Calculus and Its Applications, 2nd edition
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Overview
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 coauthor 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.
Published by Pearson (July 15th 2020)  Copyright © 2020
ISBN13: 9780136880196
Subject: Finite Math & Applied Calculus
Category: Applied Calculus
Overview
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 HigherOrder 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 (Basee) 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 LeastSquares Technique
 6.5 Constrained Optimization: Lagrange Multipliers and the ExtremeValue 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 FirstOrder Linear Differential Equations
 8.4 HigherOrder 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
 Review of Basic Algebra
 Indeterminate Forms and l'Hôpital's Rule
 Regression and Microsoft Excel
 Areas for a Standard Normal Distribution
 Using Tables of Integration Formulas
Answers
Index of Applications
Index
Your questions answered
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