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Calculus: Early Transcendentals
This edition of James Stewart's best-selling calculus book has been revised with the consistent dedication to excellence that has characterized all his books. Stewart's Calculus is successful throughout the world because he explains the material in a way that makes sense to a wide variety of readers. His explanations make ideas come alive, and his problems challenge, to reveal the beauty of calculus. Stewart's examples stand out because they are not just models for problem solving or a means of demonstrating techniques--they also encourage readers to develp an analytic view of the subject. This edition includes new problems, examples, and projects. This version of Stewart's book introduced exponential and logarithmic functions in the first chapter and their limits and derivatives are found in Chapters 2 and 3.
1344 pages, Hardcover
First published February 1, 1995
133 people are currently reading
1202 people want to read
About the author
James Stewart
1,249 books70 followersJames Stewart is a professor of mathematics and a violinist. He has written a number of textbooks, notably on calculus.
For other James Stewarts, see similar names.
For other James Stewarts, see similar names.
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Displaying 1 - 30 of 88 reviews
August 26, 2022
Honestly, probably a strong 4.8
I have done something almost no one does... I have read a maths textbook. Not only have I read a maths text, I have actually done a huge portion of the problems in the book. With regards to full disclosure, I am a professor of Mathematics, so I have definitely read this from a very different perspective compared to a student learning for the first time.
However, when I was first teaching myself Calculus a little over ten years ago, this was the text I had picked up, albeit it was an old edition, the 2nd Edition to be specific. I was not formally trained in mathematics at the time, and I was opting for a rather drastic career change from working in the Financial Industry. I did not really know what I wanted to do, but I remembered having a passing interest in maths (this is in my late 20's). I was always placed in the accelerated program for mathematics when I was in High School and Elementary School, but I definitely always had a lot of trouble engaging the material during school itself. For me, it really wasn't until I was able to remove myself from the school system and read several Algebra text books and then felt quite prepared to take on Calculus. I felt I was getting quite good at Calculus after reading what I could of Stewart (most of my way through Calc II) that I decided to take a summer Calculus 1 course at a nearby college. I wanted some confirmation that, perhaps I was not too bad at the subject and to overcome some of the mathematical anxiety I experience all through high school. I receieved an A in the course, from there I quit my job and enrolled at a university to study Applied Mathematics. I greatly enjoyed the material, and while it was very difficult after a short amount of time I eventually got a my Masters in Applied Maths, then I was given a job teaching at the university I graduated from. I have been there ever since.
Now, perhaps, a new chapter in my life unfolds where I feel the urge to potentially acquire a PhD, but it has been quite a long time since I have studied all aspects of Calculus. I have, for the past decade primarily been teaching some variation of Calculus 1 or Pre-Calculus, so I am rather decent with those subjects. While I remembered quite a bit from Integral and Multivariable Calculus, it has been quite some time since I have flexed that muscle and worked problems. I decided to return to an old favorite of a text and got the latest edition of this wonderful tome written by James Stewart.
This 8th edition did not disappoint! I have looked through and read several other Calculus texts over the years and, to me, few can compete with Stewart's exposition. The text is masterfully written and I would say it is a solid text for self study, up to a certain point. At some point you will want to confer with an expert on the material in order to make sure you are grasping the content as intended. To me, tutors and teachers are rather essential for this. It's sometimes not enough to just sit and do mathematics in your room by yourself... to make sure you are truly understanding what has been written and make sure you are using notation correctly, having a discussion with someone trained in that field goes quite a long way! Luckily, being at a university I had a lot of people I could just ask, but not everyone will have such a luxury. Either way, do not underestimate the value of conversations in technical subjects, I find they are paramount to my understanding and to my students' understanding.
If you want to do mathematics the right way, you need to put pen to paper, this is unavoidable. It is not enough to read these texts like a novel, as any mathematician will tell you. You, truly, can only learn it by doing it and I don't really care how much of a genius someone is, they are still human and will need to do this at some point. One of the complaints one of my colleagues had about the text was that the problem sets in Stewart were too easy, so that was one of the major justifications for using Thomas, despite the exposition being sub par in my opinion. I am happy to report that the 8th Edition seems to be rather different from the 2nd edition that I remember working in. The 8th Edition has definitely cranked up the difficulty level on the problem sets, in some ways this was detrimental to later sections of the text. (It's the one criticism I have of the text, but I will get into that later). This increased challenge factor to the problems has truly launched this book into the flagship Calculus book category for me.
