Introductiony to Calculus

From the Preface: (…) The book is addressed to students on various levels, to mathematicians, scientists, engineers. It does not pretend to make the subject easy by glossing over difficulties, but rather tries to help the genuinely interested reader by throwing light on the interconnections and purposes of the whole. Instead of obstructing the access to the wealth of facts by lengthy discussions of a fundamental nature we have sometimes postponed such discussions to appendices in the various chapters. Numerous examples and problems are given at the end of various chapters. Some are challenging, some are even difficult; most of them supplement the material in the text. In an additional pamphlet more problems and exercises of a routine character will be collected, and moreover, answers or hints for the solutions will be given. This first volume of concerned primarily with functions of a single variable, whereas the second volume will discuss the more ramified theories of calculus (…).

Active Prelude to Calculus is designed for college students who aspire to take calculus and who either need to take a course to prepare them for calculus or want to do some additional self-study. Many of the core topics of the course will be familiar to students who have completed high school. At the same time, we take a perspective on every topic that emphasizes how it is important in calculus. This text is written in the spirit of Active Calculus and is especially ideal for students who will eventually study calculus from that text. The reader will find that the text requires them to engage actively with the material, to view topics from multiple perspectives, and to develop deep conceptual understanding of ideas. Many courses at the high school and college level with titles such as “college algebra”, “precalculus”, and “trigonometry” serve other disciplines and courses other than calculus.

Investigate infinite sequences and test for convergence of infinite series

Calculus 1

Involving rigorous analysis, computational dexterity, and a breadth of applications, this text is ideal for an undergraduate honors calculus course or for an introduction to analysis. This fourth edition includes corrections as well as some additional material.

This Student Guide is exceptional, maybe even unique, among such guides in that its author, Fred Soon, was actually a student user of the textbook during one of the years we were writing and debugging the book. (He was one of the best students that year, by the way. ) Because of his background, Fred has taken, in the Guide, the point of view of an experienced student tutor helping you to learn calculus. \~ile we do not always think Fred's jokes are as funny as he does, we appreciate his enthusiasm and his desire to enter into communication with his readers; since we nearly always agree with the mathe­ matical judgements he has made in explaining the material, we believe that this Guide can serve you as a valuable supplement to our text.