Did you ever wonder what Jim Stewart of Stewart’s Calculus did with his ill-gotten millions? Apparently, he built a really big house one with a concert hall in the middle. In addition to his textbook writing, Stewart is also a classical violinist, and he built the hall so that he and others could use it to perform.
Robert Heinlein’s “–And He Built a Crooked House,” a story (first published in Astounding Science Fiction in February 1941, and reprinted in the collection The Unpleasant Profession of Jonathan Hoag in 1959), about the difficulties of 4-dimensional home design.
http://www.scifi.com/scifiction/classics/classics_archive/heinlein/heinlein1.html
I understand that an entrepreneur a few years ago wa selling 4-D real estate rights at a large profit.
What a horrible book! So bad and antiquated! Don’t understand why the universities have it when there are many other options around.
Well, I bought his textbooks. I feel silly that it all went to a house…with a music hall. A very unoriginal idea.
Any recommendations for better introductory calculus texts, Berkeley TA?
better books?
I’m a high school calculus teacher, and last year I evaluated 5 different HS calculus textbooks as possible replacements for the one we use now. I have to say that I was surprised at how busy they all were, and how non-mathy. By that I mean, there seemed to be little in the way of proofs and lots of CD-based material. I understand that current pedagogy suggests that we give students many ways of interacting with the material - but I’m a pencil and paper kind of guy when it comes to math.
I did look at two of Stewart’s (with and without vectors), at Cohen, and at Forester. I ended up recommending we stay with Thomas and Finney - more of a college engineering-oriented text but I thought that the explanations were just clearer. If I had been forced to choose a different one, I would have gone with Stewart, considering the alternatives.
A friend’s bright daughter liked Stewart when she used it in HS.
I was tempted by Apostol, but that was just outside our budget and perhaps too mathy for my students.
Anton is better than Stewart — it’s more readable. I own an old copy of Thomas (pre-Finney) that I picked up at a bookstore that is perfectly fine. Lots of people like “Calculus Made Easy”, which also has the advantage of being cheap (it’s pretty old).
At Caltech, 1968, we used Apostol. And he still comes into his office a couple of days a week, if I have any questions! He still wins awards for his papers, which he writes more frequently in the years since he finished his teaching. Wonderful teacher, always in good humor, and very encouraging of whippersnappers such as myself in our late 50s.
Tom Himself also taught in us ‘78. If I knew then what I know now I would have been far more appreciative.
Some of his Project Mathematics films get broadcast on the education channel here in Hawaii. I look at them and just wish I could be as lucid in my lessons.
Would Spivak be too complicated for your classes?
After teaching from Anton, Thomas, and books like those in the 1980s, I gained a great appreciation for Landau’s old textbook. For a bit of that book’s flavor, one chapter first defined the derivative, proved that a function differentiable at a point is continuous there, and proved that there exists a function which is everywhere continuous but nowhere differentiable.
Re: Better Calculus choices
Rudin’s, Principles of Mathematical Analysis
Hardy’s, Pure Math
I think we all can agree (a) the mathematical track records of students who learn from these books is far better (b) both of these books have been around many years longer (c) they are still current despite not having been revised in decades!
Many of these suggestions make me wonder if the commenters have ever taught calculus. They’re great if you’re teaching students with some mathematical aptitude, but those are few and far between at the level of a freshman calculus course in any American university.
Somehow I think Baby Rudin wouldn’t be a very good place to start learning calculus for the first time.
“We are convinced that the increasing adoption of calculus as the ultimate course in the high school curriculum has had a significant negative effect on mathematics enrollments in university. The reason is simple. Students learn (and learn how to learn!) by ‘playing’ —reinventing, reconstructing— and calculus is not so easy to play with, nor is it particularly enticing for most students. Certainly students in high school are not ready and able to play with calculus, except possibly in the hands of an exceptional teacher. As Bressoud’s data confirms, the introduction to higher mathematics provided by calculus convinces most of them that it’s an important and sophisticated subject, but not for them.”
[Letters to the Editor, Why the Sky Is Still Falling, Peter Taylor, Walter Whiteley, Ed Barbeau, Notices of the AMS, Volume 56, Number 4, April 2009, p.448]
Why not try Gilbert Strang’s “Calculus?” Pedagogically it’s a masterpiece. I also like Apostol’s two volumes on calculus (not the analysis book, of course) but they’re too hard for the standard “calculus for morons” course.
What does the sound hole of the voilin have anything to do with calculus. I can not find a direct answer anywhere
Stewart also donated money to refurbish the new math building at McMaster. It is a beautiful space with bountiful blackboards.
I also think Gilbert Strang’s “Calculus” is better.
This is my suggestion of calculus books . Easy clear introduction Leithold. Intermediate dificulty Apostol. For the really motivated students Piskunov (english translation from Russian).
