Calculus and Its Applications / Edition 9

Calculus and Its Applications / Edition 9

by Larry J. Goldstein, David Schneider, David Lay
     
 

ISBN-10: 0130873047

ISBN-13: 9780130873040

Pub. Date: 07/13/2000

Publisher: Pearson Education

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:
9780130873040
Publisher:
Pearson Education
Publication date:
07/13/2000
Edition description:
Older Edition
Pages:
706
Product dimensions:
7.99(w) x 10.00(h) x 0.49(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 The Derivative


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 Propertiesof 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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