*The Theory of Calculus*

**Author**: Kenneth A. Ross

**Publisher:** Springer Science & Business Media

**ISBN:** 1461462711

**Category:** Mathematics

**Page:** 412

**View:** 950

For over three decades, this best-selling classic has been used by thousands of students in the United States and abroad as a must-have textbook for a transitional course from calculus to analysis. It has proven to be very useful for mathematics majors who have no previous experience with rigorous proofs. Its friendly style unlocks the mystery of writing proofs, while carefully examining the theoretical basis for calculus. Proofs are given in full, and the large number of well-chosen examples and exercises range from routine to challenging. The second edition preserves the book’s clear and concise style, illuminating discussions, and simple, well-motivated proofs. New topics include material on the irrationality of pi, the Baire category theorem, Newton's method and the secant method, and continuous nowhere-differentiable functions.

Elementary Analysis, Volume 1 introduces the reader to elementary analysis in an informal manner and provides the practical experience in algebraic and analytic operations to lay a sound foundation of basic skills. The preliminary ideas are illustrated by applications to the simpler algebraic functions. Emphasis is on fundamental principles, rather than manipulative techniques. This volume is comprised of 14 chapters and begins with a discussion on number systems, covering concepts ranging from number scales to rational and real numbers, binary operations, and deductive methods. The following chapters deal with sets, vectors and congruences, and functions. Exponential and logarithmic functions, the straight line, and linear function are also considered. The remaining chapters focus on the quadratic function; the principle of mathematical induction and its applications; differentiation and the inverse process; and integration and its applications. Differential equations are presented, along with the definite integral. This book will be of particular value to teachers and students in training colleges.

Facts101 is your complete guide to Elementary Analysis. In this book, you will learn topics such as as those in your book plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.

A From the Preface: THE text of this volume is, to a considerable extent, identical with portions of corresponding chapters in Smith and Gale's "Elements of Analytic Geometry" and Granville's "Elements of the Differential and Integral Calculus." The new material is contained in the chapters on Curve Plotting (Chapter V) and Functions and Graphs (Chapter VI). At the same time, the parts which have appeared in previous books of the series have been thoroughly revised and, to a considerable extent, rewritten, to the end that the aim of the authors might be accomplished, — namely, to prepare a simple and direct exposition of those portions of mathematics beyond Trigonometry which are of importance to students of natural science. In this connection attention may be called to the intentional avoidance of anticipating difficulties, — a feature which is not common in textbooks. To particularize, processes which are natural are introduced without explanation, and exact definition is not given until the student is familiar by practice with the matter in hand. Again, in the derivation of certain formulas in the Differential Calculus the evaluation of particular limits is not undertaken until the student sees that this work must be done before the problem can be solved. In many instances, when deemed wise, a general discussion is introduced by concrete examples. This feature, so common in school texts, is strangely absent from books intended for use in colleges and technical schools. Interest in the subject is usually aroused in this way, and it is the hope of the authors that this stimulus may not be lacking when the volume is studied.