I am a mature age student studying mathematics part time through distance education. I have just finished Maths 101, where I used Stewart’s ‘Essential Calculus ‘Early Transcendentals’. Stewart seems to get a lot of bad press, but I found the book really good. And as a distance student, the textbook is very important. It does lack in some areas, such as implicit differentiation, but I have yet to find a textbook that does cover this area very well, and by this, I mean enables the student to develop and understanding of how and why it works. Fortunately, the UK’s Math Centre has an excellent article on implicit differentiation. But I also have other textbooks to help me: Thomas and Finney, which is really good, Kline, Spivak - which I use very slowly as it is more complex - and a slew of others.
I have a Stewart Book, it’s ok to use as a reference, like when you need to check some formulas. Not really a good book for proofs, I guess you can always pick up any Analysis books for proofs, those are more complete and more rigorous anyway. Does any one know a good book for vector calculus or manifolds?
Well,sadly,since I was a complete imbecile in high school and didn’t know grades mattered in life-and my parents being laborers,well,they didn’t know either-I ended up at The City University Of New York instead of a REAL college. So my first exposure to calculus WAS Stewart.
In all fairness,it’s not as bad as some people make it out to be. The real positive about the book is the IMMENSE number of exercises with complete solutions. Unfortuately,that’s a double edged sword and it’s also the main reason it’s completely unpalatable for mathematicans:It reduces calculus to a step-by-step, plug-and-chug bag of techniques without even any mathematical insight or thinking. Anything that requires more thought then a baboon is either completely omitted or shunted to a mythical “advanced calculus” course-which no longer exists,of course. The students don’t have to do any real thinking at all-which is why most students love it,of course. Let’s face it-THAT’S why the bottom feeding universities buy it every year-so the premeds,accounting students,actuaries,pre-law and all the rest of the master cheaters that form the vast majority of bodies filling the enormous lecture halls of the average 200 student calculus course can program the solutions of all thier exams into thier programmable calculators.
“This is AMERICA. Let the Japanese waste thier time thinking and just give me my f***ing A so I can go out and screw people over for 6 figures a year,geek.”
So it goes.
My favorites? Well,when anyone tells you Spivak’s CALCULUS is the best calculus book ever-EVER-it’s really hard to argue. It’s incredibly beautiful and a model of clarity. But much more then that,with every word,picture and exercise,Spivak asks the reader to THINK about the concepts before him or her before setting the task of doing it. Really THINK about it.
Is it too hard for the average student? Well,depends on what you mean by the average student. The average student cheating thier way through every homework and test and sleeping with TAs to get a 4.0 to get into Harvard medicial school,sure. But if you’re talking about the average student-not necessarily a mathematics or natural science student-who reads everything with an effort and wonders and asks real questions even if they don’t understand or particuarly like it because they’re there to LEARN something-it would be a struggle. But with a good teacher by thier side, they could definitely get through it.
And they’d be all the better for it. For the mathematically talented, the book will become a treasured keepsake for a lifetime.The chapter on infinite series alone is worth photocopying and keeping.
I refuse to recommend soft,”applied” books.To me,the pure/applied mathematics distinction is a symptom of the problem above. There is no pure math or applied math-there is only MATHEMATICS. If you don’t realize that,you’re not part of the solution,you’re part of the problem. That being said-the main problem with using Spivak is that he has virtually no applications-just one lame application of vector algebra to celestial mechanics late in the book. The main point of calculus is to calcul-ATE. Theory is important and all well and good, but teaching calculus with pure application is a little like teaching music students the complete mechanics of writing scores and symphonies,but never teaching them how to play!!!!
A book that fascinates me and I’d love to try to use for a basic calculus course one day is Donald Estep’s PRACTICAL ANALYSIS IN ONE VARIABLE. Estep,a numerical analyst, teaches a basic real analysis course combined with a basic calculus course, using numerical methods to motivate the rigorous development of the real numbers and epsilon-delta arguements-with DOZENS of actual real-world examples from chemistry and physics!!! I’d be a little scared to use the book,though-Estep makes a couple of really strange choices. The biggest one is deciding NOT TO DISCUSS INFINITE SERIES-TO ESTEP, INFINITE SERIES IS BEST DONE WITH COMPLEX VARIABLES,SO HE DECIDES TO FORGET IT. HUH?!?
My favorite all around calculus book is a nearly forgotten one by a legendary teacher-CALCULUS,2nd edition by Edwin E.Moise-based on the course in calculus that Moise taught for many years at Harvard and won several awards for. It’s completely rigorous, yet beautifully intuitive with many,many pictures and geometric insight motivated using Euclidean geometry such as lines,planes and conic sections, as well as many,many physical applications. THIS is the book I would use to teach my children calculus.Go to the library and check it out for yourself if you’re disappointed with the ton of fluff the departments are trying to push on you to teach calculus with. You’ll thank me later,I promise.
Well, Hardy is the one I’d recommend, probably since it’s the only book I’ve actually read and had lecturers who learnt from Hardy as well—in fact one of them studied at Cambridge while Hardy was there, and the Hardy-esque leisurely (verbose?) exposition was very obvious.
The best way to learn from his book is to understand that no mention is made of the level of the difficulty of the book except that it is for the top 20% of high-school leavers (in the foreword)—the point being that the level of background knowledge needed is not that great.