Calculus and Its Applications, Brief Version, 12th edition

  • Marvin L. Bittinger, 
  • David J. Ellenbogen, 
  • Scott A. Surgent, 
  • Gene Kramer

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Overview

Calculus and Its Applications: Brief Version uses an intuitive approach and anticipates your needs to help you understand, apply, and master principles of calculus.

Published by Pearson (July 15th 2020) - Copyright © 2020

ISBN-13: 9780136880257

Subject: Finite Math & Applied Calculus

Category: Applied Calculus

Table of contents

Table of Contents

  • Preface
  • Prerequisite Skills Diagnostic Test
  1. Functions, Graphs, and Models
    • R.1 Graphs and Equations
    • R.2 Functions and Models
    • R.3 Finding Domain and Range
    • R.4 Slope and Linear Functions
    • R.5 Nonlinear Functions and Models
    • R.6 Exponential and Logarithmic Functions
    • R.7 Mathematical Modeling and Curve Fitting
    • Chapter Summary
    • Chapter Review Exercises
    • Chapter Test
    • Extended Technology Application: Average Price of a Movie Ticket
  1. Differentiation
    • 1.1 Limits: A Numerical and Graphical Approach
    • 1.2 Algebraic Limits and Continuity
    • 1.3 Average Rates of Change
    • 1.4 Differentiation Using Limits and Difference Quotients
    • 1.5 Leibniz Notation and the Power and Sum—Difference Rules
    • 1.6 The Product and Quotient Rules
    • 1.7 The Chain Rule
    • 1.8 Higher-Order Derivatives
    • Chapter Summary
    • Chapter Review Exercises
    • Chapter Test
    • Extended Technology Application: Path of a Baseball: The Tale of the Tape
  2. Exponential and Logarithmic Functions
    • 2.1 Exponential and Logarithmic Functions of the Natural Base, e
    • 2.2 Derivatives of Exponential (Base-e) Functions
    • 2.3 Derivatives of Natural Logarithmic Functions
    • 2.4 Applications: Uninhibited and Limited Growth Models
    • 2.5 Applications: Exponential Decay
    • 2.6 The Derivatives of ax and loga x
    • Chapter Summary
    • Chapter Review Exercises
    • Chapter Test
    • Extended Technology Application: The Business of Motion Picture Revenue and DVD Release
  3. Applications of Differentiation
    • 3.1 Using First Derivatives to Classify Maximum and Minimum Values and Sketch Graphs
    • 3.2 Using Second Derivatives to Classify Maximum and Minimum Values and Sketch Graphs
    • 3.3 Graph Sketching: Asymptotes and Rational Functions
    • 3.4 Optimization: Finding Absolute Maximum and Minimum Values
    • 3.5 Optimization: Business, Economics, and General Applications
    • 3.6 Marginals, Differentials, and Linearization
    • 3.7 Elasticity of Demand
    • 3.8 Implicit Differentiation and Logarithmic Differentiation
    • 3.9 Related Rates
    • Chapter Summary
    • Chapter Review Exercises
    • Chapter Test
    • Extended Technology Application: Maximum Sustainable Harvest
  4. Integration
    • 4.1 Antidifferentiation
    • 4.2 Antiderivatives as Areas
    • 4.3 Area and Definite Integrals
    • 4.4 Properties of Definite Integrals: Additive Property, Average Value, and Moving Average
    • 4.5 Integration Techniques: Substitution
    • 4.6 Integration Techniques: Integration by Parts
    • 4.7 Numerical Integration
    • Chapter Summary
    • Chapter Review Exercises
    • Chapter Test
    • Extended Technology Application: Business and Economics: Distribution of Wealth
  5. Applications of Integration
    • 5.1 Consumer and Producer Surplus; Price Floors, Price Ceilings, and Deadweight Loss
    • 5.2 Integrating Growth and Decay Models
    • 5.3 Improper Integrals
    • 5.4 Probability
    • 5.5 Probability: Expected Value; the Normal Distribution
    • 5.6 Volume
    • 5.7 Differential Equations
    • Chapter Summary
    • Chapter Review Exercises
    • Chapter Test
    • Extended Technology Application: Curve Fitting and Volumes of Containers
  6. Functions of Several Variables
    • 6.1 Functions of Several Variables
    • 6.2 Partial Derivatives
    • 6.3 Maximum—Minimum Problems
    • 6.4 An Application: The Least-Squares Technique
    • 6.5 Constrained Optimization: Lagrange Multipliers and the Extreme-Value Theorem
    • 6.6 Double Integrals
    • Chapter Summary
    • Chapter Review Exercises
    • Chapter Test
    • Extended Technology Application: Minimizing Employees’ Travel Time in a Building

Cumulative Review

Appendix A: Review of Basic Algebra

Appendix B: Indeterminate Forms and l’Hôpital’s Rule

Appendix C: Regression and Microsoft Excel

Appendix D: Areas for a Standard Normal Distribution

Appendix E: Using Tables of Integration Formulas

Answers

Index of Applications

Index

Your questions answered

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