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ISBN 10: 1337291242
ISBN 13: 978-1337291248
Author: Stefan Waner, Steven Costenoble
APPLIED CALCULUS, Seventh Edition, uses a large number of applications based on real data from business, economics, and the life and social sciences to help you see how mathematics relates to your own life and interests. Thorough TI Graphing Calculator and spreadsheet instructions appear throughout the text, and optional WebAssign platform support your learning with detailed teaching videos by an award-winning instructor. With these tools, plus online interactive tutorials and videos on every topic, this text will help you “get” mathematics — whatever your learning style may be.
Applied Calculus 7th Table of contents:
Acknowledgements
0. Precalculus Review
0.1. Real Numbers
Intervals
Operations
Entering Formulas
Accuracy and Rounding
0.1. Exercises
0.2. Exponents and Radicals
Integer Exponents
Radicals
Rational Exponents
Radical Form, Positive Exponent Form, and Power Form
Solving Equations with Exponents
0.2. Exercises
0.3. Multiplying and Factoring Algebraic Expressions
Multiplying Algebraic Expressions
Factoring Algebraic Expressions
0.3. Exercises
0.4. Rational Expressions
0.4. Exercises
0.5. Solving Polynomial Equations
Solution of Linear Equations
Solution of Quadratic Equations
Solution of Cubic Equations
Solution of Higher Order Polynomial Equations
0.5. Exercises
0.6. Solving Miscellaneous Equations
0.6. Exercises
0.7. The Coordinate Plane
The Graph of an Equation
Distance
0.7. Exercises
0.8. Logarithms
Algebraic Properties of Logarithms
Using Logarithms to Solve for Unknowns in the Exponent
0.8. Exercises
1. Functions and Applications
1.1. Functions from the Numerical, Algebraic, and Graphical Viewpoints
Introduction
Functions and Equations
Piecewise-Defined Functions
Vertical Line Test
Common Functions
1.1. Exercises
1.2. Functions and Models
Cost, Revenue, and Profit Models
Demand and Supply Models
Modeling Change Over Time
Algebra of Functions
1.2. Exercises
1.3. Linear Functions and Models
Linear Functions from the Numerical and Graphical Point of View
Finding a Linear Equation from Data
Applications: Linear Models
1.3. Exercises
1.4. Linear Regression
Observed and Predicted Values
Residuals, Sum-of-Squares Error
The Regression Line
Coefficient of Correlation
1.4. Exercises
Key Concepts
Review Exercises
Case Study. Modeling Spending on Mobile Advertising
Technology Guide. TI-83/84 Plus
Technology Guide. Spreadsheet
2. Nonlinear Functions and Models
2.1. Quadratic Functions and Models
Quadratic Functions
Quadratic Functions from the Graphical Point of View: Parabolas
Applications
Fitting a Quadratic Function to Data: Quadratic Regression
2.1. Exercises
2.2. Exponential Functions and Models
Exponential Functions
Exponential Functions from the Numerical and Graphical Points of View
Applications
The Number e and More Applications
Exponential Regression
2.2. Exercises
2.3. Logarithmic Functions and Models
Logarithms and Logarithmic Functions
Applications
Logarithmic Regression
2.3. Exercises
2.4. Logistic Functions and Models
Logistic Functions
Modeling with the Logistic Function
Logistic Regression
2.4. Exercises
Key Concepts
Review Exercises
Case Study. Checking up on Malthus
Technology Guide. TI-83/84 Plus
Technology Guide. Spreadsheet
3. Introduction to the Derivative
3.1. Limits: Numerical and Graphical Viewpoints
Evaluating Limits Numerically
Limits at Infinity
Estimating Limits Graphically
Application
3.1. Exercises
3.2. Limits and Continuity
Continuous Functions
Singularities
3.2. Exercises
3.3. Limits and Continuity: Algebraic Viewpoint
Closed-Form Functions
Functions Not in Closed Form
Limits at Infinity
Some Determinate and Indeterminate Forms
3.3. Exercises
3.4. Average Rate of Change
Change and Average Rate of Change
Formulas for Change and Average Rate of Change
Average Rate of Change of a Function Specified Algebraically
3.4. Exercises
3.5. The Derivative: Numerical and Graphical Viewpoints
Instantaneous Rate of Change of a Function
Secant and Tangent Lines
Quick Approximation of the Derivative
Leibniz d Notation
The Derivative Function
3.5. Exercises
3.6. The Derivative: Algebraic Viewpoint
Calculating the Derivative Algebraically
A Function Not Differentiable at a Point
3.6. Exercises
Key Concepts
Review Exercises
Case Study: Reducing Sulfur Emissions
Technology Guide. TI-83/84 Plus
Technology Guide. Spreadsheet
4. Techniques of Differentiation with Applications
4.1. Derivatives of Powers, Sums, and Constant Multiples
Shortcut Rules
The Power Rule
Another Notation: Differential Notation
The Rules for Sums and Constant Multiples
Applications
An Application to Limits: L’Hospital’s Rule
4.1. Exercises
4.2. A First Application: Marginal Analysis
Marginal Cost, Revenue, and Profit
Average Cost
4.2. Exercises
4.3. The Product and Quotient Rules
Motivating the Product Rule
Product and Quotient Rules
Application
4.3. Exercises
4.4. The Chain Rule
Introducing the Chain Rule
Application
4.4. Exercises
4.5. Derivatives of Logarithmic and Exponential Functions
Derivative of ln x and log b x
Derivatives of Logarithms of Functions
Derivatives of Exponential Functions
Derivatives of Exponentials of Functions
Applications
Application to Limits
4.5. Exercises
4.6. Implicit Differentiation
Implicit Functions
Implicit Differentiation
Logarithmic Differentiation
Application
4.6. Exercises
Key Concepts
Review Exercises
Case Study. Projecting Market Growth
5. Further Applications of the Derivatives
5.1. Maxima and Minima
Relative Extrema
Absolute Extrema
Locating Extrema
First Derivative Test
5.1. Exercises
5.2. Applications of Maxima and Minima
5.2. Exercises
5.3. Higher Order Derivatives: Acceleration and Concavity
The Second Derivative and Acceleration
Differential Notation for the Second Derivative
Geometric Interpretation of Second Derivative: Concavity
The Second Derivative Test for Relative Extrema
Higher Order Derivatives
5.3. Exercises
5.4. