Applied Calculus

by Waner, Stefan; Costenoble, Steven

• ISBN13: 9781439049235
• ISBN10: 1439049238
• Edition: 5th
• Format: Hardcover
• Copyright: 2010-01-01
• Publisher: Brooks Cole

Summary

Full of relevant and current real-world applications, Stefan Waner and Steven Costenoble's APPLIED CALCULUS, Fifth Edition helps your students relate to mathematics! Throughout the text is clearly delineated, thorough Microsoft® Excel® and Graphing Calculator instruction, optional so instructors can include any amount of technology instruction in their courses. Acclaimed for accuracy and readability, APPLIED CALCULUS, Fifth Edition connects with all types of teaching and learning styles. Resources like the accompanying website allow the text to support a range of course formats, from traditional lectures to strictly online courses.

Table of Contents

Precalculus Review

Real Numbers

Exponents and Radicals

Multiplying and Factoring Algebraic Equations

Rational Expressions

Solving Polynomial Equations

Solving Miscellaneous Equations

The Coordinate Plane

Functions and Linear Models

Functions from the Numerical, Algebraic, and Graphical Viewpoints

Applications: Functions and Models

Linear Functions and Models

Linear Regression

Key Concepts

Review Exercises

Case Study: Modeling Spending on Internet Advertising

Technology Guides

Optional Internet Topic: New Functions from Old: Scaled and Shifted Functions

Nonlinear Functions and Models

Quadratic Functions and Models

Exponential Functions and Models

Logarithmic Functions and Models

Logistic Functions and Models

Key Concepts

Review Exercises

Case Study: Checking up on Malthus

Technology Guides

Optional Internet Topics: Inverse Functions

Using and Deriving Algebraic Properties of Logarithms

Introduction to the Derivative

Limits: Numerical and Graphical Approaches

Limits and Continuity

Limits: Algebraic Approach

Average Rate of Change

Derivatives: Numerical and Graphical Viewpoints

Derivatives: Algebraic Viewpoint

Key Concepts

Review Exercises

Case Study: Reducing Sulfur Emissions

Technology Guides

Optional Internet Topics: Sketching the Graph of the Derivative

Proof of the Power Rule

Continuity and Differentiability

Techniques of Differentiation with Applications

Derivatives of Powers, Sums, and Constant Multiples

A First Application: Marginalnalysis

The Product and Quotient Rules

The Chain Rule

Derivatives of Logarithmic and Exponential Functions

Implicit Differentiation

Key Concepts

Review Exercises

Case Study: Projecting Market Growth

Technology Guides

Optional Internet Topic: Linear Approximation and Error Estimation

Further Applications of the Derivative

Maxima and Minima

Applications of Maxima and Minima

Higher Order Derivatives: Acceleration and Concavity

Analyzing Graphs

Related Rates

Elasticity

Key Concepts

Review Exercises

Case Study: Production Lot Size Management

Technology Guides

The Integral

The Indefinite Integral

Substitution

The Definite Integral: Numerical and Graphical Approaches

The Definite Integral: Algebraic Approach and the Fundamental Theorem of Calculus

Key Concepts

Review Exercises

Case Study: Wage Inflation

Technology Guides

Optional Internet Topic: Numerical Integration

Further Integration Techniques and Applications of the Integral

Integration by Parts

Area Between Two Curves and Applications

Averages and Moving Averages

Applications to Business and Economics: Consumers' and Producers' Surplus and Continuous Income Streams

Improper Integrals and Applications

Differential Equations and Applications

Key Concepts

Review Exercises

Case Study: Estimating Tax Revenues

Technology Guides

Optional Internet Topic: Taylor Polynomials

Functions of Several Variables

Functions of Several Variables from the Numerical, Algebraic, and Graphical Viewpoints

Partial Derivatives

Maxima and Minima

Constrained Maxima and Minima and Applications

Double Integrals and Applications

Key Concepts

Review Exercises

Case Study: Modeling Household Income

Technology Guides

Optional Internet Topic: The Chain Rule for Functions of Several Variables

Trigonometric Models

Trigonometric Functions, Models, and Regression

Derivatives of Trigonometric Functions and Applications

Integrals of Trigonometric Functions and Applications

Key Concepts

Review Exercises

Case Study: Predicting Cocoa Inventories

Technology Guides

Answers to Selected Exercises

Index

Optional Internet Topic

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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