Calculus I've just finished Stewart's calculus, now what?

[IntegralBeing]

I hated that book so much; I had the opportunity to change to Spivak or Apostol in holidays but I didn't do it. I feel like I will have to read a good rigorous calculus text from the beggining since Stewart's textbook is sheer rubbish in many senses. Which book should I read to continue my mathematical education? Was it a huge mistake to do Stewart's instead of a more difficult book if I want to major in mathematical physics?

 

[micromass]

No, it's not a huge mistake at all. Sure, you could have made a better choice than Stewart. But right now you do have the concepts of calculus down, even though you don't know them rigorously. This is a huge thing, don't underestimate that. Furthermore, you also are able to compute calculus concepts very well, which is also very important. And third, now you have the desire to do things rigorously. If you read a rigorous book right away then perhaps it was not very motivating to you. So don't worry, you're still right on track to become good at mathematical physics!

Now, there is a book exactly for people like you. People who already know computational and conceptual calculus, but nothing rigorous. It is meant for a second course in calculus (as the name says). I think it's perfect for you. It's Nitecki's calculus deconstructed. This book is entirely rigorous and builds up from your current knowledge to a very rigorous knowledge of calculus. Doing analysis after this should be a breeze for you.
https://www.amazon.com/dp/0883857561/?tag=pfamazon01-20

 

[Logical Dog]

Yes stewarts calculus is weak compared to other books on the matter but now you know computational calculus, any knowledge is better than no knowledge so pat yourself on the back. It is good enough for those who want to apply calculus. you know more now.

https://global.oup.com/academic/pro...athematics-major-9780199661312?cc=de&lang=en&

how to think about analysis
https://www.amazon.com/Think-About-...8&sr=8-1&keywords=how+to+think+about+analysis

 

[IntegralBeing]

Now, there is a book exactly for people like you. People who already know computational and conceptual calculus, but nothing rigorous. It is meant for a second course in calculus (as the name says). I think it's perfect for you. It's Nitecki's calculus deconstructed. This book is entirely rigorous and builds up from your current knowledge to a very rigorous knowledge of calculus. Doing analysis after this should be a breeze for you.
https://www.amazon.com/dp/0883857561/?tag=pfamazon01-20

Thank you! I looked inside a bit on amazon and I didn't really like the 'super friendly' language. 'f(x) blows up at x= 2' made me cringe a little to be honest. I've been searching through my university library and I really liked Apostol's Mathematical Analysis and Taylor's Advanced Calculus. What do you think of those? Too difficult for a Stewart-level undergraduate?

 

[IntegralBeing]

Yes stewarts calculus is weak compared to other books on the matter but now you know computational calculus, any knowledge is better than no knowledge so pat yourself on the back. It is good enough for those who want to apply calculus. you know more now.

https://global.oup.com/academic/pro...athematics-major-9780199661312?cc=de&lang=en&

how to think about analysis
https://www.amazon.com/Think-About-...8&sr=8-1&keywords=how+to+think+about+analysis

Thanks for the advice! But I must say this particular review https://www.amazon.com/dp/0198723539/?tag=pfamazon01-20 discouraged me a little. Thank you again fellow

 

[Logical Dog]

Thanks for the advice! But I must say this particular review https://www.amazon.com/review/R2DV9...e&nodeID=283155&store=books&tag=pfamazon01-20 discouraged me a little. Thank you again fellow

N
.

Thanks for the advice! But I must say this particular review https://www.amazon.com/review/R2DV9...e&nodeID=283155&store=books&tag=pfamazon01-20 discouraged me a little. Thank you again fellow

Its funny because the author of that book mentions that it is not a rigourous analysis course, on the intro, at the back, and several hundred times in the book itself, but meant to accompany those looking for a goo introcution to analysis or college mathematics. You really shouldn't rely on one persons opinion, she is a published author with a Phd mathematics and 20 years teaching experience. Its a really good book, honest about what it is and written in a great fashion.

 

[Demystifier]

Was it a huge mistake to do Stewart's instead of a more difficult book if I want to major in mathematical physics?

Well, Stewart is for engineers, and now you know how engineers think of it. If you meet an engineer who claims that he knows calculus, now you will know what that means.

 

[atyy]

Thank you! I looked inside a bit on amazon and I didn't really like the 'super friendly' language. 'f(x) blows up at x= 2' made me cringe a little to be honest. I've been searching through my university library and I really liked Apostol's Mathematical Analysis and Taylor's Advanced Calculus. What do you think of those? Too difficult for a Stewart-level undergraduate?

Just try them and see for yourself. If you're stuck on a point, ask here or look up another book's explanation.

 

[amorrow]

There is a new fast introduction to Calculus. It is available at:
https://en.wikiversity.org/wiki/Calculus_I
Give it a try and please tell other math students and faculty.

 

[snatchingthepi]

What is wrong with Stewart's calculus book? It certainly got me through four terms of calculus, a good chunk of a term of linear algebra, and half a year-long course in mathematical methods. I don't think it's meant to be a book for an analysis course where you worry about proofs and other things.

 

[amorrow]

I have been working on a lightning fast introduction to calculus for youthful minds. It is available at:

http://thermo4thermo.org/

 

[Demystifier]

What is wrong with Stewart's calculus book? It certainly got me through four terms of calculus, a good chunk of a term of linear algebra, and half a year-long course in mathematical methods. I don't think it's meant to be a book for an analysis course where you worry about proofs and other things.

Nothing is wrong with Stewart, it's simply that pure mathematicians don't like it. To understand why, let me tell my personal anecdote with a pure mathematician (I am a theoretical physicist). At some point during a discussion he told me: "You physicists are strange, I noticed that you like to actually compute things."

