How good is good ? Calculus, but too any Math or Science book

[symbolipoint]

how good is "good"? Calculus, but too any Math or Science book

How good is "good" when someone wants a book on any course, such as Calculuses one through three or more or Linear Algebra? The recent topic is in progress for "what is a good Calculus book", and it seems there are different opinions based on students' goals and the nature of the textbook and how well the style fits the student.

Currently my favorite Calculus 1 book is Single Variable Calculus, Fourth Edition, by James Stewart, (c) 1999. One reason I like it is that it includes a very good, maybe excellent proof of the Chain Rule. The treatment of Fundamental Theorem of Calculus is also very good and has helped me to understand this better. I had previously believed certain other books were just as good or even better, but I no longer believe so. An old, big thick, Anton book on Calculus has a great many exercises and examples and seems to have good instructive discussion but some of the proofs are lacking or too difficult to follow. The old Larson & Hostetler book was very well designed to help students learn to use Calculus as a tool, but some of the development still seems lacking in proofs. I have never ever seen the Courant nor Apostel nor Spivak books, so I do not know how they are.

While I say the Stewart book is very good/excellent, I cannot say that the Larson&Hostetler nor Anton books are bad; only that I LIKE the Stewart book better. All three were meant for undergraduates who need a Calculus & Analytic Geometry course series for degrees in physical sciences and engineering.

So how good in what way are the popular and less well known books for Calculus, Linear Algebra, Differential Equations, or any other Mathematics or science textbooks?

 

[n10Newton]

You are an old member on this forum so you are more experienced than me.

If Students ask for a good book then the opinions are may be controversy. but if they use prefixes like Intro books, Self-study books, Intermediate level or advance level book then the suggestions of books are of same level.

And your listed book Stewart to Anton to Larson all are fit for AP Calculus BC course. And you like Stewart because of its writing style , your learning style suits this book better than others.

Also in choosing books many Factors matters as for me I know Spivak Calculus and Calculus on manifolds books are best but I am from developing country so the book costs very high and I choose Apostol and Courants Calculus book (Indian Edition) instead of Spivaks International Edition.

 

[Vargo]

Tough question. It is easy to get a little bit snobby about textbooks and insist that only books like Spivak/Apostol/Courant can do justice to calculus. I originally learned from a Stewart-like book (I sold it and don't remember the author now). At the time it was interesting and I thought the problems were good. Now I teach from Stewart. My complaint is that most of my students only ever learn to do exercises that closely follow the models of the examples in the text. Perhaps I should blame myself or my students but not the book, I don't know. Maybe it is just a stage in the learning process.

Those harder texts actually prove all the theorems, such as the intermediate value theorem. And the exercises are more diverse and challenging. The books are rigorous. In some sense, if you use these books you will not get a false sense of understanding calculus. You will understand it or you will know that you don't. In contrast, plenty of people pass Stewart without understanding Calculus. I just finished teaching two sections of Differential equations full of students who used Stewart. Many of them did not properly understand the logarithm function. /sigh

 

[member 392791]

Yeah, but at some level, one must ask, is the student expected to fully grasp and understand calculus after finishing the freshman/sophomore series? Perhaps one would really have a firm grasp on the subject after a more advanced treatment of the subject.

 

[Vargo]

I talked to a mathematician a couple years ago who vehemently defended Stewart's book against the complaints of another mathematician. I remember part of his defense was that Stewart is willing to tailor his book to the needs of individual institutions. If you want to do early transcendentals, you can do that. If you want early vectors, or no vectors, he can do that. I think this must be part of why his book has been adopted by so many different departments.

What I have noticed lately is that a lot of students don't look in their textbook that much anymore. They go to Youtube or some other online source. When I ask them about it, they say the textbook explanations are useless. Recently on a test, I got a lot of students giving an answer citing "c>0" therefore the solution goes counterclockwise. I thought, "what the heck is c? There is no c in this problem..." It took me forever to figure out what they meant. Unfortunately for them, there really was no "c" in that problem :). I guess that is a pitfall of mathematics by Youtube.

 

[nabil0]

Apostol is the best calculus textbook I've found . Courant is also very good . I think that stewart-like calculus texts are good if some one wants to know how to apply calculus to standard problems but It doesn't give you a solid understanding of the concepts which is needed if you want to solve more difficult problems .