Understanding Calculus / Edition 2

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Overview

Everything you need to know-basic essential concepts-about calculus

For anyone looking for a readable alternative to the usual unwieldy calculus text, here's a concise, no-nonsense approach to learning calculus. Following up on the highly popular first edition of Understanding Calculus, Professor H. S. Bear offers an expanded, improved edition that will serve the needs of every mathematics and engineering student, or provide an easy-to-use refresher text for engineers.

Understanding Calculus, Second Edition provides in a condensed format all the material covered in the standard two-year calculus course. In addition to the first edition's comprehensive treatment of one-variable calculus, it covers vectors, lines, and planes in space; partial derivatives; line integrals; Green's theorem; and much more. More importantly, it teaches the material in a unique, easy-to-read style that makes calculus fun to learn. By explaining calculus concepts through simple geometric and physical examples rather than formal proofs, Understanding Calculus, Second Edition, makes it easy for anyone to master the essentials of calculus.

If the dry "theorem-and-proof" approach just doesn't work, and the traditional twenty pound calculus textbook is just too much, this book is for you.

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Editorial Reviews

From the Publisher
"...expands coverage to vectors and calculus of several variables...plenty of worked out problems..." (American Mathematical Monthly, August/September 2003)

"...material included is well formulated and approachable...recommended." (Choice, Vol. 41, No. 1, September 2003)

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Product Details

  • ISBN-13: 9780471433071
  • Publisher: Wiley
  • Publication date: 2/21/2003
  • Series: IEEE Press Understanding Science and TEC
  • Edition description: REV
  • Edition number: 2
  • Pages: 320
  • Product dimensions: 7.03 (w) x 9.98 (h) x 0.59 (d)

Meet the Author

H. S. BEAR, PhD, is a prolific author who has published several pre-calculus texts and an intermediate-level differential equations text, in addition to numerous research articles. His most recent works include two more advanced texts in analysis: A Primer of Lebesgue Integration, Second Edition and An Introduction to Mathematical Analysis. A dedicated educator, Dr. Bear has taught at six major western state universities before moving to Hawaii, where he has spent most of his career. Dr. Bear has served both as Department Chairman and Graduate Chairman at the University of Hawaii.

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Table of Contents

Author’s Message to the Reader.

Annotated Table of Contents.

Acknowledgments.

Chapter 1: Lines.

Chapter 2: Parabolas, Ellipses, Hyperbolas.

Chapter 3: Differentiation.

Chapter 4: Differentiation Formulas.

Chapter 5: The Chain Rule.

Chapter 6: Trigonometric Functions.

Chapter 7: Exponential Functions and Logarithms.

Chapter 8: Inverse Functions.

Chapter 9: Derivatives and Graphs.

Chapter 10: Following the Tangent Line.;

Chapter 11: The Indefinite Integral.

Chapter 12: The Definite Integral.

Chapter 13: Work, Volume, and Force.

Chapter 14: Parametric Equations.

Chapter 15: Change of Variable.

Chapter 16: Integrating Rational Functions.

Chapter 17: Integrations by Parts.

Chapter 18: Trigonometric Integrals.

Chapter 19: Trigonometric Substitution.

Chapter 20: Numerical Integration.

Chapter 21: Limit At ∞; Sequences.

Chapter 22: Improper Integrals.

Chapter 23: Series.

Chapter 24: Power Series.

Chapter 25: Taylor Polynomials.

Chapter 26: Taylor Series.

Chapter 27: Separable Differential Equations.

Chapter 28: First-Order Linear Equations.

Chapter 29: Homogeneous Second-Order Linear Equations.

Chapter 30: Nonhomogeneous Second-Order Equations.

Chapter 31: Vectors.

Chapter 32: The Dot Product.

Chapter 33: Lines and Planes in Space.

Chapter 34: Surfaces.

Chapter 35: Partial Derivatives.

Chapter 36: Tangent Plane and Differential Approximation.

Chapter 37: Chain Rules.

Chapter 38: Gradient and Directional Derivatives.

Chapter 39: Maxima and Minima.

Chapter 40: Double Integrals.

Chapter 41: Line Integrals.

Chapter 42: Green’s Theorem.

Chapter 43: Exact Differentials.

Answers.

Index.

About the Authors.

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