What is a good book to review basic calculus?

In summary, the conversation discusses the need for a calculus textbook that is not too wordy and covers both single-variable and multi-variable calculus. The person has forgotten a lot of the material and wants to review it. Several recommendations are given, including "Quick Calculus: A Self-Teaching Guide" by Kleppner for single variable calculus, the Schaum's Outline series, and the "Calculus" book by George B. Thomas. The conversation also mentions the importance of continuity, differentiability, and integrability in both one and several variable calculus, as well as common topics such as infinite series and differential equations. The 3rd edition of Thomas' book is suggested as a good resource, but it may be more difficult to
  • #1
Eclair_de_XII
1,083
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I want a book that isn't too wordy, explains things concisely, and covers single-variable and multi-variable calculus. I regret that I forgot so much of the stuff I learned in Calculus III and IV (especially the important theorems I learned but forgot in the latter), and now I want to review it over again. If anyone is able to help me with this, it would be much appreciated. Thank you.
 
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  • #2
Shortcuts will not do. Any typical undergraduate Calculus textbook can hold instruction for at least the first year's-worth of Calculus. You can find these at most public libraries, especially or also college libraries and some used-book sources. Check the tables of contents and compare with what you also expect to be in Calculus III and IV.
 
  • #3
This page has a strong recommendation.
 
  • #5
I have always liked the Schaum's Outline series. They have a lot of worked examples and exercises. Look for a calculus one that fits your needs.
 
  • #6
I don't know, whether there's an English translation of the great intro-calculus books by Richard Courant, but if so, I'd recommend them strongly!
 
  • #8
Eclair_de_XII said:
I want a book that isn't too wordy, explains things concisely, and covers single-variable and multi-variable calculus. I regret that I forgot so much of the stuff I learned in Calculus III and IV (especially the important theorems I learned but forgot in the latter), and now I want to review it over again. If anyone is able to help me with this, it would be much appreciated. Thank you.

Since you are a mathematics major. Maybe review the Real Analysis book used in Intro Analysis Course or a better book. What do you want to use Calculus for?
 
  • #9
there are three concepts in one variable calculus, continuity, differentiability, and integrability. Then there are several basic theorems: intermediate value theorem (basic property of continuity), existence of maxima and minima of continuous functions on closed bounded intervals, and mean value theorem. the key theorem relating these concepts is the fundamental theorem of calculus, showing how to compute integrals by anti differentiation. There is also the inverse function theorem, largely a corollary of the intermediate value theorem.

In several variable calculus the same three concepts occur. Basic theorems are the inverse function theorem, the fubini theorem (reducing an integral of several variables down to a sequence of one variable integrals), and the stokes theorem, (generalizing the fundamental theorem of calculus).

Other common topics include summability of infinite series, and solvability of simple differential equations, especially linear ones with constant coefficients. Then there are applications of these ideas to computing volumes, and physical concepts like work. One good book is an old version of the book of George B. Thomas, formerly available used for a couple of dollars. Omiword, those old books are now hundreds of dollars. It seems to be understood that the newer books with names like Finney, Haas, Weir, Giordano, on them are greatly inferior. But maybe the alternate 9th edition with just Finney on it is ok.
https://www.abebooks.com/servlet/Bo...centlyadded=all&cm_sp=snippet-_-srp1-_-title3
But I suggest going to a library for an older edition from the 50's or 60's.
 
  • #10
mathwonk said:
there are three concepts in one variable calculus, continuity, differentiability, and integrability. Then there are several basic theorems: intermediate value theorem (basic property of continuity), existence of maxima and minima of continuous functions on closed bounded intervals, and mean value theorem. the key theorem relating these concepts is the fundamental theorem of calculus, showing how to compute integrals by anti differentiation. There is also the inverse function theorem, largely a corollary of the intermediate value theorem.

In several variable calculus the same three concepts occur. Basic theorems are the inverse function theorem, the fubini theorem (reducing an integral of several variables down to a sequence of one variable integrals), and the stokes theorem, (generalizing the fundamental theorem of calculus).

Other common topics include summability of infinite series, and solvability of simple differential equations, especially linear ones with constant coefficients. Then there are applications of these ideas to computing volumes, and physical concepts like work. One good book is an old version of the book of George B. Thomas, formerly available used for a couple of dollars. Omiword, those old books are now hundreds of dollars. It seems to be understood that the newer books with names like Finney, Haas, Weir, Giordano, on them are greatly inferior. But maybe the alternate 9th edition with just Finney on it is ok.
https://www.abebooks.com/servlet/Bo...centlyadded=all&cm_sp=snippet-_-srp1-_-title3
But I suggest going to a library for an older edition from the 50's or 60's.
I was able to peruse all the editions of Thomas starting from 3 to 11th. There may be more editions now. The 3rd edition of Thomas is much different book then the later editions. I believe the 4th and 5th edition are similar, but not the same. I would definitely go for the 3rd edition. Then supplement it with problem sets from another source. Problem sets can be found for free online. However, the multivariable material in the 3rd edition may be a bit harder to understand then more modern dumb down books.
 

Related to What is a good book to review basic calculus?

What is a good book to review basic calculus?

There are many good books available for reviewing basic calculus. Some popular options include "Calculus: Early Transcendentals" by James Stewart, "Calculus" by Michael Spivak, and "Calculus: A Complete Course" by Robert A. Adams.

What topics should a good calculus review book cover?

A good calculus review book should cover topics such as limits, derivatives, integration, applications of derivatives and integrals, and basic differential equations. It should also include plenty of practice problems and examples.

Should I choose a book with a specific focus, such as business calculus or engineering calculus?

It depends on your specific needs and goals. If you are studying calculus for a specific field, such as business or engineering, then a book with that focus may be more beneficial. However, if you just need a general review of calculus, a book with a broader focus may be more suitable.

Are there any online resources that can supplement a calculus review book?

Yes, there are many online resources available, such as Khan Academy, MIT OpenCourseWare, and Coursera, that offer free calculus courses and tutorials. These can be helpful supplements to a review book.

How can I determine if a calculus review book is suitable for my level of understanding?

You can determine the level of a calculus review book by looking at the prerequisites and the level of difficulty of the problems. You can also read reviews and ask for recommendations from other students or professors who have used the book.

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