# Calculus and Its Applications

**by**Goldstein, Larry J.; Schneider, David I.; Lay, David C.; Asmar, Nakhle H.

### 9780321571304

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## Summary

**KEY BENFIT: Goldstein’s Calculus and Its Applications, Twelfth Edition** is a comprehensive print and online program for readers interested in business, economics, life science, or social sciences. Without sacrificing mathematical integrity, the book clearly presents the concepts with a large quantity of exceptional, in-depth exercises. The authors' proven formula–pairing substantial amounts of graphical analysis and informal geometric proofs with an abundance of exercises–has proven to be tremendously successful with both students and instructors. The textbook is supported by a wide array of supplements as well as MyMathLab® and MathXL®, the most widely adopted and acclaimed online homework and assessment system on the market.

Functions; The Derivative; Applications of the Derivative; Techniques of Differentiation; Logarithm Functions; Applications of the Exponential and Natural Logarithm Functions; The Definite Integral; Functions of Several Variables; The Trigonometric Functions; Techniques of Integration; Differential Equations; Taylor Polynomials and Infinite Series; Probability and Calculus

**For all readers interested in applied calculus.**

## Author Biography

**Larry Goldstein** has received several distinguished teaching awards, given more than fifty Conference and Colloquium talks & addresses, and written more than fifty books in math and computer programming. He received his PhD at Princeton and his BA and MA at the University of Pennsylvania. He also teaches part time at Drexel University.

**David Schneider**, who is known widely for his tutorial software, holds a BA degree from Oberlin College and a PhD from MIT. He is currently an associate professor of mathematics at the University of Maryland. He has authored eight widely used math texts, fourteen highly acclaimed computer books, and three widely used mathematics software packages. He has also produced instructional videotapes at both the University of Maryland and the BBC.

** **

**David C. Lay **holds a BA from Aurora University (Illinois), and an MA and PhD from the University of California at Los Angeles. Lay has been an educator and research mathematician since 1966, mostly at the University of Maryland—College Park. He has also served as visiting professor at the University of Amsterdam, the Free University in Amsterdam, and the University of Kaiserslautern in Germany. He has published more than thirty research articles in functional analysis and linear algebra.

**Nakhle H. Asmar**received his PhD in mathematics from the University of Washington in 1986. After spending two years on the faculty at California State University—Long Beach, he joined the University of Missouri—Columbia in 1988, where he is currently Professor of Mathematics. He has received several teaching awards from the University of Missouri, including the William T. Kemper Fellowship Award, the Arts and Science Student Government Purple Chalk Award, and the Provost’s Outstanding Junior Faculty Teaching Award.

## Table of Contents

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Functions | |

Functions and Their Graphs | |

Some Important Functions | |

The Algebra of Functions | |

Zeros of Functions-The Quadratic Formula and Factoring | |

Exponents and Power Functions | |

Functions and Graphs in Applications | |

The Derivative | |

The Slope of a Straight Line | |

The Slope of a Curve at a Point | |

The Derivative | |

Limits and the Derivative | |

Differentiability and Continuity | |

Some Rules for Differentiation | |

More About Derivatives | |

The Derivative as a Rate of Change | |

Applications of the Derivative | |

Describing Graphs of Functions | |

The First and Second Derivative Rules | |

The First and Second Derivative Tests and Curve Sketching | |

Curve Sketching (Conclusion) | |

Optimization Problems | |

Further Optimization Problems | |

Applications of Derivatives to Business and Economics | |

Techniques of Differentiation | |

The Product and Quotient Rules | |

The Chain Rule and the General Power Rule | |

Implicit Differentiation and Related Rates | |

Logarithm Functions | |

Exponential Functions | |

The Exponential Functione x | |

Differentiation of Exponential Functions | |

The Natural Logarithm Function | |

The Derivative of lnx | |

Properties of the Natural Logarithm Function | |

Applications of the Exponential and Natural Logarithm Functions | |

Exponential Growth and Decay | |

Compound Interest | |

Applications of the Natural Logarithm Function to Economics | |

Further Exponential Models | |

The Definite Integral | |

Antidifferentiation | |

Areas and Riemann Sums | |

Definite Integrals and the Fundamental Theorem | |

Areas in thexy-Plane | |

Applications of the Definite Integral | |

Functions of Several Variables | |

Examples of Functions of Several Variables | |

Partial Derivatives | |

Maxima and Minima of Functions of Several Variables | |

Lagrange Multipliers and Constrained Optimization | |

The Method of Least Squares | |

Double Integrals | |

The Trigonometric Functions | |

Radian Measure of Angles | |

Table of Contents provided by Publisher. All Rights Reserved. |