proper classes and sets, ur-elements, and all that. I am plenty interested in maths foundations myself, but its a double edged sword. I have mixed feelings about the benefits of it. On the one hand, you can gain more certainty about certain proofs or math concepts, and certainty is usually a good thing in maths. On the other hand you can become more doubtful about maths, e.g. burali forti paradox (russels paradox doesnt bother me that much). But then I start to wonder what is the definition of a paradox - and before i know it i just opened a rabbit hole.
I love love love this book. So clear.
TCWAG!!! I lugged an 8th edition around for almost 3 years in college. It was like a mini-graduation for me that I finished the book. I studied BS Math majoring CS.
Hi from Brazil, after this, I realised I'm also a "leitholdist" in my solving strategics
Calculus changed my life.
I used that book when I took calculus in 1968. I kept it for years and may still have it.
Wow that’s awesome
One of those books that I will Never throw out or sell.
Thank you so much for this review of this book. You do a GREAT! job.
It's a great book! I used it in my engineering lessons. Great information professor! Thank you!
Nice!!
@@TheMathSorcerer I wish also to know the criticism of sorcerer. What are the weaknesses? The order of presentation of stuff which is more or less conventional (versus "historic approach" of Apostol)? The absence of graphics or computer algorithms or direct approach with physical applications (versus MIT Gilbert Sprang)? Etc etc The lack of enough demonstrations of theorems (versus Spivak)? Leithold remains wonderful anyway. However, I believe in poetry paideuma concept (as say Ezra Pound book of the archetypal branched head-to-head complementary best poetic verses in history). I believe that Leithold could be part of that calculus paideuma. And the others? Make a classification's criticism and automatically you make guesses.
Ricardo
Brazil
I spent a couple months looking for the correct book to buy for my own at home when studying Calculus. I always asked my professors, looking for something with more proofs and low-level maths than the usual "apply the formula"; well, by myself I discovered Leithold and bought Calculus with Analytical Geometry 3rd ed., both volumes. It's really a great experience. As you progress, things make sense; but be careful: you'll need to put your mind to work because the author tends to jump steps, logical ones (but that's fine, because you get tougher and start developing skills).
Also, the solutions are still there at the end. The ones missing are usually the ones answered by a phrase/text or drawings (except for the first chapter's ones about basic geometry).
OH MY GOSH. Another edition of the book, the Calculus 7 by Leithold is very popular for Math and Engineering majors here in the Philippines especially in the 90's and 00's
Nice!
This is really wonderful ❤
I delivered to a guy that told me about this book. He used this at college in the 70’s
My sister had that book, I think 9th Ed. She used it in college and then I used it. I really liked it. It helped me a lot. We had the Spanish translation. When I moved to USA I missed it so much that I had to buy it again.
I always thought it was Thomas' Calculus, 1953. I have a book called "Problems in the Calculus" from 1915. Its a little tiny thing. I used Thomas/Finney 5th ed in high school BC Calc in the early 80's. I use Saxon to teach my high school juniors AB AP Calc. They are a little young to take in Calculus in the manner and sequence of modern calculus books.
I used the 6th edition when I was learning calculus as an undergrad. I later bought the 7th edition ; unfortunately, it went out of print so schools stopped using the book as the main reference.
Thanks for this covering and appreciate you. Is this book still exists in the market
I used that book in college and I found it to be excellent in many ways. One drawback, which you mentioned, is that the author left out some steps in the process of simplifying the text. As a student using the book for study and learning, the missing steps was a significant roadblock because I didn't realize for awhile that certain steps had been left out of some examples yet other examples were complete. Thus, understanding those examples with missing steps was somewhat challenging. Filling in the missing steps was left to the student - perhaps not a bad idea, but one that was not explained up front.
About that infernal epsilon-delta limit stuff, I'm pretty sure it's not hard so much as poorly explained. In case anyone cares, here's my stab at it.
