Technical Calculus with Analytic Geometry

Автор: Richard A. Silverman
Название: Modern Calculus and Analytic Geometry
ISBN: 0486421007 ISBN-13(EAN): 9780486421001
Издательство: Dover
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Описание: A self-contained text for an introductory course, this volume places strong emphasis on physical applications. Key elements of differential equations and linear algebra are introduced early and are consistently referenced, all theorems are proved using elementary methods, and numerous worked-out examples appear throughout. The highly readable text approaches calculus from the student's viewpoint and points out potential stumbling blocks before they develop. A collection of more than 1,600 problems ranges from exercise material to exploration of new points of theory -- many of the answers are found at the end of the book; some of them worked out fully so that the entire process can be followed. This well-organized, unified text is copiously illustrated, amply cross-referenced, and fully indexed.

Автор: Eisenhart Luther Pfahler
Название: Coordinate Geometry
ISBN: 0486442616 ISBN-13(EAN): 9780486442617
Издательство: Dover
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Описание: A thorough, complete, and unified introduction, this volume affords exceptional insights into coordinate geometry. It makes extensive use of determinants, but no previous knowledge is assumed; they are introduced from the beginning as a natural tool for coordinate geometry. Invariants of conic sections and quadric surfaces receive full treatments. Algebraic equations on the first degree in two and three unknowns are carefully reviewed and carried farther than is usual in algebra courses. Throughout the book, results are formulated precisely, with clearly stated theorems. More than 500 helpful exercises throughout the text incorporate -- often in rather novel settings -- each idea after its full and careful explanation. 1939 edition.

Автор: Silverman, Richard A.
Название: Essential Calculus with Applications
ISBN: 0486660974 ISBN-13(EAN): 9780486660974
Издательство: Dover
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Описание: Calculus is an extremely powerful tool for solving a host of practical problems in fields as diverse as physics, biology, and economics, to mention just a few. In this rigorous but accessible text, a noted mathematician introduces undergraduate-level students to the problem-solving techniques that make a working knowledge of calculus indispensable for any mathematician.
The author first applies the necessary mathematical background, including sets, inequalities, absolute value, mathematical induction, and other "precalculus" material. Chapter Two begins the actual study of differential calculus with a discussion of the key concept of function, and a thorough treatment of derivatives and limits. In Chapter Three differentiation is used as a tool; among the topics covered here are velocity, continuous and differentiable functions, the indefinite integral, local extrema, and concrete optimization problems. Chapter Four treats integral calculus, employing the standard definition of the Riemann integral, and deals with the mean value theorem for integrals, the main techniques of integration, and improper integrals. Chapter Five offers a brief introduction to differential equations and their applications, including problems of growth, decay, and motion. The final chapter is devoted to the differential calculus of functions of several variables.
Numerous problems and answers, and a newly added section of "Supplementary Hints and Answers," enable the student to test his grasp of the material before going on. Concise and well written, this text is ideal as a primary text or as a refresher for anyone wishing to review the fundamentals of this crucial discipline.

Автор: Keisler H. Jerome
Название: Elementary Calculus: An Infinitesimal Approach
ISBN: 0486484521 ISBN-13(EAN): 9780486484525
Издательство: Dover
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Описание: This first-year calculus book is centered around the use of infinitesimals, an approach largely neglected until recently for reasons of mathematical rigor. It exposes students to the intuition that originally led to the calculus, simplifying their grasp of the central concepts of derivatives and integrals. The author also teaches the traditional approach, giving students the benefits of both methods.
Chapters 1 through 4 employ infinitesimals to quickly develop the basic concepts of derivatives, continuity, and integrals. Chapter 5 introduces the traditional limit concept, using approximation problems as the motivation. Later chapters develop transcendental functions, series, vectors, partial derivatives, and multiple integrals. The theory differs from traditional courses, but the notation and methods for solving practical problems are the same. The text suggests a variety of applications to both natural and social sciences.

Автор: Grant, Gail
Название: Technical Manual and Dictionary of Classical Ballet
ISBN: 0486218430 ISBN-13(EAN): 9780486218434
Издательство: Dover
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Описание: From "adagio" to "voyage, " over 800 steps, movements, poses, and concepts are fully defined. A pronunciation guide and cross-references to alternate names for similar steps and positions that vary from the Russian to the French or Italian schools are also invaluable aids. "More information available in one book than we have ever had before." "Dance Magazine.""

Автор: Posamentier, Alfred S.
Название: Geometry, Its Elements and Structure: Second Edition
ISBN: 0486492672 ISBN-13(EAN): 9780486492674
Издательство: Dover
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Описание: Analyses oral argument transcripts from every case decided from 1998 through 2007 as well as the complete collection of notes kept during oral arguments by Justice Lewis F. Powell and Justice Harry A. Blackmun. This study represents a major step forward in the understanding of coalition formation, which is a crucial aspect of many areas of political debate and decision making.