For the most part the ordering of the topics is quite well done. The first part of the book sort of runs through a crash course in Pre-Calculus topics, which is nice if you were good at Pre-Calc and want a refresher. I do not recommedn starting with this book, though. If you have an okay Algebra background, but a poor Pre-Calculus background, you will have a very hard time getting through Stewart. Pre-Calculus books are notoriously horribly written, the ordering, to me, is often atrocious and confusing. Important geometric motivations that should be used throughout the course are taught halfway through etc. It's all just backwards and it's no wonder I had a hard time in Pre-Calc and couldn't follow the material well. However, a real gem my university is using now is Precalculus. After having read a decent portion of this book's content, I think it is very well written. I think this book would be the best preparation for tackling something like Stewart. There are portions of this book I would make harder and a few choice pieces I would add to the content, but overall it is good preparation.
The core criticism I will level at Stewart is a couple missed opportunities in my opinion. I think they were very concerned about how long the book already was, but, in my opinion, when books are this long, what's 100 more pages? Since Stewart has passed away, sadly, it would probably be nearly impossible to add meaningful content in his style. In any event, one thing that is easily rectified is putting the Differential Equations (DE) chapters into one chapter. I feel like Stewart wrote a chapter about Differential Equations and then the publisher decided to split it up, but, truly, the content he wrote about makes the most sense after Integral Calculus. But, strangely, half of the DE chapter is after the chapter on Vector Calculus. You don't even solve any of the problems with Multivariable Calculus, so what is this even doing at the end? It's far more cohesive and has better flow if you just make one differential equations chapter.
That being said, his DE chapter is very well done, but it starts to waver a little bit when we get to Variation of Parameters and Series Solutions of ODE's. I like having this content in here and I think the problems are fascinating and I truly think the problem sets are good, but these problems assume quite a bit of mathematical maturity that just isn't spelled out in the text. The way you need to manipulate power series via re-indexing and studying the partial sequences, there just aren't any good examples to walk you through how complex some of the problems get. Nor is there much in the series section on re-indexing your series or just the general algebraic mechanics being used in the context of the DE questions. Getting Power Series to match so that you can use the distributive property is not always the most obvious thing based on the discussion found in this book. So, some students reading this on their own may find this as a bit of a stumbling block.
So, if they put all the ODE material into a single chapter that would be wonderful. The truly missed opportunity at the end of Multivariable Calculus is that the student is equipped to study some of the lower level Partial Differential Equations (PDEs) that are out there. Such as just finding characteristic equations and such would be a huge boost to the students. PDE books notoriously don't write out step by step examples, but Stewart could have put them in at this location and doing a few basic problems.
In the Vector Calculus section, I think Stewart assumes a relatively high maturity level when it comes to working with Analytic Solid Geometry. While I have worked on such material, it has been quite some time. This is also where a lot of the graphical content seems to fall off. Throughout the book Stewart often provides a lot of geometric motivation for the problems and so on, but in the Vector Calc section I feel like far more maturity beyond the general Quadric Surfaces was assumed, so the transition from reading a section, looking at examples, to doing problems on your own had a bit of a steeper uptick. I think his section was decently written, but I frequently felt like something was missing.
However, I have always maintained that Vector Calculus should be its own course and not even part of the standard 3-semester Calculus track most universities employ. I think the student needs a fair amount of time playing with the general geometry around Vector Fields before attempting serious calculus techniques on objects within the field. This was really the only time I felt like the problem sets somewhat got away from what was written in the sections. I felt the way the material was laid out I wanted a little bit more hand holding along the way before I was really left to my own devices.
