Calculus Problems and Solutions Textbook - Comprehensive Guide with Step-by-Step Answers | Dover Books on Mathematics | Ideal for College Students, Self-Study & Exam Prep

When I was a young student, I assumed I would become a scientist, rather than the lawyer I turned into. So I didn't have any idea of how little use I would actually have in life for active skills in calculating integrals and the like. Inspired by the pandemic lockdown, I decided now might be a chance to review and brush up the knowledge I once acquired, and also to atone for the fact that I never exerted myself to understand trigonometric substitutions in high school calculus almost a half century ago.This book is written in the uncompromising style of the 1960s, when a career in STEM (other than in pure math, perhaps) meant you wore a lab coat and smoked a pipe. There isn't any hand-holding of the reader, and the expository interludes are terse. Many of the topics included develop the sorts of skills our ancestors found handy before they had Mathematica or even hand-held calculators, but that have been forgotten today. For example, when was the last time you saw a textbook ask you to find an explicit expression in terms of n for the nth derivative of some function (sec. 4.8)? Or put you through your paces in graphical differentiation (4.9)? Obviously, some of these lost techniques might vary in their utility today, but they give one great respect for one's elders.Despite the title of the book, solutions are rare. Mostly the book has answers, instead of solutions that show you how to do the problem. The emphasis is on calculation, not proof. Students of this book were clearly expected to send people to the Moon and such, not to dwell on abstractions.There are just shy of 1,300 problems, which is more than probably anyone would want to attempt in a single textbook. So you will have to deal with your own feelings of guilt for possibly cherry-picking only simpler ones. Cherry-picking may also explain why so many reviewers feel the problems are too easy.The author, though, notes in his Preface that "To improve understanding, some problems of a more difficult character are included, the solution of which requires deeper insight in the topics treated." He wastes no time in delivering on this promise.Take a look at problem #6 (p. 5), in a "pre-calculus" chapter on sequences. If you think this is simple in principle just by eyeballing it, take a look at the answer (p. 274), which is provided without solution. Unless you are a number-theoretic savant, could you ever reach anything remotely close to the answer without knowing it beforehand? Even knowing it, is it obvious how to reproduce it step-by-step? That fluttery feeling in your gut may encourage you to face this book with the respect it deserves.