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Calculus & Its Applications / Edition 14
Calculus & Its Applications / Edition 14
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Overview
Product Details
| ISBN-13: | 2900134437773 |
|---|---|
| Publication date: | 01/13/2017 |
| Pages: | 672 |
| Product dimensions: | 6.50(w) x 1.50(h) x 9.50(d) |
About the Author
David Lay holds a BA from Aurora University (Illinois), and an MA and PhD from the University of California at Los Angeles. David Lay has been an educator and research mathematician since 1966, mostly at the University of Maryland, College Park. He has published more than 30 research articles on functional analysis and linear algebra, and he has written several popular textbooks. Lay has received four university awards for teaching excellence, including, in 1996, the title of Distinguished Scholar—Teacher of the University of Maryland. In 1994, he was given one of the Mathematical Association of America’s Awards for Distinguished College or University Teaching of Mathematics. Since 1992, he has served several terms on the national board of the Association of Christians in the Mathematical Sciences.
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.
Nakhle Asmar received his PhD from the University of Washington. He is currently a professor of mathematics and Chair of the Mathematics Department at the University of Missouri, Columbia. He is the author and coauthor of widely used calculus texts as well as textbooks on complex analysis, partial differential equations and Fourier series. He has received several awards for outstanding teaching. His popular textbooks have been translated into Chinese and Portuguese.
Read an Excerpt
PREFACE:
Preface
We have been very pleased with the enthusiastic response to the first eight editions of Calculus and Its Applications by teachers and students alike. The present work incorporates many of the suggestions they have put forward.
Although there are many changes, we have preserved the approach and the flavor. Our goals remain the same: to begin the calculus as soon as possible; to present calculus in an intuitive yet intellectually satisfying way; and to illustrate the many applications of calculus to the biological, social, and management sciences.
The distinctive order of topics has proven over the years to be successful—easier for students to learn, and more interesting because students see significant applications early. For instance, the derivative is explained geometrically before the analytic material on limits is presented. This' approach gives the students an understanding of the derivative at least as strong as that obtained from the traditional approach. To reach the applications in Chapter 2 quickly, we present only the differentiation rules and the curve sketching needed for those applications. Advanced topics come later when they are needed. Other aspects of this student-oriented approach follow below.
Applications
We provide realistic applications that illustrate the uses of calculus in other disciplines. See the Index of Applications on the inside cover. Wherever possible, we have attempted to use applications to motivate the mathematics.
Examples
The text includes many more worked examples than is customary. Furthermore, we have included computational details toenhance readability by students whose basic skills are weak.
Exercises
The exercises comprise about one-quarter of the text—the most important part of the text in our opinion. The exercises at the ends of the sections are usually arranged in the order in which the text proceeds, so that the homework assignments may easily be made after only part of a section is discussed. Interesting applications and more challenging problems tend to be located near the ends of the exercise sets. Supplementary exercises at the end of each chapter expand the other exercise sets and include problems that require skills from earlier chapters. Practice Problems
The practice problems have proven to be a popular and useful feature. Practice Problems are carefully selected questions located at the end of each section, just before the exercise set. Complete solutions are given following the exercise set. The practice problems often focus on points that are potentially confusing or are likely to be overlooked. We recommend that the reader seriously attempt the practice problems and study their solutions before moving on to the exercises. In effect, the practice problems constitute a built-in workbook.
Minimal Prerequisites
In Chapter 0, we review those concepts that the reader needs to study calculus. Some important topics, such as the laws of exponents, are reviewed again when they are used in a later chapter. Section 0.6 prepares students for applied problems that appear throughout the text. A reader familiar with the content of Chapter 0 should begin with Chapter 1 and use Chapter 0 as a reference, whenever needed.
New in this Edition
Among the many changes in this edition, the following are the most significant:
- Delta Notation We introduce delta notation in Chapter 0 and use it in our discussion of the derivative. As in previous editions, we have tried to minimize the use of complicated notation, preferring instead verbal descriptions. However, in the case of the delta notation, we feel that the clarity achieved is worth the extra notation.