That being said, once an enterprising student has gone through this text they may be ready to tackle the likes of Advanced Calculus or Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach. These books aren't necessarily for the faint of heart. They are challenging books, but I found them to be well written. You may want to study Linear Algebra as a stand alone course before attempting courses with the blend of Linear and Vector Calculus. With regards to taking further upper level mathematics courses, Stewart does not adequately prepare you to jump into the likes of Real Analysis, Topology, etc. To supplement this material books covering Logic and Set Theory in more detail, along with general Proof Techniques should be looked at. Discrete Mathematics and Its Applications by Kenneth Rosen is considered one of the flagship books covering this content. I have read this book and I find it's material to be very well done. Once you've covered proof techniques in this fashion, perhaps you will have enough mathematical maturity to take on a course like Real Analysis. I would not recommend jumping to Principles of Mathematical Analysis by Rudin right away, at least not without an expert to help walk you through it. Calculus by Spivak is certainly a classic Real Analysis book, his problem sets can get quite maddening, but if you can figure them out you will have a wonderful time in that book. Spivak does assume quite a lot of mathematical maturity and I'm not sure one has that coming direct from Stewart. Best to do some more work on Proofs and Set Theory, especially Set Theoretic ideas as they apply to the Real line.
In the end, I wholly endorse Stewart's Calculus. It's one of the finest introductory Calculus books ever written and it is no secret that this is considered the gold standard for a students' first experience with the wonders of Calculus. I truly can't endorse this book enough, just be aware towards the very end you may need more assistance through the problem sets than the exposition can provide. In the end, Stewart's presence in the mathematical community will surely be missed, but the legacy of his text will live on. I only wish I could have told him the story of my drastic career change and how his text strangely facilitated my success into a career I had never even considered having.
I have done something almost no one does... I have read a maths textbook. Not only have I read a maths text, I have actually done a huge portion of the problems in the book. With regards to full disclosure, I am a professor of Mathematics, so I have definitely read this from a very different perspective compared to a student learning for the first time.
However, when I was first teaching myself Calculus a little over ten years ago, this was the text I had picked up, albeit it was an old edition, the 2nd Edition to be specific. I was not formally trained in mathematics at the time, and I was opting for a rather drastic career change from working in the Financial Industry. I did not really know what I wanted to do, but I remembered having a passing interest in maths (this is in my late 20's). I was always placed in the accelerated program for mathematics when I was in High School and Elementary School, but I definitely always had a lot of trouble engaging the material during school itself. For me, it really wasn't until I was able to remove myself from the school system and read several Algebra text books and then felt quite prepared to take on Calculus. I felt I was getting quite good at Calculus after reading what I could of Stewart (most of my way through Calc II) that I decided to take a summer Calculus 1 course at a nearby college. I wanted some confirmation that, perhaps I was not too bad at the subject and to overcome some of the mathematical anxiety I experience all through high school. I receieved an A in the course, from there I quit my job and enrolled at a university to study Applied Mathematics. I greatly enjoyed the material, and while it was very difficult after a short amount of time I eventually got a my Masters in Applied Maths, then I was given a job teaching at the university I graduated from. I have been there ever since.
Now, perhaps, a new chapter in my life unfolds where I feel the urge to potentially acquire a PhD, but it has been quite a long time since I have studied all aspects of Calculus. I have, for the past decade primarily been teaching some variation of Calculus 1 or Pre-Calculus, so I am rather decent with those subjects. While I remembered quite a bit from Integral and Multivariable Calculus, it has been quite some time since I have flexed that muscle and worked problems. I decided to return to an old favorite of a text and got the latest edition of this wonderful tome written by James Stewart.
This 8th edition did not disappoint! I have looked through and read several other Calculus texts over the years and, to me, few can compete with Stewart's exposition. The text is masterfully written and I would say it is a solid text for self study, up to a certain point. At some point you will want to confer with an expert on the material in order to make sure you are grasping the content as intended. To me, tutors and teachers are rather essential for this. It's sometimes not enough to just sit and do mathematics in your room by yourself... to make sure you are truly understanding what has been written and make sure you are using notation correctly, having a discussion with someone trained in that field goes quite a long way! Luckily, being at a university I had a lot of people I could just ask, but not everyone will have such a luxury. Either way, do not underestimate the value of conversations in technical subjects, I find they are paramount to my understanding and to my students' understanding.
