Thomas Calculus Vs Stewart Calculus
Boleslao Drinker
I want to master calculus in every possible way, I'm working in my bases like algebra and trigonometry (Precalculus) since I haven't had a good start in calculus, I want to read books like Calculus by Spivak, Calculus by Apostol and Courant books from Calculus and analysis.
I want to know which books of calculus those 3 authors (Stewart, Larsom, Thomas) could help me to make a good aproach to calculus, if they are any substantial differences, if you think they are others best books please tell me
Finney, et al., Calculus: Graphical, Numerical, Algebraic (2003). This is clearly a standard high school textbook, which seems to provide the most basic of AP Calculus BC training. While the limit is defined in epsilon-delta form, it doesn't seem to be used except for some exercises in an appendix, and I didn't find any proofs in the book. The material, including definitions, does seem carefully presented, but it's a very elementary text, and there are quite a few exercises rather than challenging problems. There is a very, very heavy use of graphing calculators to give a graphical view of functions, limits, etc. -- not necessarily bad, but I'm trying to give an idea of the type of text. While the text has a strong school text feel, it isn't plagued by excessive, distracting sidebars, at least in the edition I reviewed. The text is too basic for us, but I could see the text's usefulness to explain concepts which are not grasped via the primary text you're using. The order of most of the texts seems pretty standard, except for some including transcendental functions earlier vs. some later, so some cross-use of texts isn't out of the question.
Strang also has a calculus text available for free download on the MIT Open Courseware site. I have not had a chance to review it yet, but his Linear Algebra and Its Applications text was my favorite math text as an undergraduate. My prof. (admittedly) was a terrible teacher, but I had no problem learning the material from the text, and I've heard that his calculus text is clear and direct too. At the same MIT OCW site, Dr. Strang has a series of videos "to show ways calculus is important in our lives."
ETA: some of the links and the Finney text review. Some later notes shown in green and will be discussed in a later post. The review of Thomas' Calculus below was added in response to a question by Mike:
Thomas' Calculus: Early Transcendentals 12th edition (2010) based on the original work by George Thomas as revised by Weir and Hass. There are many editions of Thomas' Calculus and this one is intended as a college course either for those with high school calculus or without. (For example, the text University Calculus by the same authors is a streamlined version meant for those who took calculus in high school, so it's outside the scope of this review. The next text to be reviewed is an older, explicitly high school text by George Thomas.) Thomas' Calculus seems to be at about the same level as Anton; there's perhaps more theory in Thomas' text but there's a good amount of rigor in Anton, and probably more than Thomas, if you select it, and Anton seems to have a significantly greater depth of practical problems. Thomas' Calculus 12 ed. appears rigorous, although it does not prove every result -- none of the texts except perhaps Spivak and Apostol do, but that's not what we or most high school students want anyhow. Thomas' has a lot of exercises, both simple and medium in difficulty. Thomas' seems like a good book, although I like Anton better for deeper applied problems and seemingly more flexibility with the theory. The most important thing, however, is how well the text explains concepts to the new learner, and, unfortunately, I can't say for sure. I'll just say it's worth considering.
Thomas Elements of Calculus and Analytic Geometry 2nd edition (1976) is an adaptation of George Thomas' calculus for high school students, by George Thomas himself. It looks like a 1970s high school textbook. Transcendental functions are covered late in the book, which I'm not a fan of since it leaves less time for working with transcendental functions during the course -- this is hotly debated, which is why most textbooks nowadays have versions with late transcendentals and early transcendentals. The presentation in this relatively simple, short book does strike me as straightforward and probably fairly easy to follow. There are a few simple theorems proved. Most of the problems are simple exercises with little sense for the range of applications of calculus and not many challenging problems. In summary, I don't think this is the best choice as the core text, but it seems to have value in having around as a way of describing a problematic topic if a student is struggling.
My ds finished the AoPS Calc text, but then to prepare for his university class, he has also done the Anton text. He has loved doing both, back to back. Go figure. He said that it was so good to have the theoretical understanding from AoPS before he went into the applied Anton. But he definitely feels like Anton has helped him to understand the uses of Calc and to drive home *when* the different approaches are more efficient for each type of problem. He will begin multivariate with Anton in July, and I think I will get him Spivik for the theory he craves.
Glad to hear those two worked out well together. It seemed to me that Anton, or his collaborators or commenters, really understood science and that it wasn't written by someone with no experience outside math, so Anton seems like a nice complement. Spivak seems like a great next step; although you may want to get a later edition, his first edition of "basic" calculus is free online.
Interesting reviews. Have you looked at Thomas, Leithold, or Swokowski? Leithold, to me, is one of the classics. It's simple, to the point, elegant, and doesn't skip a single necessary proof. I haven't seen a recent "AP" edition, though, so there's that. Same for Swokowski. Thomas is a favorite for many in AP courses, but I've never really checked it out.
I think they're available for all of the texts mentioned, at least those that have their own paragraph. Cost is a different issue. AoPS is only $49 new, including the solutions manual. Some are over $250 new. Usually earlier editions are far cheaper than new editions, but earlier editions vary so much based on the market that's it's hard to say anything definite.
Thanks, Mike! I haven't looked at any of these as part of this review. I tried to go through most of the texts in the WTM High School Math thread, those on the College Board list, those that had an AP course plan using them, plus a few more odds and ends. I've got a few more in my garage, more oriented for college use, but nothing since 2000 that's not listed. Maybe someone else will have a review. Thanks again for your comments!
ETA: I looked at various comments on the internet about calculus texts by those three authors. There were a number of comments about how clearly Thomas explained things, so I did review two of the many Thomas Calculus texts. Those brief reviews are shown in green added to the bottom of the original post. Thanks again.
The main difference between these two textbooks is the approach to teaching calculus. "Calculus" textbooks typically focus on traditional methods and techniques, while "Early Transcendentals" textbooks incorporate more modern and conceptual approaches.
Both "Calculus" and "Early Transcendentals" textbooks can be used for MST124, but it ultimately depends on the preferences and learning style of the individual student. It is recommended to review both textbooks and choose the one that best aligns with your learning style.
"Early Transcendentals" textbooks are often considered more suitable for beginners due to their emphasis on conceptual understanding and real-world applications. However, "Calculus" textbooks may also be suitable for beginners as they provide a more traditional and step-by-step approach to learning calculus.
Yes, there may be some differences in the exercises and examples between "Calculus" and "Early Transcendentals" textbooks. "Calculus" textbooks may have more traditional and straightforward exercises, while "Early Transcendentals" textbooks may include more real-world and challenging exercises.
In general, Thomas and Stewart calculus books are known for their rigorous approach to teaching calculus concepts and their focus on real-world applications. They also tend to have more challenging exercises and problems compared to other calculus books.
One strategy is to first review the fundamental concepts and techniques covered in the Thomas or Stewart book and make sure you have a solid understanding of them. Then, compare the organization and notation used in the new book and practice applying the concepts to new problems.
It is important to pay attention to the specific notation and terminology used in the new book, as it may differ from what you are used to. Additionally, topics such as limits, derivatives, and integrals are fundamental in calculus and should be thoroughly reviewed.
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