- Derivative as a Rate of Change We preview the derivative as a rate of change at the beginning of Chapter 1, anticipating the more detailed discussion in Section 1.8. Since students have difficulty interpreting the derivative as a rate of change, we felt it prudent to allow them to practice repeatedly with the concept.
- Analysis of Data We added a broad theme that might best be described as "calculus for functions defined by data." Throughout the book, we include discussions about real-life applications whose underlying functions are defined by tables of data.
- More on Regression (optional) We added the optional Section 7.6 on multiple and nonlinear regression analysis. The goal in this section is to provide a taste of what a business student will encounter in a course in regression analysis. Our emphasis is on using technology, especially spreadsheets, to do the computations for various flavors of regression (multiple-linear, quadratic, exponential, etc.).
- Additional Technology (optional) The new technology appendix to Chapter 0 includes the graphing calculator material previously found within the chapter, a discussion of calculus and spreadsheets, and a new exercise set testing student technology skills.
- Real-Life Data We have collected spreadsheets containing real-life statistical data and made them available to students and faculty on the Web site www.prenhall.com/goldstein.
- Projects Each chapter now includes a project, designed to provide more open-ended problem solving, critical thinking, verbal expression, and integration of mathematical techniques, both manual and technological.
- Other Changes We made improvements throughout the text based on suggestions from students, teachers, reviewers, and editors. Our thanks to all who assisted us with their valuable suggestions.
This edition contains more material than can be covered in most two-semester courses. Optional sections are starred in the table of contents. In addition, the level of theoretical material may be adjusted to the needs of the students. For instance, only the first two pages of Section 1.4 are required in order to introduce the limit notation.
A Study Guide for students containing detailed explanations and solutions for every sixth exercise is available. The Study Guide also includes helpful hints and strategies for studying that will help students improve their performance in the course. In addition, the Study Guide contains a copy of Visual Calculus, the popular, easy-to-use software for IBM compatible computers. Visual Calculus contains over 20 routines that provide additional insights into the topics discussed in the text. Also, instructors find the software valuable for constructing graphs for exams.
An Instructor's Solutions Manual contains worked solutions to every exercise.
TestGen EQ provides nearly 1000 suggested test questions, keyed to chapter and section. TestGen EQ is a text-specific testing program networkable for administering tests and capturing grades online. Edit and add your own questions, or use the new "Function Plotter" to create a nearly unlimited number of tests and drill worksheets.
Designed to complement and expand upon the text, the text Web site offers a variety of interactive teaching and learning tools. Since many of the text projects use real-life data, we made the data easier to use by making it available in Excel spreadsheets on the Web site. The Web site also includes links to related Web sites, quizzes, Syllabus Builder, and more. For more information, visit www.prenhall.com/goldstein or contact your local Prentice Hall representative.
Table of Contents
(NOTE: Calculus and Its Applications, 10/E consists of Chs. 0-12. Brief Calculus and Its Applications, 10/E consists of Chs. 0-8.)
Index of Applications.
Preface.
Introduction.
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 DefiniteIntegral.
Antidifferentiation. 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.
Appendices.
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.
Preface
We have been very pleased with the enthusiastic response to the first eight editions of Calculus and Its Applications by teachers and students alike. The present work incorporates many of the suggestions they have put forward.
Although there are many changes, we have preserved the approach and the flavor. Our goals remain the same: to begin the calculus as soon as possible; to present calculus in an intuitive yet intellectually satisfying way; and to illustrate the many applications of calculus to the biological, social, and management sciences.
The distinctive order of topics has proven over the years to be successful—easier for students to learn, and more interesting because students see significant applications early. For instance, the derivative is explained geometrically before the analytic material on limits is presented. This' approach gives the students an understanding of the derivative at least as strong as that obtained from the traditional approach. To reach the applications in Chapter 2 quickly, we present only the differentiation rules and the curve sketching needed for those applications. Advanced topics come later when they are needed. Other aspects of this student-oriented approach follow below.
Applications
We provide realistic applications that illustrate the uses of calculus in other disciplines. See the Index of Applications on the inside cover. Wherever possible, we have attempted to use applications to motivate the mathematics.
Examples
The text includes many more worked examples than is customary. Furthermore, we have included computational details to enhance readability by students whose basic skillsare weak.