If you want to do mathematics the right way, you need to put pen to paper, this is unavoidable. It is not enough to read these texts like a novel, as any mathematician will tell you. You, truly, can only learn it by doing it and I don't really care how much of a genius someone is, they are still human and will need to do this at some point. One of the complaints one of my colleagues had about the text was that the problem sets in Stewart were too easy, so that was one of the major justifications for using Thomas, despite the exposition being sub par in my opinion. I am happy to report that the 8th Edition seems to be rather different from the 2nd edition that I remember working in. The 8th Edition has definitely cranked up the difficulty level on the problem sets, in some ways this was detrimental to later sections of the text. (It's the one criticism I have of the text, but I will get into that later). This increased challenge factor to the problems has truly launched this book into the flagship Calculus book category for me.
For the most part the ordering of the topics is quite well done. The first part of the book sort of runs through a crash course in Pre-Calculus topics, which is nice if you were good at Pre-Calc and want a refresher. I do not recommedn starting with this book, though. If you have an okay Algebra background, but a poor Pre-Calculus background, you will have a very hard time getting through Stewart. Pre-Calculus books are notoriously horribly written, the ordering, to me, is often atrocious and confusing. Important geometric motivations that should be used throughout the course are taught halfway through etc. It's all just backwards and it's no wonder I had a hard time in Pre-Calc and couldn't follow the material well. However, a real gem my university is using now is Precalculus. After having read a decent portion of this book's content, I think it is very well written. I think this book would be the best preparation for tackling something like Stewart. There are portions of this book I would make harder and a few choice pieces I would add to the content, but overall it is good preparation.
The core criticism I will level at Stewart is a couple missed opportunities in my opinion. I think they were very concerned about how long the book already was, but, in my opinion, when books are this long, what's 100 more pages? Since Stewart has passed away, sadly, it would probably be nearly impossible to add meaningful content in his style. In any event, one thing that is easily rectified is putting the Differential Equations (DE) chapters into one chapter. I feel like Stewart wrote a chapter about Differential Equations and then the publisher decided to split it up, but, truly, the content he wrote about makes the most sense after Integral Calculus. But, strangely, half of the DE chapter is after the chapter on Vector Calculus. You don't even solve any of the problems with Multivariable Calculus, so what is this even doing at the end? It's far more cohesive and has better flow if you just make one differential equations chapter.
That being said, his DE chapter is very well done, but it starts to waver a little bit when we get to Variation of Parameters and Series Solutions of ODE's. I like having this content in here and I think the problems are fascinating and I truly think the problem sets are good, but these problems assume quite a bit of mathematical maturity that just isn't spelled out in the text. The way you need to manipulate power series via re-indexing and studying the partial sequences, there just aren't any good examples to walk you through how complex some of the problems get. Nor is there much in the series section on re-indexing your series or just the general algebraic mechanics being used in the context of the DE questions. Getting Power Series to match so that you can use the distributive property is not always the most obvious thing based on the discussion found in this book. So, some students reading this on their own may find this as a bit of a stumbling block.
So, if they put all the ODE material into a single chapter that would be wonderful. The truly missed opportunity at the end of Multivariable Calculus is that the student is equipped to study some of the lower level Partial Differential Equations (PDEs) that are out there. Such as just finding characteristic equations and such would be a huge boost to the students. PDE books notoriously don't write out step by step examples, but Stewart could have put them in at this location and doing a few basic problems.
In the Vector Calculus section, I think Stewart assumes a relatively high maturity level when it comes to working with Analytic Solid Geometry. While I have worked on such material, it has been quite some time. This is also where a lot of the graphical content seems to fall off. Throughout the book Stewart often provides a lot of geometric motivation for the problems and so on, but in the Vector Calc section I feel like far more maturity beyond the general Quadric Surfaces was assumed, so the transition from reading a section, looking at examples, to doing problems on your own had a bit of a steeper uptick. I think his section was decently written, but I frequently felt like something was missing.
However, I have always maintained that Vector Calculus should be its own course and not even part of the standard 3-semester Calculus track most universities employ. I think the student needs a fair amount of time playing with the general geometry around Vector Fields before attempting serious calculus techniques on objects within the field. This was really the only time I felt like the problem sets somewhat got away from what was written in the sections. I felt the way the material was laid out I wanted a little bit more hand holding along the way before I was really left to my own devices.
