Brief Calculus and Its Applications

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  • Edition: 12th
  • Format: Paperback
  • Copyright: 3/3/2009
  • Publisher: Pearson
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Normal 0 false false false Goldsteinrs"sBriefCalculus and Its Applications, Twelfth Editionis 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 formulapairing substantial amounts of graphical analysis and informal geometric proofs with an abundance of exerciseshas proven to be tremendously successful with both students and instructors. The textbook is supported by a wide array of supplements as well as MyMathLab reg; and MathXL reg; , 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 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 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 Function e 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
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.

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