Integration is treated before differentiation--this is a departure from most modern texts, but it is historically correct, and it is the best way to establish the true connection between the integral and the derivative. Proofs of all the important theorems are given, generally preceded by geometric or intuitive discussion. This Second Edition introduces the mean-value theorems and their applications earlier in the text, incorporates a treatment of linear algebra, and contains many new and easier exercises. As in the first edition, an interesting historical introduction precedes each important new concept.

    Basic concepts of algebra are introduced which leads to discussion of quadratic and cubic equations, simultaneous equations as well as imaginary & transcendental numbers.

    It should be read by prospective and current calculus students and by their teachers. Even someone who has completely mastered the technical side of the subject can benefit from being reminded of the essentially simple ideas and the calculational needs that led mathematicians to develop the rather complex machinery of calculus. Sawyer deals with it all, from what background a student needs to begin, to the study of speed and acceleration, to graphing (slope and curvature), to areas, volumes, and the integral. Calculus, invented by Newton and Leibniz in the seventeenth century, has played a decisive role in the development of mathematics and the growth of our present technological society. It is an indispensable tool of both the pure and applied sciences and is one of the cornerstones of modern mathematics. It has provided ways of understanding such phenomena as the velocity of a moving object at any moment, the rate at which moving objects change their speeds and, more generally, the way in which quantities vary as factors affecting them change. In this book, the author tells what calculus is about in simple nontechnical language, understandable to any interested reader. W.W. Sawyer was born in St Ives, Hunts, England in 1911. He attended Highgate School and St. John's College, Cambridge, where he specialized in the mathematics of quantum theory and relativity. He has taught at Leicester College of Technology and has lectured in mathematics at universities in Dundee, Manchester, Ghana, New Zealand, Illinois and Connecticut. In 1965 he became a professor jointly to the departments of mathematics and education at the University of Toronto, retiring in July 1976. His books include Mathematician's Delight, Prelude to Mathematics, A Concrete Approach to Abstract Algebra and An Engineering Approach to Linear Algebra.Content: What must you know to learn about calculus? The study of speed The simplest case of varying speed The higher powers Extending our results Calculus and graphs Acceleration and curvature The reverse problem Circles and spheres, squares and cubes Intuition and logic.

    Along the way, you will see characterizations of the rationals and of certain special (Liouville) transcendental numbers. pThis material is basic to all of algebra and analysis. Professor Niven's book may be read with profit by interested high school students as well as by college students and others who want to know more about the basic aspects of pure mathematics. Most readers will find the early chapters well within their grasp while ambitious readers will profit by the more advanced material to be found in later chapters.

    It sounds simple…but is it? This elegant, accessible, and playful book artfully illuminates one of the most intriguing ideas in mathematics. Lillian Lieber presents an entertaining, yet thorough, explanation of the concept and cleverly connects mathematical reasoning to larger issues in society. Infinity includes a new foreword by Harvard professor Barry Mazur."Another excellent book for the lay reader of mathematics…In explaining [infinity], the author introduces the reader to a good many other mathematical terms and concepts that seem unintelligible in a formal text but are much less formidable when presented in the author's individual and very readable style."—Library Journal"Mrs. Lieber, in this text illustrated by her husband, Hugh Gray Lieber, has tackled the formidable task of explaining infinity in simple terms, in short line, short sentence technique popularized by her in The Education of T.C. MITS."—Chicago Sunday TribuneLillian Lieber was the head of the Department of Mathematics at Long Island University. She wrote a series of lighthearted (and well-respected) math books in the 1940s, including The Einstein Theory of Relativity and The Education of T.C. MITS (also published by Paul Dry Books).Hugh Gray Lieber was the head of the Department of Fine Arts at Long Island University. He illustrated many books written by his wife Lillian.Barry Mazur is a mathematician and is the Gerhard Gade University Professor at Harvard University. He is the author of Imagining Numbers (particularly the square root of minus fifteen). He has won numerous honors in his field, including the Veblen Prize, Cole Prize, Steele Prize, and Chauvenet Prize.

    B. Sevart, Department of Mechanical Engineering, University of Wichita"An extremely useful textbook for both formal classes and for self-study." — Society for Industrial and Applied MathematicsEngineers often do not have time to take a course in complex variable theory as undergraduates, yet is is one of the most important and useful branches of mathematics, with many applications in engineering. This text is designed to remedy that need by supplying graduate engineering students (especially electrical engineering) with a course in the basic theory of complex variables, which in turn is essential to the understanding of transform theory. Presupposing a good knowledge of calculus, the book deals lucidly and rigorously with important mathematical concepts, striking an ideal balance between purely mathematical treatments that are too general for the engineer, and books of applied engineering which may fail to stress significant mathematical ideas.The text is divided into two basic parts: The first part (Chapters 1–7) is devoted to the theory of complex variables and begins with an outline of the structure of system analysis and an explanation of basic mathematical and engineering terms. Chapter 2 treats the foundation of the theory of a complex variable, centered around the Cauchy-Riemann equations. The next three chapters — conformal mapping, complex integration, and infinite series — lead up to a particularly important chapter on multivalued functions, explaining the concepts of stability, branch points, and riemann surfaces. Numerous diagrams illustrate the physical applications of the mathematical concepts involved.The second part (Chapters 8–16) covers Fourier and Laplace transform theory and some of its applications in engineering, beginning with a chapter on real integrals. Three important chapters follow on the Fourier integral, the Laplace integral (one-sided and two-sided) and convolution integrals. After a chapter on additional properties of the Laplace integral, the book ends with four chapters (13–16) on the application of transform theory to the solution of ordinary linear integrodifferential equations with constant coefficients, impulse functions, periodic functions, and the increasingly important Z transform. Dr. LePage's book is unique in its coverage of an unusually broad range of topics difficult to find in a single volume, while at the same time stressing fundamental concepts, careful attention to details and correct use of terminology. An extensive selection of interesting and valuable problems follows each chapter, and an excellent bibliography recommends further reading. Ideal for home study or as the nucleus of a graduate course, this useful, practical, and popular (8 printings in its hardcover edition) text offers students, engineers, and researchers a careful, thorough grounding in the math essential to many areas of engineering. "An outstanding job." — American Mathematical Monthly

    This book serves both as a completely self-contained introduction and as an exposition of new results in the field of recursive function theory and its application to formal systems.

    But professional mathematicians, in dealing with quantities that can be ordered according to their size, often are more interested in unequal magnitudes that areequal. This book provides an introduction to the fascinating world of inequalities, beginning with a systematic discussion of the relation "greater than" and the meaning of "absolute values" of numbers, and ending with descriptions of some unusual geometries. In the course of the book, the reader wil encounter some of the most famous inequalities in mathematics.