Calculus & Its Applications

Description

• The student-oriented presentation helps students as they complete homework. The text’s numerous examples are designed to help students learn independently.
• Time-tested exercise sets have been carefully designed and sorted by level of difficulty, allowing instructors to choose the most appropriate exercises for their students. Each section also has technology exercises, encouraging students to use technology to solve problems. These problems are clearly labeled for instructor convenience.
• Applications contain up-to-date data to illustrate the relevance of the mathematical concepts. Topics include health expenditures, the federal deficit, mortgages, debt per capita, and price of gasoline.
• Check Your Understanding exercises at the end of each section target the concepts that can cause confusion for students. Complete solutions are provided for these unique exercises following the exercise sets within the text.
• “Caution!” notes provide tips on common pitfalls and mistakes by students and appear at relevant times throughout the text.
• Incorporating Technology features at the end of most sections include useful information about the use of graphing calculators. These features are optional and clearly marked. Additional support material can be downloaded from this book’s Companion Website.

Calculus and Its Applications, Thirteenth Edition is a comprehensive, yet flexible, text for students majoring in business, economics, life science, or social sciences. The authors delve into greater mathematical depth than other texts while motivating students through relevant, up-to-date, applications drawn from students’ major fields of study. The authors motivate key ideas geometrically and intuitively, providing a solid foundation for the more abstract treatments that follow. Every chapter includes a large quantity of exceptional exercises—a hallmark of this text–that address skills, applications, concepts, and technology. The Thirteenth Edition includes updated applications, exercises, and technology coverage. The authors have also added more study tools, including a prerequisite skills diagnostic test and a greatly improved end-of-chapter summary, and made content improvements based on user reviews.

Calculus and Its Applications, Thirteenth Edition is a comprehensive, yet flexible, text for students majoring in business, economics, life science, or social sciences. The authors delve into greater mathematical depth than other texts while motivating students through relevant, up-to-date, applications drawn from students’ major fields of study. The authors motivate key ideas geometrically and intuitively, providing a solid foundation for the more abstract treatments that follow. Every chapter includes a large quantity of exceptional exercises—a hallmark of this text–that address skills, applications, concepts, and technology. The MyMathLab^® course for the text features thousands of assignable exercises, built-in support for gaps in basic skills, and an array of interactive figures designed to help students visualize key concepts.

 

The Thirteenth Edition includes updated applications, exercises, and technology coverage. The authors have also added more study tools, including a prerequisite skills diagnostic test and a greatly improved end-of-chapter summary, and made content improvements based on user reviews.

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.

 

Martha Siegel holds a BA from Russell Sage College, attended Rensselear Polytechnic Institute as a special student, and received his PhD at the University of Rochester. From 1966 until 1971 she taught at Goucher University in Baltimore. Since 1971 she has been a professor at Towson State University, also in Maryland. Professor Siegel has been on the writing team of this book since the fifth edition and is also the co-author of a precalculus reform book.

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 Section 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. The Exponential and Natural 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 The Definite Integral and Net Change of a Function

6.3 The Definite Integral and Area Under a Graph

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: Areas under the Standard Normal Curve

Answers to Exercises

Index

• Annotated Instructor’s Edition includes helpful teaching tips plus answers on the same page as exercises.
• Prerequisite Skills Diagnostic Test within the text helps students gauge their level of readiness for this course. Answers are available in the back of the book.
• “Now Try” Exercises appear after selected examples—mirroring how an instructor might stop in class to ask students to try a problem on their own, allowing them to immediately apply their understanding of the skills and concepts. 
• Check Your Understanding problems (formerly called Practice Problems) have been extensively revised to better prepare students for the homework exercises.
• End-of-chapter material has been extensively revised and supplemented with additional material to help students prepare for tests.
  • Key Concepts and Formulas are organized by section. The grid design makes it easy to find and organize information.
  • Fundamental Concept Check exercises include answers at the back of the book so that students can be sure they understand the main ideas before continuing to the Chapter Review exercises.
  • Chapter Review Exercises include answers at the back of the book; these are excellent for test preparation.
• Technology coverage has been updated to include the TI-84-plus its new operating system.
• Calculus content in Chapters 1, 2, and 6 is extensively revised to better build students’ intuitive understanding of calculus. 
• Extensively revised examples and exercises help students learn and practice the material. 
• MyMathLab has been extensively updated to include:
  • Hundreds more assignable exercises than the previous edition
  • Interactive Figures for key concepts in the course–great for use in lecture as a tool to build geometric understanding. Interactive Figure exercises provide a way to engage students with the figures.
  • Chapter-by-chapter “Getting Ready” content provides an easy way to remediate gaps in prerequisite skills.

Additional information

Dimensions	1.10 × 8.60 × 11.00 in
Imprint	Pearson
Format	gen
ISBN-13	09780321848901
ISBN-10	032184890X
Author	David I. Schneider, Larry J. Goldstein, David C. Lay, Nakhle H. Asmar
Subjects	mathematics, higher education, applied calculus, applied math, Calculus, Applied & Advanced Math