Exercises
The exercises comprise about one-quarter of the text—the most important part of the text in our opinion. The exercises at the ends of the sections are usually arranged in the order in which the text proceeds, so that the homework assignments may easily be made after only part of a section is discussed. Interesting applications and more challenging problems tend to be located near the ends of the exercise sets. Supplementary exercises at the end of each chapter expand the other exercise sets and include problems that require skills from earlier chapters. Practice Problems
The practice problems have proven to be a popular and useful feature. Practice Problems are carefully selected questions located at the end of each section, just before the exercise set. Complete solutions are given following the exercise set. The practice problems often focus on points that are potentially confusing or are likely to be overlooked. We recommend that the reader seriously attempt the practice problems and study their solutions before moving on to the exercises. In effect, the practice problems constitute a built-in workbook.
Minimal Prerequisites
In Chapter 0, we review those concepts that the reader needs to study calculus. Some important topics, such as the laws of exponents, are reviewed again when they are used in a later chapter. Section 0.6 prepares students for applied problems that appear throughout the text. A reader familiar with the content of Chapter 0 should begin with Chapter 1 and use Chapter 0 as a reference, whenever needed.
New in this Edition
Among the many changes in this edition, the following are the most significant:
- Delta Notation We introduce delta notation in Chapter 0 and use it in our discussion of the derivative. As in previous editions, we have tried to minimize the use of complicated notation, preferring instead verbal descriptions. However, in the case of the delta notation, we feel that the clarity achieved is worth the extra notation.
- Derivative as a Rate of Change We preview the derivative as a rate of change at the beginning of Chapter 1, anticipating the more detailed discussion in Section 1.8. Since students have difficulty interpreting the derivative as a rate of change, we felt it prudent to allow them to practice repeatedly with the concept.
- Analysis of Data We added a broad theme that might best be described as "calculus for functions defined by data." Throughout the book, we include discussions about real-life applications whose underlying functions are defined by tables of data.
- More on Regression (optional) We added the optional Section 7.6 on multiple and nonlinear regression analysis. The goal in this section is to provide a taste of what a business student will encounter in a course in regression analysis. Our emphasis is on using technology, especially spreadsheets, to do the computations for various flavors of regression (multiple-linear, quadratic, exponential, etc.).
- Additional Technology (optional) The new technology appendix to Chapter 0 includes the graphing calculator material previously found within the chapter, a discussion of calculus and spreadsheets, and a new exercise set testing student technology skills.
- Real-Life Data We have collected spreadsheets containing real-life statistical data and made them available to students and faculty on the Web site our site.
- Projects Each chapter now includes a project, designed to provide more open-ended problem solving, critical thinking, verbal expression, and integration of mathematical techniques, both manual and technological.
- Other Changes We made improvements throughout the text based on suggestions from students, teachers, reviewers, and editors. Our thanks to all who assisted us with their valuable suggestions.
This edition contains more material than can be covered in most two-semester courses. Optional sections are starred in the table of contents. In addition, the level of theoretical material may be adjusted to the needs of the students. For instance, only the first two pages of Section 1.4 are required in order to introduce the limit notation.
A Study Guide for students containing detailed explanations and solutions for every sixth exercise is available. The Study Guide also includes helpful hints and strategies for studying that will help students improve their performance in the course. In addition, the Study Guide contains a copy of Visual Calculus, the popular, easy-to-use software for IBM compatible computers. Visual Calculus contains over 20 routines that provide additional insights into the topics discussed in the text. Also, instructors find the software valuable for constructing graphs for exams.
An Instructor's Solutions Manual contains worked solutions to every exercise.
TestGen EQ provides nearly 1000 suggested test questions, keyed to chapter and section. TestGen EQ is a text-specific testing program networkable for administering tests and capturing grades online. Edit and add your own questions, or use the new "Function Plotter" to create a nearly unlimited number of tests and drill worksheets.
Designed to complement and expand upon the text, the text Web site offers a variety of interactive teaching and learning tools. Since many of the text projects use real-life data, we made the data easier to use by making it available in Excel spreadsheets on the Web site. The Web site also includes links to related Web sites, quizzes, Syllabus Builder, and more. For more information, visit our site or contact your local Prentice Hall representative.