Best Books to Teach Yourself Calculus
Can I learn calculus on my own? What are the best calculus books for self-study?
Studying calculus on your own is doable, and there are many reasons why people may choose to study calculus outside the classroom. Some are home-schooled students, some are college students planning to take a class for which calculus is a pre-requisite, some have attempted a calculus class before, while others are continuing their education beyond college, or are just mathematically curious with no particular use for calculus. Whatever the reason, buying the right self-study textbook can make independent learning more enjoyable and effective.
Standard college calculus textbooks cost $100-$120 and present math concepts in a dry manner without much explanation, since it's assumed students have a teacher to guide them. But luckily there are many high-quality, thorough, well-written calculus books that won't break your budget. Here are reviews of three excellent calculus textbooks ideal for the self-directed student.
Calculus Made Easy, by Silvanus Thompson and Martin Gardner
Silvanus Thompson's classic calculus primer offers the self-study student the best of both worlds: mathematical rigor, and down-to-earth plain English explanations of complicated concepts thanks to Martin Gardner's modern editing. This book is ideal for people in engineering and sciences who want to learn calculus formally with out getting lost in the details of mathematical proofs.
Calculus Made Easy was first published in 1910, and the original text is now in the public domain and available for download as an ebook at Project Gutenberg. Nonetheless, the modern print edition from St. Martin's Press has valuable additions by Martin Gardner, one of the most renowned writers of popular math and science. The latest edition has introductory chapters covering algebra, functions, and limits, so it's more accessible to students with a weaker mathematical background.
Not only does the book cover the how of basic procedures -- taking derivatives, computing integrals -- but it also explains the why in a more straightforward manner than standard calculus textbooks, which emphasize formal mathematical rigor at the expense of clarity, or gloss over complex topics due to limited space. The proofs that are presented are more elegant and less technnical than in a traditional calculus textbook, and as a result the book is only 300 pages long.
Calculus Made Easy aims to give students an intuitive understanding of calculus they might have missed out on in a traditional classroom course. Martin Gardner also added an index of recreational calculus exercises as an appendix, so students can appreciate both the practicality and beauty of calculus in solving a wide variety of practical and theoretical problems.
Calculus For Dummies, by Mark Ryan, from the "For Dummies" Series
The "For Dummies" math and science guides always live up to their name and break down complex topics in a way that even a self-proclaimed dummy can understand. Calculus For Dummies is no exception. If you're a student who just needs to learn how to do calculus, and you neither care why nor have much interest in formal proofs, this is the book for you.
Calculus For Dummies works like an instruction manual for solving typical problems in differential calculus and integral calculus, or Calc I and Calc II, as the courses are often named. This book lays out definitions of terms commonly used in calculus with clear and plain English, which will ease the minds of students who run the other way when they see technical math jargon. In fact, the book consciously avoids overuse of jargon.
All example problems are carefully worked out in step-by-step detail, rather than "left to the reader" as is the case with standard calculus texts. Calculus For Dummies is so friendly and gentle, students enrolled in regular classroom courses often buy this book to supplement to the more imposing Stewart Calculus textbook.
Essential Calculus with Applications (Dover Books on Mathematics), by Richard Silverman
Mathematicians and scientists love Dover Publication's cheap reprints of classic textbooks, and many of the books in their catalogue are classics for good reason. Essential Calculus with Applications is lean with little fluff, appropriate for a student who appreciates mathematical rigor and formal proofs. Content-wise, it's nearly as dense as Stewart Calculus or any other standard classroom text, but only a fraction of the cost.
Originally published in 1977, Silverman's book covers the essential calculus techniques needed for engineering and science, and even includes some worked-out example problems. The section on differential calculus is thorough, while the chapter on integration has been pared down to highlight only the most important techniques for the most commonly encountered problems.
Essential Calculus with Applications also includes a section on solving certain types of differential equations, and touches on multivariable calculus, which is going a lot further than any other book in its price range. This book is great for a real self-starter, but maybe not so good for a student who needs more hand-holding.