Calculus Made Easy Revised, Updated, Expanded Edition
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From Scientific American
“Calculus Made Easy is arguably the best math teaching ever. To a non-mathematician, its simplicity and clarity reveals the mathematical genius of Newton, Leibniz, and Thompson himself. Martin Gardner deserves huge thanks for renewing this great book.” ―Julian Simon, author of Population Matters
“A remarkable and user-friendly approach to the study of calculus, made even more so by Martin Gardner, the most highly acclaimed mathematical expositor of our time.” ―R.L. Graham, Chief Scientist, AT&T Labs, and author of Concrete Mathematics
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I do wish Gardner had resisted the temptation to insert chapters on functions and limits at the beginning of the book. There is much better motivation for that material after Thompson's introduction to derivatives. A footnote in the discussion of orders of smallness saying that a more rigorous explanation could be found at the end of the book would let a beginning student see what this calculus stuff was all about, and would also motivate the work on limits as a way to paper over the thin ice, to mangle a metaphor. It seems to be very hard for mathematicians to distinguish between logical development of a discipline and pedagogical discovery of that discipline. If you reconstruct what motivated people to create a branch of mathematics, and then teach that path of discovery, you can hope to motivate the development of more logical exposition and proofs. You can also hope to communicate some idea of what mathematics is about even to people whose minds do not require the full proof, or follow it if it is forced down their throats. Unfortunately, most fully qualified mathematicians should never be allowed near beginning students. Gardner seems to understand the problem in his discussion of why this book is so attractive compared with most introductory calculus texts, but he still wasn't able to resist the temptation to go down the same rathole.
Gardner has still produced a lovely edition of Thompson's book, updated to conform to current notational practice, so as long as you can skip over his two introductory chapters and come back to them later if you feel the need, it can be recommended with no other reservations.
if you wish to learn calculus, there is no substitute for example problems. This book has dearth of example compared to other
modern text books out there. I would stay away from this book, unless historical approach is of your interest.
Though this book does a great job at teaching calculus in a down-to-earth sort of way, it may be too much for you still if you aren't competent in algebra and basic trigonometry. So I would recommend brushing up on those two things before really hitting this book hard. Whenever you find a concept difficult, look up alternative explanations to see if they help (for example khanacademy videos help many people), you still are having difficulty with something after working through other explanations, then you must analyze yourself in conjunction with the problem to pinpoint exactly what is preventing you from understanding it, then master that point and come back to the original with better understanding. Also sometimes it just takes time for new concepts to sink-in (for your brain to process and organize them in relation to already known things).
If you don't know how to read analytically, then you must learn, because that is important to teaching yourself things. One book I would recommend highly concerning reading skills is "How to read a book" by Mortimer A. Adler. It walks you through the various stages of reading. Another tool that you can use to improve your reading skills, which are critical in learning anything including mathematics, is the sq3r or psq5r method. You can google these for a better explanation but they stand for this: sq3r, skim/survey, question, read, recite, review, and psq5r, purpose, survey, question, read-selectively, recite, reduce/record, reflect, review. You can google those for a more complete understanding of them and how to apply them to your reading, but know this, if you want to be able to teach yourself anything, then you must improve your reading skills. Reading for understanding and reading for pleasure or entertainment are completely different task.
Forgive my clumsy writing, but I learnt to read later than normal because the school system failed me and I had to teach myself, which is why I know the difference between reading for entertainment and reading for understanding, these types of reading must be approached differently. My writing skills have a long way to go, but I'm more focused on mathematics and general knowledge right now. Oh, I just remembered another book that is really helpful in problem sovling "How to solve it" by George Polya, I highly recommend that book for general problem solving strategies esp. for mathematics.
So, if you want to be able to teach yourself things as well as possible then buy these two books:
How to read a book
How to solve it
Find useful resources like Khanacademy and forums concerning your issue and ask questions
Think and work through the problem, if you get stuck, then analyze it and isolate the thing that is causing you trouble, research that thing and practice it until you feel confident then come back to the original problem.
Questions you can ask yourself when you get stuck are:
Do I really understand the problem?
Which part of the problem is causing me trouble?
Is there a problem from my past that is similar in part or whole that can help me with this one?
What do I know about the problem?
What is/are the unknown/s
Can I break the problem down into a series of simpler problems that I can solve?
Those are some general questions you could ask yourself while trying to solve problems, you will learn those type of questions in "How to solve it". As Francis Bacon said "A prudent question is one half of wisdom". Asking questions is very important in the learning process and asking the right questions even more so, it forces you to think deeper and reading more actively. Good luck to all.
This is not something to replace a standard calculus textbook. This is supplementary material that is intended to nail home some of the key concepts in calculus that are difficult for most people to grasp because they are more abstract concepts than they are used to dealing with in lower-level math courses. Even if you already have a passable grasp of the concepts, this book is still great because of its unusual presentation; it will add another dimension to your understanding. You can use it to weave together concepts from other subjects more easily.
One warning is that this book is not a panacea. Just reading will help but not be so effective.
You have to read and do some work. See similar types of problems and applications.
And really spent time with the book.
I regret not doing so :(
Still I learned a lot :D
Top international reviews
Color would be nice, but considering it's low price, that may be asking too much.
With the exercises, I can understand the points thoroughly.