Imagine a function, and there's a point on that function (a, L) where you want to prove that it is continuous: that means that we want to show the limit of f(x) is L as x approaches a. So, imagine a rectangle centered on that point, of a size that the function never touches the top or bottom edges of that rectangle. Can you shrink that rectangle down to nothing and the function still never touches the top or bottom of the rectangle? If so, then the limit exists and it is L.
Epsilon-delta is all about establishing that you can indeed construct rectangles that behave as described; the point is sorting out the dimensions of the rectangle, where the height is 2*epsilon and the width is 2*delta. So if you can establish some sort of relationship between epsilon and delta, then you can construct rectangles with those proportions and that means the limit exists.
The technique has you start out with the inequality | f(x) - f(a) | < epsilon, and we will ideally want to rework things into a form like | (x - a)*(some expression that doesn't contain x) | < epsilon. So there is a lot of algebra to get to that point, and usually, you have to pull a trick at some point: you can change the contents of the absolute value on the left in some fashion that always makes the expression bigger (or at least no smaller), and then continue your epsilon-delta work against THAT expression. And since that expression is always bigger, squeeze proof logic applies: if you can prove epsilon-delta against that bigger function, it likewise applies to the original smaller function. To pull this off, though, you usually have to constrain yourself to a region of x-values near x=a. Which is fine, because limits are really what happens near a point, not far away from it.
One tactic you usually have to apply early on is, you need to combine the "f(x)" and the "f(a)" terms in some fashion that forces an "x - a" to show up. Once you've done that, you can start massaging things so that the "x-a" finally pops out as a factor. that "x-a" will become our delta. Then you have to find some way to dispose of any other x's that are still lingering, and that will usually require some "bigger expression" logic.
Example: suppose we want to prove that the limit of e^x is e^a at x=a. So we start with | e^x - e^a | < epsilon.
I'd like to arrange an "x - a" in the expression, so I'll make one happen by factoring out an e^a. Then it becomes | e^a*(e^(x-a) - 1) | < epsilon.
I'll move that e^a to the other side, so it's | e^(x-a) - 1 | < epsilon / e^a. (Since e^a is always positive, no absolute value issues emerge.)
I need to bounce that "1" to the other side. This is tricky because there are actually two conditions, depending on whether x is greater than a. So what we really need to do is expand the absolute value so it becomes:
-epsilon / e^a < e^(x-a) - 1 < epsilon / e^a
Now we can add 1 to each part:
1 - epsilon / e^a < e^(x-a) < 1 + epsilon / e^a
Take the natural log of all three parts -- and we need to make sure that this doesn't break the inequalities (and it doesn't, if we hold that epsilon is less than e^a):
ln (1 - epsilon / e^a) < x - a < ln(1 + epsilon / e^a)
And now we want to put things back in absolute value form. The problem is, the left and right terms are no longer mirror images, so what we do? Well, |x-a| has got to be smaller than both, so take the one with the smaller magnitude (and absolute value it if necessary). The one with the smaller magnitude is the one on the right, so go with that; and it's already positive so no absolute value is required.
| x-a | < ln(1 + epsilon / e^a)
Finally, we can say that delta = ln(1 + epsilon / e^a). That gives us proportions for our rectangles, and since we were able to get to this point, it means that the original function must indeed have a limit of e^a at x=a.
Appreciated 🤝
I had a hard time with episilon delta proofs. The problem was that the prof would start with the condition needed for episilon, and get to a function for delta. The problem was that he never went back and showed that the delta function worked. What he had done was always use equivalence relations between the statements rather than implication.
With equivalent statements, you can just traverse the proof backwards. He never explained that that was what he was doing.
His method did not work for a constant function. He just went directly to any delta will work.
this is still my favourite calculus textbook
The greatest calculus book off all time was G.H. Hardy's Pure Mathematics. That book set the ball rolling on getting calc taught in colleges. Close to it was Thomas's book.
Oh yes, GREAT books!!!