Calculus and Its Applications, Brief Version
by Marvin L. Bittinger, David J. Ellenbogen, Scott A. Surgent
12th Edition
Publisher: Pearson
Book Details
| Print ISBN | 9780135165928 |
| eText ISBN | 9780136880257 |
| Publisher | Pearson |
| Publishing Year | 2021 |
| Edition | 12th Edition |
| Language | en |
Calculus and Its Applications, Brief Version, 12th Edition, is a textbook designed to motivate students and help them understand calculus principles. The work pairs clear explanations with crafted figures to assist readers in visualizing mathematical concepts.
Broad areas of coverage include functions, graphs, and models, as well as differentiation and integration. The textbook connects these methods to practical problems in business and economics, and it introduces functions of several variables.
Key revisions in this twelfth edition introduce logarithmic and exponential functions earlier to support student learning. This organization is intended to help readers understand these functions and apply them to quantitative scenarios.
Table of Contents
Chapter 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
Chapter 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
Chapter 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 a x and log a x
- • Chapter Summary
- • Chapter Review Exercises
- • Chapter Test
- • Extended Technology Application: The Business of Motion Picture Revenue and DVD Release
Chapter 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
Chapter 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
Chapter 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
Chapter 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
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