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Applied Calculus

Applied Calculus - 3rd edition

ISBN13: 978-0534419585

Cover of Applied Calculus 3RD 04 (ISBN 978-0534419585)
ISBN13: 978-0534419585
ISBN10: 0534419585
Cover type:
Edition: 3RD 04
Copyright: 2004
Publisher: Brooks/Cole Publishing Co.
Published: 2004
International: No

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Applied Calculus - 3RD 04 edition

ISBN13: 978-0534419585

Stefan Waner

ISBN13: 978-0534419585
ISBN10: 0534419585
Cover type:
Edition: 3RD 04
Copyright: 2004
Publisher: Brooks/Cole Publishing Co.
Published: 2004
International: No
Summary

Stefan Waner and Steven Costenoble's APPLIED CALCULUS, Third Edition is designed to address the considerable challenge of generating enthusiasm and developing mathematical sophistication in applied mathematics courses offered on many college campuses. The new edition retains its engaging conversational style and focus on real data and real world applications of mathematics--a strategy that has proven to be pedagogically successful. The wealth of applications, the highly effective integrated, yet optional, use of graphing calculators or spreadsheets, and the robust supplemental Web site that has received praise from around the world, make Waner/Costenoble's text an outstanding choice.

Benefits:

  • NEW! Chapter One has been revised to include expanded coverage of linear regression.
  • NEW! The number of exercises has been increased by 17 percent with additional easier computational exercises at the start of many exercise sets and significantly more Communication and Reasoning exercises. Exercises and examples based on dated information have generally been replaced by more current versions.
  • NEW! A new arrangement of exercise sets reflects increasing level of difficulty.
  • NEW! A new four-color design calls out the many excellent pedagogical tools, making them more efficient tools for instructors and students.
  • Unique integration of graphing calculators, spreadsheets (using Excel), and the Web, supports a wide range of instructional settings. The text is suitable for classes relying exclusively on graphing calculators, web-based technology, or Excel, a combination of these, or none of them.
  • Clearly delineated and carefully structured discussions introduce many of the central concepts in three ways: numerically, graphically, and algebraically.
  • Written in a conversational, student-oriented style, the text combines interactive pedagogical devices with solid mathematics and a flexible approach to technology, and effectively addresses the difficult issues of teaching less-than-enthusiastic students.
  • A text-specific Web site rich in features offers interactive tutorials, review exercises, and online utilities for a variety of tasks like graphing, regression, and matrix algebra. The site enhances interest, learning, and comprehension.
  • A large number of the examples and exercises use referenced real data from business, economics, the life sciences, and the social sciences, appropriately modified and streamlined to keep the applications tractable.
  • A case study framework for chapter topics begins each chapter with a statement of an interesting problem that is revisited at the end of the chapter.
  • NEW! The integrated discussions of Excel and graphing calculators as optional tools have been expanded.
  • NEW! Trigonometric functions material has been placed in a separate chapter.
  • NEW! An expanded treatment of limits includes an additional section on the concept of continuity. The discussion of the algebraic approach to limits is now in a section by itself.
  • NEW! Chapter 2 has additional material on regression for all the non-linear functions, and this coverage has been added to the new Trigonometry chapter.
  • NEW! A new (optional) section on logistic models and regression has been added to Chapter 2.
  • NEW! The significantly revised Chapter 3 on derivatives consolidates the graphical and numerical approaches and includes more on the algebraic approach.
  • NEW! The highly effective pedagogy from the second edition has been expanded with more "Quick Examples", more "Question and Answer Dialog" boxes, additional Excel and graphing calculator instructions, and additional Web site information.
  • NEW! A new boxed-feature called "Guidelines" appears at the ends of sections to assist students in problem-solving.

Author Bio

Waner, Stefan : Hofstra University


Costenoble, Steven : Hofstra University

Table of Contents

1. LINEAR FUNCTIONS AND MODELS

Introduction
Functions from the Numerical and Algebraic Viewpoints
Functions from the Graphical Viewpoint
Linear Functions
Linear Models
Linear Regression
Case Study: Modeling Spending on Internet Advertising
Optional Internet Topic: New Functions from Old: Scaled and Shifted Functions

2. NONLINEAR MODELS

Introduction
Quadratic Functions and Models
Exponential Functions and Models
Logarithmic Functions and Models
Logistic Functions and Models
Case Study: Checking up on Malthus
Optional Internet Topics: Inverse Functions
Linear and Exponential Regression
Using and Deriving Algebraic Properties of Logarithms

3. INTRODUCTION TO THE DERIVATIVE

Introduction
Average Rate of Change
The Derivative: Numerical and Graphical Viewpoints
The Derivative : Algebraic Viewpoint
Derivatives of Powers, Sums, and Constant Multiples
A First Application: Marginal Analysis
Limits: Numerical and Graphical Approaches
Limits and Continuity
Limits and Continuity: Algebraic Approach
Case Study: Reducing Sulfur Emissions
Optional Internet Topics: Sketching the Graph of the Derivative
Proof of the Power Rule
Continuity and Differentiability

4. TECHNIQUES OF DIFFERENTIATION

Introduction
The Product and Quotient Rules
The Chain Rule
Derivatives of Logarithmic and Exponential Functions
Implicit Differentiation
Case Study: Projecting Market Growth
Optional Internet Topic: Linear Approximation and Error Estimation

5. APPLICATIONS OF THE DERIVATIVE

Introduction
Maxima and Minima
Applications of Maxima and Minima
The Second Derivative and Analyzing Graphs
Related Rates
Elasticity
Case Study: Production Lot Size Management

6. THE INTEGRAL

Introduction
The Indefinite Integral
Substitution
The Definite Integral as a Sum: A Numerical Approach
The Definite Integral as Area: A Geometric Approach
The Definite Integral: An Algebraic Approach and the Fundamental Theorem of Calculus
Case Study: Wage Inflation
Optional Internet Topic: Numerical Integration

7. FURTHER INTEGRATION TECHNIQUES AND APPLICATIONS OF THE INTEGRAL

Introduction
Integration by Parts
Area Between Two Curves and Applications
Averages and Moving Averages
Continuous Income Streams
Improper Integrals and Applications
Differential Equations and Applications
Case Study: Estimating Tax Revenues

8. FUNCTIONS OF SEVERAL VARIABLES

Introduction
Functions of Several Variables from the Numerical and Algebraic Viewpoints
Three Dimensional Space and the Graph of a Function of Two Variables
Partial Derivatives
Maxima and Minima
Constrained Maxima and Minima and Applications
Double Integrals
Case Study: Modeling Household Income

9. TRIGONOMETRIC MODELS

Introduction
Trigonometric Functions, Models, and Regression
Derivatives of Trigonometric Functions and Applications
Integrals of Trigonometric Functions and Applications
Case Study: Predicting Cocoa Inventories
Appendix A: Algebra Review
Introduction
Real Numbers
Exponents and Radicals
Multiplying and Factoring Algebraic Equations
Rational Expressions
Solving Polynomial Equations
Solving Miscellaneous Equations

OPTIONAL INTERNET CHAPTERS

S
Calculus Applied to Probability and Statistics
Introduction
Continuous Random Variables and Histograms
Probability Density Functions: Uniform, Exponential, Normal, and Beta
Mean, Median, Variance and Standard Deviation
Case Study: Creating a Family Trust

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