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Calculus and Its Applications

Calculus and Its Applications - 10th edition

Calculus and Its Applications - 10th edition

ISBN13: 9780130466105

ISBN10: 0130466107

Calculus and Its Applications by Larry J. Goldstein, David I. Schneider and David C. Lay - ISBN 9780130466105
Edition: 10TH 04
Copyright: 2004
Publisher: Prentice Hall, Inc.
Published: 2004
International: No
Calculus and Its Applications by Larry J. Goldstein, David I. Schneider and David C. Lay - ISBN 9780130466105

ISBN13: 9780130466105

ISBN10: 0130466107


These extremely readable, highly regarded, and widely adopted texts present innovative ways for applying calculus to real-world situations in the business, economics, life science, and social science disciplines. The texts' straightforward, engaging approach fosters the growth of both the student's mathematical maturity and his/her appreciation for the usefulness of mathematics. The authors' tried and true formula -- pairing substantial amounts of graphical analysis and informal geometric proofs with an abundance of hands-on exercises -- has proven to be tremendously successful with both students and instructors.


  • NEW -- With contributions from Nahkle Asmar, University of Missouri, Columbia.
  • NEW -- Additional and Revised Exercises.
  • Over 400 new and revised exercises include problems that challenge the more capable students and problems designed to aid students with limited math background.
  • New genre of problems tests the students' understanding of mathematical formulas.
  • Increased number of problems that stress the ability to read graphs.
  • Many new applications from business, medicine, life and social sciences -- based on current real-world data.
  • Over 90 new problems on differential equations and their applications.
  • NEW -- Additional and Revised Art -- Over 80 new and revised graphs have been added.
  • Enhances examples and exercises.
  • NEW -- Revision of Sections.
  • Section 2.6 topics have been reordered and a detailed example and figures were added to allow an easier access to the inventory control problem from business.
  • Worked examples and figures were added to Section 5.3 to provide clearer and more accessible discussion of the topic of elasticity of demand from economics.
  • The topics of Section 7.6 on nonlinear regression have been reordered. The Pareto distribution is used as an example of a power regression function to model the distribution of income of the US male population in 2001. Results from this section are compared to actual statistical data.
  • Section 10.1 has been expanded to include the topic of slope fields and the geometric interpretation of a differential equation. Using graphs to study solutions of differential equations and their real-life applications is emphasized.
  • NEW -- Two new sections on differential equations.
  • Section 10.3 contains several worked examples and figures that provide a smooth and accessible study of the technique of integrating factor for solving first order linear differential equations.
  • Section 10.4 presents exciting real-life applications, including investment accounts, paying off car loans, home mortgages, Newton's law of cooling, population models with migration and many problems from medicine.
  • Carefully designed exercise sets.
  • Challenges students to make their own connections.
  • Practice Problems.
  • Motivates students with supported tasks.
  • Self-Contained Material.
  • Allows students with limited math knowledge to access information.
  • Real-life applications/scenarios.
  • Demonstrates to students the relevance of their studies.
  • Easy-to-understand instructions for using calculators are provided.
  • Eliminates the need for a manual.
  • Provides more help available on the website.

Author Bio

Goldstein,Larry J. : Goldstein Educational Technologies

Schneider, David I. : University of Maryland

Lay, David C. : University of Maryland

Table of Contents

Table of Contents

Index of Applications.

0. 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.
Appendix: Graphing Functions Using Technology.

1. 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.

2. Applications of the Derivative.

Describing Graphs of Functions.
The First and Second Derivative Rules.
Curve Sketching (Introduction.)
Curve Sketching (Conclusion.)
Optimization Problems.
Further Optimization Problems.
Applications of Derivatives to Business and Economics.

3. Techniques of Differentiation.

The Product and Quotient Rules.
The Chain Rule and the General Power Rule.
Implicit Differentiation and Related Rates.

4. The Exponential and Natural Logarithm Functions.

Exponential Functions.
The Exponential Function e^x.
Differentiation of Exponential Functions.
The Natural Logarithm Function.
The Derivative of ln x.
Properties of the Natural Logarithm Function.

5. 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.

6. The Definite Integral.

Areas and Reimann Sums.
Definite Integrals and the Fundamental Theorem.
Areas in the xy-Plane.
Applications of the Definite Integral.

7. 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.
Nonlinear Regression.
Double Integrals.

8. The Trigonometric Functions.

Radian Measure of Angles.
The Sine and the Cosine.
Differentiation of sin t and cos t.
The Tangent and Other Trigonometric Functions.

9. Techniques of Integration.

Integration by Substitution. Integration by Parts. Evaluation of Definite Integrals. Approximation of Definite Integrals. Some Applications of the Integral. Improper Integrals.

10. Differential Equations.

Solutions of Differential Equations.
Separation of Variables.
Numerical Solution of Differential Equations.
Qualitative Theory of Differential Equations.
Applications of Differential Equations.

11. Taylor Polynomials and Infinite Series.

Taylor Polynomials.
The Newton-Raphson Algorithm.
Infinite Series.
Series with Positive Terms.
Taylor Series.

12. Probability and Calculus.

Discrete Random Variables.
Continuous Random Variables.
Expected Value and Variance.
Exponential and Normal Random Variables.
Poisson and Geometric Random Variables.


A. Calculus and the TI-82 Calculator.
B. Calculus and the TI-83 Calculator.
C. Calculus and the TI-85 Calculator.
D. Calculus and the TI-86 Calculator.
E. Areas Under the Standard Normal Curve.

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