 

[vanhees71]

I've the same experience. I'm also a theoretical physicist (during my studies I got convinced to be a theoretician by suffering the introductory and advanced labs ;-)) with always liking math very much. At the time in my university also the math lectures were often better than the physics lectures; so I went to much more maths lectures than mandatory for studying physics. The mathematicians are not interested in "calculus" in the sense of developing techniques to "actually get the numbers out", as a theoretical physicist has to do to make contact to experiments, where you have to compare concrete numbers from your calculation from concrete numbers from the measurement. They even think that this is some minor business they don't like to get their hands to become dirty with. In my opinion that's as ignorant as the other side, where physicists think pure math and strict proofs are superfluous academic exercises. I think it's good when mathematicians get their hands dirty with being able to do really a practical calculation to the end as well as it's good for physicists to learn some mathematical rigorous reasoning.

The funny thing was that sometimes the physicists had some advantages in solving also formal math problems in the mathematicians' recitations, simply because they had a versatile notation. E.g., in the introductory linear algebra course (1st semester) the mathematicians had great difficulties in figuring out, which transformation matrix has to be multiplied with which vector components in a change of bases. For us physicists this was no problem at all, using what we've learned in our "quick and dirty" "math for physicists" lecture, using the Ricci calculus and writing down the vectors as components and basis like $\vec{x}=x^{\mu} \vec{e}_{\mu} = x^{\prime \mu} \vec{e}_{\mu}'$. So although being a bit rough concerning the proofs the physicists approach to math as an applied (and in fact applicable!) science to solve real-world problems gave some advantage. So books like Stewart's have their value and one should not think they are a priori bad. They simply have a different purpose than pure-math textbooks.

 

[snatchingthepi]

Nothing is wrong with Stewart, it's simply that pure mathematicians don't like it. To understand why, let me tell my personal anecdote with a pure mathematician (I am a theoretical physicist). At some point during a discussion he told me: "You physicists are strange, I noticed that you like to actually compute things."

I get it. Thanks.

 

[kent davidge]

My professor says the same about that book. But personally, I don't think it is a poor book at all. In my first year at the university, what I learned in Calculus is not much beyond what I found in Stewart's book.

 

[dkotschessaa]

What is wrong with Stewart's calculus book? It certainly got me through four terms of calculus, a good chunk of a term of linear algebra, and half a year-long course in mathematical methods. I don't think it's meant to be a book for an analysis course where you worry about proofs and other things.

I hated Stewart's book, but then I stumbled across an older edition of it in the library at some point. It was much larger and much better IMO. I'm not sure it was more "rigorous" but the explanations were clearer. I think at some point he decided to make a smaller version of the book and posted a bunch of stuff online as supplements.

In particular, the notorious chapter 8 on sequences and series baffled pretty much every student I met, until I gave them a supplemental printout I had found online from his website. "Oh, this makes sense now."

-Dave K

 

[ElectricRay]

I bought Stewart a week ago as an extra book for my calculus adventure. I am studying Bsc Electrical Engineering via a distance learning program on a university in the Netherlands. The original book we use doesn't really get into the topic of calculus i mean not to deep. Well distance learning is basically 90% sels-study IMO so i thought Stewart's book must be great to buy. Reading the topic here makes me a bit hesitating. Nevertheless i bought it and it was really expensive together with the student solutions manual so I will start using it in the near future but I hope it will bring me on the right track.

 

[MidgetDwarf]

The problem with Stewart, I used it for the middle of my Calculus 1 course and ditched it soon after, is that it teaches a superficial viewpoint of Calculus. I do like it for what it is, a starter book in calculus,whom students after completing the book, must read another Calculus book for a better understanding. I did like the Chapter of sequences/series, and the end of section problems. The calculus 3 portion of the book was readable, but is superficial in its context.

Stewart is a great book for Engineers and Physicist, who use mathematics mostly as a TOOL. It is not adequate for a Mathematician.
However, I think books like Stewart are a great place for students to get acquainted with Calculus, but it should not be the only book they read on the subject.

 

[MidgetDwarf]

I hated that book so much; I had the opportunity to change to Spivak or Apostol in holidays but I didn't do it. I feel like I will have to read a good rigorous calculus text from the beggining since Stewart's textbook is sheer rubbish in many senses. Which book should I read to continue my mathematical education? Was it a huge mistake to do Stewart's instead of a more difficult book if I want to major in mathematical physics?

Maybe try learning Linear Algebra first. In my experience, I got better at reading and understanding proofs, the more I attempted to read and write proofs. One day I was restudying elementary Euclidean Geometry from Moise/Downs, and revisiting Linear Algebra. Moise gave me the understanding I lacked in reading mathematical text, the Chapter on Condratiction was an eye opening. I applied what I learned in Moise, to the assigned textbook I had for Linear Algebra. I began proving every Theorem before the author did it. I would check my proof with his and see the issues with my proof. I even proved earlier results, then the author, this allowed me to make even nice proofs.

Maybe practicing proof writing from a Linear Algebra textbook, and then applying to a rigorous Calculus book may help you out?

 

[ElectricRay]

Thanks for sharing your insight. I think i will use it now as I am new to calculus but i will remember your advise and will search for better books later.

 

[mathwonk]

as others have said, there is no one "stewart's calculus", since he revised it many times to keep selling more and more copies. i believe i rather liked the 3rd edition. in general the first edition of any book is usually the best. later editions are usually expanded unnaturally and dumbed down to increase sales. But whatever you learn fropm any book is a plus. and stewart usually has some proofs, even if they are hidden in an appendix. there is no law against actually reading the appendix.