That being said, once an enterprising student has gone through this text they may be ready to tackle the likes of Advanced Calculus or Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach. These books aren't necessarily for the faint of heart. They are challenging books, but I found them to be well written. You may want to study Linear Algebra as a stand alone course before attempting courses with the blend of Linear and Vector Calculus. With regards to taking further upper level mathematics courses, Stewart does not adequately prepare you to jump into the likes of Real Analysis, Topology, etc. To supplement this material books covering Logic and Set Theory in more detail, along with general Proof Techniques should be looked at. Discrete Mathematics and Its Applications by Kenneth Rosen is considered one of the flagship books covering this content. I have read this book and I find it's material to be very well done. Once you've covered proof techniques in this fashion, perhaps you will have enough mathematical maturity to take on a course like Real Analysis. I would not recommend jumping to Principles of Mathematical Analysis by Rudin right away, at least not without an expert to help walk you through it. Calculus by Spivak is certainly a classic Real Analysis book, his problem sets can get quite maddening, but if you can figure them out you will have a wonderful time in that book. Spivak does assume quite a lot of mathematical maturity and I'm not sure one has that coming direct from Stewart. Best to do some more work on Proofs and Set Theory, especially Set Theoretic ideas as they apply to the Real line.
In the end, I wholly endorse Stewart's Calculus. It's one of the finest introductory Calculus books ever written and it is no secret that this is considered the gold standard for a students' first experience with the wonders of Calculus. I truly can't endorse this book enough, just be aware towards the very end you may need more assistance through the problem sets than the exposition can provide. In the end, Stewart's presence in the mathematical community will surely be missed, but the legacy of his text will live on. I only wish I could have told him the story of my drastic career change and how his text strangely facilitated my success into a career I had never even considered having.
Read
May 12, 2020A bit short
January 8, 2022
caused me a lot of pain.
March 13, 2025
I’m a survivor. This book and I have gone through life together. We cried together, we laughed together, and even occasionally shed blood together. I would recommend for anyone wanting to pursue a career or future in math.
August 6, 2022
Got a 5 on the exam 🙃🙃 plus it didn’t make me cry THAT much. 4.5/5
Read
January 18, 2023saddest book I've ever read
May 2, 2022
solid, really helped during 1ZB3.
September 14, 2022
Took me like two years to read this book. The examples were helpful but the way the information was presented could be clearer and better organized
March 13, 2025
not just a book — an ✨ experience ✨
July 13, 2017
Once again, an update to avoid confusing friends in my strange recent goodreads habits: In preparation for the qualifying exam, I will be rapidly binge reading my undergrad texts for the next few weeks. I liked Stewart while reading it, but I loved returning to it in a reference. While I didn't feel the need for examples and problems in all but a few areas, I appreciated the quality of available exercises in passing. Glad with my ug professors' choices.
December 13, 2018
My university uses this for Calculus I thru III (differentiation, integration, and multivariate, respectively), and it's a well-rounded textbook. The application chapters - including sections on differential equations - were useful stepping stones to more advanced classes, and the introduction of vectors is handy for those who expect to take linear algebra.
May 31, 2022
Considering the amount of time I referenced this book this year I think it's fair to put this down (fight me) :P
It's a solid textbook. Unfortunately I don't think I'll ever have it in me to rate a calculus textbook 5 stars but it was very helpful for calc I and II.
It's a solid textbook. Unfortunately I don't think I'll ever have it in me to rate a calculus textbook 5 stars but it was very helpful for calc I and II.
July 10, 2023
Calculus for Engineers
May 21, 2024
amazing book.. must read- i loved it personally.
December 21, 2012
Reusing this for Calc III.
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I read this textbook for my AP Calculus BC class. It wasn't too dry, fortunately, and used lots of pictures / tables / charts as reading aids. Many of the exercises included had to do with interesting applications in other areas of math, physics, and engineering — much more fun than the standard "sliding-ladder" problem types that showed up in previous courses. I just wish the authors would have skipped steps less often in the examples.
---
I read this textbook for my AP Calculus BC class. It wasn't too dry, fortunately, and used lots of pictures / tables / charts as reading aids. Many of the exercises included had to do with interesting applications in other areas of math, physics, and engineering — much more fun than the standard "sliding-ladder" problem types that showed up in previous courses. I just wish the authors would have skipped steps less often in the examples.
February 14, 2021
Excellent!!
