Calculus and Its Applications / Edition 10

Calculus and Its Applications / Edition 10

by Larry Joel Goldstein, David C. Lay, David I. Schneider, David I. Schneider
     
 

ISBN-10: 0130466107

ISBN-13: 9780130466105

Pub. Date: 03/26/2003

Publisher: Prentice Hall

This extremely readable, highly regarded, and widely adopted text present innovative ways for applying calculus to real-world situations in the business, economics, life science, and social science disciplines. The text's straightforward, engaging approach fosters the growth of both mathematical maturity and an appreciation for the usefulness of mathematics. The

Overview

This extremely readable, highly regarded, and widely adopted text present innovative ways for applying calculus to real-world situations in the business, economics, life science, and social science disciplines. The text's straightforward, engaging approach fosters the growth of both mathematical maturity and an 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 exercizes — has proven to be tremendously successful. Functions, derivatives, applications of the derivative, techniques of differentiations, exponential and natural logarithm functions, definite integral, variables, trigonometric functions, integration, differential equations, Taylor polynomials and probability. For individuals interested in an introduction to calculus applications.

Product Details

ISBN-13:
9780130466105
Publisher:
Prentice Hall
Publication date:
03/26/2003
Edition description:
Older Edition
Pages:
736
Product dimensions:
8.10(w) x 10.22(h) x 1.30(d)

Related Subjects

Table of Contents

Contents

Preface

Introduction 

 

0 Functions

0.1 Functions and Their Graphs

0.2 Some Important Functions

0.3 The Algebra of Functions

0.4 Zeros of Functions—The Quadratic Formula and Factoring

0.5 Exponents and Power Functions

0.6 Functions and Graphs in Applications

 

1 The Derivative

1.1 The Slope of a Straight Line

1.2 The Slope of a Curve at a Point

1.3 TheDerivative

1.4 Limits and the Derivative

1.5 Differentiability and Continuity

1.6 Some Rules for Differentiation

1.7 More About Derivatives

1.8 The Derivative as a Rate of Change

 

2 Applications of the Derivative

2.1 Describing Graphs of Functions

2.2 The First and Second Derivative Rules

2.3 The First and Second Derivative Tests and Curve Sketching 

2.4 Curve Sketching (Conclusion)

2.5 Optimization Problems

2.6 Further Optimization Problems

2.7 Applications of Derivatives to Business and Economics

 

3 Techniques of Differentiation

3.1 The Product and Quotient Rules

3.2 The Chain Rule and the General Power Rule

3.3 Implicit Differentiation and Related Rates

 

4 Logarithm Functions

4.1 Exponential Functions

4.2 The Exponential Function ex

4.3 Differentiation of Exponential Functions

4.4 The Natural Logarithm Function

4.5 The Derivative of ln x

4.6 Properties of the Natural Logarithm Function 

 

5 Applications of the Exponential and

Natural Logarithm Functions

5.1 Exponential Growth and Decay

5.2 Compound Interest

5.3 Applications of the Natural Logarithm Function to Economics

5.4 Further Exponential Models

 

6 The Definite Integral

6.1 Antidifferentiation

6.2 Areas and Riemann Sums

6.3 Definite Integrals and the Fundamental Theorem

6.4 Areas in the xy-Plane

6.5 Applications of the Definite Integral

 

7 Functions of Several Variables

7.1 Examples of Functions of Several Variables

7.2 Partial Derivatives

7.3 Maxima and Minima of Functions of Several Variables

7.4 Lagrange Multipliers and Constrained Optimization

7.5 The Method of Least Squares

7.6 Double Integrals

 

 

8 The Trigonometric Functions

8.1 Radian Measure of Angles

8.2 The Sine and the Cosine

8.3 Differentiation and Integration of sin t and cos t

8.4 The Tangent and Other Trigonometric Functions

 

9 Techniques of Integration

9.1 Integration by Substitution

9.2 Integration by Parts

9.3 Evaluation of Definite Integrals

9.4 Approximation of Definite Integrals

9.5 Some Applications of the Integral

9.6 Improper Integrals

 

10 Differential Equations

10.1 Solutions of Differential Equations

10.2 Separation of Variables

10.3 First-Order Linear Differential Equations

10.4 Applications of First-Order Linear Differential Equations

10.5 Graphing Solutions of Differential Equations

10.6 Applications of Differential Equations

10.7 Numerical Solution of Differential Equations

 

11 Taylor Polynomials and Infinite Series

11.1 Taylor Polynomials

11.2 The Newton-Raphson Algorithm

11.3 Infinite Series

11.4 Series with Positive Terms

11.5 Taylor Series

 

12 Probability and Calculus

12.1 Discrete Random Variables

12.2 Continuous Random Variables

12.3 Expected Value and Variance

12.4 Exponential and Normal Random Variables

12.5 Poisson and Geometric Random Variables

 

Appendix A Calculus and the TI-82 Calculator

Appendix B Calculus and the TI-83/TI-83 Plus/TI-84 Plus

Calculators

Appendix C Calculus and the TI-85 Calculator

Appendix D Calculus and the TI-86 Calculator

Appendix E Areas under the Standard Normal Curve

Answers to Exercises

Index I1

 

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