**Author**: Kenneth A. Ross

**Publisher:** CUP Archive

**ISBN:**

**Category:**

**Page:** 276

**View:** 965

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.

Elementary Analysis, Volume 2 introduces several of the ideas of modern mathematics in a casual manner and provides the practical experience in algebraic and analytic operations that lays a sound foundation of basic skills. This book focuses on the nature of number, algebraic and logical structure, groups, rings, fields, vector spaces, matrices, sequences, limits, functions and inverse functions, complex numbers, and probability. The logical structure of analysis given through the treatment of differentiation and integration, with applications to the trigonometric and logarithmic functions, is also briefly discussed. This volume begins with a description of the trigonometric functions of the general angle and an introduction to the binomial theorem and series. The rest of the chapters cover the numerical solution of equations, analytical geometry, Argand Diagram, numerical methods, and methods of approximation that form an important section of modern applied mathematics. This publication is valuable to teachers and students in training colleges.

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.