Calculus and Its Applications

by Goldstein, Larry J.; Schneider, David I.; Lay, David C.

• ISBN13: 9780130466105
• ISBN10: 0130466107
• Edition: 10th
• Format: Hardcover
• Copyright: 2004-01-01
• Publisher: Pearson College Div

Summary

For Applied Calculus courses. 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 formulapairing substantial amounts of graphical analysis and informal geometric proofs with an abundance of hands-on exerciseshas proven to be tremendously successful with both students and instructors.

Table of Contents

Preface

Introduction

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

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

Applications of the Derivative

Describing Graphs of Functions

The First and Second Derivative Rules

The First and Second Derivative Tests and Curve Sketching

Curve Sketching (Conclusion)

Optimization Problems

Further Optimization Problems

Applications of Derivatives to Business and Economics

Techniques of Differentiation

The Product and Quotient Rules

The Chain Rule and the General Power Rule

Implicit Differentiation and Related Rates

Logarithm Functions

Exponential Functions

The Exponential Function ex

Differentiation of Exponential Functions

The Natural Logarithm Function

The Derivative of ln x

Properties of the Natural Logarithm Function

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

The Definite Integral

Antidifferentiation

Areas and Riemann Sums

Definite Integrals and the Fundamental Theorem

Areas in the xy-Plane

Applications of the Definite Integral

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

Double Integrals

The Trigonometric Functions

Radian Measure of Angles

The Sine and the Cosine

Differentiation and Integration of sin t and cos t

The Tangent and Other Trigonometric Functions

Techniques of Integration

Integration by Substitution

Table of Contents provided by Publisher. All Rights Reserved.

Excerpts

We have been very pleased with the enthusiastic response to the first nine editions ofCalculus & Its Applicationsby 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. 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. 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 work 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: 1.Additional Exercises.We have added and revised over 400 exercises. These include 90 new problems on differential equations and their applications. Many new exercises from business, medicine, life and social sciences, are based on current real-world data. At the beginning of more challenging sections, such as Section 2.6, we added straightforward exercises, designed to aid students with limited math background. We also added more exercises with figures. These exercises challenge the students' ability to read graphs and examine their grasp of fundamental concepts such as rates of change, the chain rule, and areas under a graph. We introduced a new genre of problems designed to test the students' understanding of ma