Calculus and Its Applications, 2nd edition

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

Choose the option that's right for you

$9.99 / mo

4-month term, pay monthly or pay $39.96

Enjoy these features

  • Up to 2 devices
  • Discounted tutor access
  • Exclusive offers

$14.99 / mo

4-month term, pay monthly or pay $59.96

Enjoy these features

  • Up to 2 devices
  • Discounted tutor access
  • Exclusive offers

Learn more, spend less

  • Watch and learn

    Videos & animations bring concepts to life

  • Listen on the go

    Learn how you like with full eTextbook audio

  • Learn anytime, anywhere

    Get the app to access your eTextbook whenever you need it

  • Make it your own

    Your notes. Your highlights. Your eTextbook

  • Find it fast

    Quickly navigate your eTextbook with search

Overview

Calculus and Its Applications 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: 9780136880196

Subject: Finite Math & Applied Calculus

Category: Applied Calculus

Table of contents

Prerequisite Skills Diagnostic Test

R. 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

7. Trigonometric Functions

  • 7.1 Basics of Trigonometry
  • 7.2 Derivatives of Trigonometric Functions
  • 7.3 Integration of Trigonometric Functions
  • 7.4 Inverse Trigonometric Functions and Applications
  • Chapter Summary
  • Chapter Review Exercises
  • Chapter Test
  • Extended Technology Application

8. Differential Equations

  • 8.1 Direction Fields, Autonomic Forms, and Population Models
  • 8.2 Applications: Inhibited Growth Models
  • 8.3 First-Order Linear Differential Equations
  • 8.4 Higher-Order Differential Equations and a Trigonometry Connection
  • Chapter Summary
  • Chapter Review Exercises
  • Chapter Test
  • Extended Technology Application

9. Sequences and Series

  • 9.1 Arithmetic Sequences and Series
  • 9.2 Geometric Sequences and Series
  • 9.3 Simple and Compound Interest
  • 9.4 Annuities and Amortization
  • 9.5 Power Series and Linearization
  • 9.6 Taylor Series and a Trigonometry Connection
  • Chapter Summary
  • Chapter Review Exercises
  • Chapter Test
  • Extended Technology Application

10. Probability Distributions

  • 10.1 A Review of Sets
  • 10.2 Theoretical Probability
  • 10.3 Discrete Probability Distributions
  • 10.4 Continuous Probability Distributions: Mean, Variance, and Standard Deviation
  • Chapter Summary
  • Chapter Review Exercises
  • Chapter Test
  • Extended Technology Application

11. Systems and Matrices (online only)

  • 11.1 Systems of Linear Equations
  • 11.2 Gaussian Elimination
  • 11.3 Matrices and Row Operations
  • 11.4 Matrix Arithmetic: Equality, Addition, and Scalar Multiples
  • 11.5 Matrix Multiplication, Multiplicative Identities, and Inverses
  • 11.6 Determinants and Cramer's Rule
  • 11.7 Systems of Linear Inequalities and Linear Programming
  • Chapter Summary
  • Chapter Review Exercises
  • Chapter Test
  • Extended Technology Application

12. Combinatorics and Probability (online only)

  • 12.1 Compound Events and Odds
  • 12.2 Combinatorics: The Multiplication Principle and Factorial Notation
  • 12.3 Permutations and Distinguishable Arrangements
  • 12.4 Combinations and the Binomial Theorem
  • 12.5 Conditional Probability and the Hypergeometric Probability Distribution Model
  • 12.6 Independent Events, Bernoulli Trials, and the Binomial Probability Model
  • 12.7 Bayes Theorem
  • Chapter Summary
  • Chapter Review Exercises
  • Chapter Test
  • Extended Technology Application
  • Cumulative Review

APPENDICES

  1. Review of Basic Algebra
  2. Indeterminate Forms and l'Hôpital's Rule
  3. Regression and Microsoft Excel
  4. Areas for a Standard Normal Distribution
  5. Using Tables of Integration Formulas

Answers

Index of Applications

Index

Your questions answered

Introducing Pearson+. Reimagined learning, designed for you. Choose from one eTextbook or over 1,500 eTextbooks and study tools, all in one place, for one low monthly subscription. A new way to buy books that fits your budget. Make the most of your study time with offline access, enhanced search, notes and flashcards — to get organized, get the work done quicker and get results. Plus, with the app, put textbooks in your pocket and learn wherever. It's time to upgrade the textbook and simplify learning, so you can have time to live too.

Pearson eTextbook is an easy-to-use digital textbook available from Pearson+. Make it your own by adding notes and highlights. Download the Pearson+ mobile app to learn on the go, even offline. Listen on the go with our new audiobook feature, available for most titles.

When you choose a plan, you're signing up for a 4-month 'term'. You can opt to make a one-time payment for the initial 4-month term or pay monthly. If you opt for monthly payments, we will charge your payment method each month until your 4-month term has ended. You can turn on auto-renew in My account at any time to continue your subscription before your 4-month term has ended.

When you purchase a Pearson+ subscription, it will last 4 months. Before your initial 4-month term ends, you can extend your subscription by turning auto-renew on in My account.

If you turn auto-renew on, we’ll automatically renew your subscription and charge you every month until you turn off auto-renew. If you made a one-time payment for your initial 4-month term, you’ll now pay monthly.

To avoid the next payment charge, make sure you turn auto renewal off 1 day before the auto renewal date. You can subscribe again after auto-renew has been turned off by purchasing another Pearson+ subscription. We use your credit card to renew your subscription automatically. To make sure your learning is uninterrupted, please check your card details before your first monthly payment.

With a Multi Pearson+ subscription plan, you can download up to 10 titles on the Pearson+ app from My list on each of your authorized devices every month.

When you're using your Multi Pearson+ subscription plan in a browser, you can select and read from as many titles as you like.