Essential Calculus with Applications

John Dewey, Richard A. Silverman

$34.95

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English

Dover
01 August 1989

Mathematics & Sciences; Calculus

Series: Dover Books on Mathema 1.4tics

"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."

By: John Dewey, Richard A. Silverman
Imprint: Dover
Country of Publication: United States
Dimensions: Height: 235mm, Width: 155mm, Spine: 15mm
Weight: 406g
ISBN: 9780486660974
ISBN 10: 0486660974
Series: Dover Books on Mathema 1.4tics
Publication Date: 01 August 1989
Audience: College/higher education , A / AS level
Format: Paperback
Publisher's Status: Unspecified

To the Instructor; To the Student Chapter 1. Mathematical Background 1.1 Introductory Remarks 1.2 Sets 1.3 Numbers 1.4 Inequalities 1.5 The Absolute Value 1.6 Intervals and Neighborhoods 1.7 Rectangular Coordinates 1.8 Straight Lines 1.9 More about Straight Lines Chapter 2. Differential Calculus 2.1 Functions 2.2 More about Functions 2.3 Graphs 2.4 Derivatives and Limits 2.5 More about Derivatives 2.6 More about Limits 2.7 Differentiation Technique 2.8 Further Differentiation Technique 2.9 Other Kinds of Limits Chapter 3. Differentiation as a Tool 3.1 Velocity and Acceleration 3.2 Related Rates and Business Applications 3.3 Properties of Continuous Functions 3.4 Properties of Differentiable Functions 3.5 Applications of the Mean Value Theorem 3.6 Local Extrema 3.7 Concavity and Inflection Points 3.8 Optimization Problems Chapter 4. Integral Calculus 4.1 The Definite Integral 4.2 Properties of Definite Integrals 4.3 The Logarithm 4.4 The Exponential 4.5 More about the Logarithm and Exponential 4.6 Integration Technique 4.7 Improper Integrals Chapter 5. Integration as a Tool 5.1 Elementary Differential Equations 5.2 Problems of Growth and Decay 5.3 Problems of Motion Chapter 6. Functions of Several Variables 6.1 From Two to n Dimensions 6.2 Limits and Differentiation 6.3 The Chain Rule 6.4 Extrema in n Dimensions Tables; Selected Hints and Answers; Supplementary Hints and Answers; Index

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Essential Calculus with Applications

John Dewey, Richard A. Silverman

$34.95

Paperback

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