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Calculus and Its Applications, 2nd edition

Published by Pearson (July 15, 2020) © 2020

  • Marvin L. Bittinger Indiana University Purdue University Indianapolis
  • David J. Ellenbogen Community College of Vermont
  • Scott A. Surgent Arizona State University
  • Gene Kramer University of Cincinnati Blue Ash College
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Calculus and Its Applications is known for an approach that anticipates and meets students' needs, pairing clear explanations with carefully crafted figures to help you visualize concepts. Key revisions in the 2nd Edition include the earlier introduction of logarithmic and exponential functions to help you master these important functions and their applications. New co-author Gene Kramer revisited every homework question and learning aid to improve clarity and accuracy. All aspects of this revision aim to motivate and help students more readily understand and apply calculus principles.

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

  • A. Review of Basic Algebra
  • B. Indeterminate Forms and l'Hôpital's Rule
  • C. Regression and Microsoft Excel
  • D. Areas for a Standard Normal Distribution
  • E. Using Tables of Integration Formulas

Answers

Index of Applications

Index

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