December 10, 2021
saddest book i have ever read, cried almost every chapter
December 26, 2022
0/10 ruined my life
December 22, 2023
Pretty expensive, especially given the ratio of educational content to practice problems. If you're learning from elsewhere and just need something that gives you an absurd amount of work to do without actually explaining how to do it, then this book is for you.
Otherwise, stay away. Well, that might also be difficult, given how WebAssign has irreversibly tied itself into my college Calculus classes.
Still though, this book was very short on genuine instruction or explanation of the theorems and the methods of solving these problems. There are other Calculus textbooks out there that are way better with this.
Otherwise, stay away. Well, that might also be difficult, given how WebAssign has irreversibly tied itself into my college Calculus classes.
Still though, this book was very short on genuine instruction or explanation of the theorems and the methods of solving these problems. There are other Calculus textbooks out there that are way better with this.
May 23, 2025
Revisited this book several times through out my schooling. Currently using the 9th edition for refreshers.
Realized recently that it is optimal for everyone to keep even the most basic of skills fresh at anytime, especially for those in the Data Science, Computer Science and/or Information Technology. Yes, a program you cobbled up with all the mathematic specific dependencies installed can get you through most of the heavy calculations, but it is always key to know how the modules work inside-out to use it optimally.
Realized recently that it is optimal for everyone to keep even the most basic of skills fresh at anytime, especially for those in the Data Science, Computer Science and/or Information Technology. Yes, a program you cobbled up with all the mathematic specific dependencies installed can get you through most of the heavy calculations, but it is always key to know how the modules work inside-out to use it optimally.
February 12, 2021
Calculus Early Transcendentals 8th Edition ebook arrived quickly and that was a help since I have been needing to use it for my class. Quick delivery ensured I did not miss a beat. It seems to be a good textbook. I am glad to be able to rent it for such a reasonable price.
Buy
Calculus Early Transcendentals 8th Edition
Buy
Calculus Early Transcendentals 8th Edition
May 13, 2024
After going through calculus 2 and calculus 3 I can finally say I’m done with it. Jesus Christ did this give me long nights of suffering and crying, but holy shit James Stewart you have a beautiful mind with your crazy ass integral house. I literally don’t know how you compiled this in all its entirety but to each their own. Also I found out this dude was gay #ally #lgbt #pyFAGoras - don’t cancel I’m bisexual
June 30, 2017
Its a thorough reference manual for Calculus, will touch every topic in detail.
You are not going to like reading it like you'd like reading Spivak's Calculus book, which is more like a tutorial not just reference manual and I gave it one star lesser than I have given to Spivak's book. ( Because we have google for reference, right?)
You are not going to like reading it like you'd like reading Spivak's Calculus book, which is more like a tutorial not just reference manual and I gave it one star lesser than I have given to Spivak's book. ( Because we have google for reference, right?)
May 14, 2023
3 and a half stars honestly! It’s quite a succinct book but in doing so it introduces vocabulary a little too rushed. I think it’s important for a mathematics author to think about the experience of those going in, and I would hate to be a first-time calculus student reading this book as my only introduction!
January 29, 2018
Clear, easy to understand, to the point. Simple, well thought out graphics and nice design. All textbooks (especially biology textbooks) can learn from this one. All textbooks should be written like this.
July 31, 2019
This book will be of help to students who will need a good understanding of Calculus. Don't be intimidated by the number of pages. Great for understanding concepts. This book quotes a lot of real-world examples.
June 9, 2023
Does not work on my kindle
The equations don’t render correctly and I’m unable to read any math in this. Like integrals, fractions, etc they all come out as gibberish like lim f std 2 fsdv-tl2t220.
The encoding is all messed up and I can’t use the book
The equations don’t render correctly and I’m unable to read any math in this. Like integrals, fractions, etc they all come out as gibberish like lim f std 2 fsdv-tl2t220.
The encoding is all messed up and I can’t use the book
March 11, 2025
I thought this would just be funny to review. It does what it says on the tin. Less rigorous than Spivak but more comprehensive. If you read this you either were forced to for school, or you’re a recreational reader who probably has a very similar YouTube feed to me.
January 14, 2018
This is an excellent presentation of calculus, and includes very good material on functions, series, vectors, and good examples.
August 7, 2018
Wonderful for self teaching with some what creative problems to solve
Displaying 1 - 30 of 88 reviews