Buy Best Schaum's Outline of Vector Analysis, 2ed (Schaum's Outline Series) for $13.83

Schaum's Outline of Vector Analysis, 2ed (Schaum's Outline Series)

The guide to vector analysis that helps students study faster, learn better, and get top grades

More than 40 million students have trusted Schaum's to help them study faster, learn better, and get top grades. Now Schaum's is better than ever-with a new look, a new format with hundreds of practice problems, and completely updated information to conform to the latest developments in every field of study.

Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores!

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Buy A Guide to Cauchy's Calculus - A Translation and Analysis of Calcul Infinitesimal for $130.91

A Guide to Cauchy's Calculus - A Translation and Analysis of Calcul Infinitesimal

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A Guide to Cauchy's Calculus follows Augustin-Louis Cauchy's development of the rigorous version of calculus we are taught today in an introductory calculus sequence. Cauchy's original 1823 text (his first devoted to calculus), Résumé des leçons sur le calcul infinitésimal, "Summary of Lectures on the Infinitesimal Calculus," is the central focus of this book and will be studied in depth. Contained here are the complete English translations of the relevant lectures within Cauchy's text covering his real, single variable, differential and integral calculus. In addition, a simply written line-by-line explanation for each of Cauchy's lectures is included which clarifies his thinking and his proofs, solves his example problems, discusses his misconceptions, and contains supplemental proofs of fundamental concepts Cauchy felt were self-evident. Comparisons between Cauchy's method of presentation and a modern treatment are made throughout the book by including today's standard definitions and proofs of the fundamental theorems of the calculus alongside those developed by Cauchy in his text. In total, this book will serve as a complete resource for anyone who teaches calculus or is interested in fully understanding the first calculus sequence at the high school or college level.

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Buy Limits, Limits Everywhere: The Tools of Mathematical Analysis for $30.66

Limits, Limits Everywhere: The Tools of Mathematical Analysis

A quantity can be made smaller and smaller without it ever vanishing. This fact has profound consequences for science, technology, and even the way we think about numbers. In this book, we will explore this idea by moving at an easy pace through an account of elementary real analysis and, in particular, will focus on numbers, sequences, and series.

Almost all textbooks on introductory analysis assume some background in calculus. This book doesn't and, instead, the emphasis is on the application of analysis to number theory. The book is split into two parts. Part 1 follows a standard university course on analysis and each chapter closes with a set of exercises. Here, numbers, inequalities, convergence of sequences, and infinite series are all covered. Part 2 contains a selection of more unusual topics that aren't usually found in books of this type. It includes proofs of the irrationality of e and ?, continued fractions, an introduction to the Riemann zeta function, Cantor's theory of the infinite, and Dedekind cuts. There is also a survey of what analysis can do for the calculus and a brief history of the subject.

A lot of material found in a standard university course on "real analysis" is covered and most of the mathematics is written in standard theorem-proof style. However, more details are given than is usually the case to help readers who find this style daunting. Both set theory and proof by induction are avoided in the interests of making the book accessible to a wider readership, but both of these topics are the subjects of appendices for those who are interested in them. And unlike most university texts at this level, topics that have featured in popular science books, such as the Riemann hypothesis, are introduced here. As a result, this book occupies a unique position between a popular mathematics book and a first year college or university text, and offers a relaxed introduction to a fascinating and important branch of mathematics.

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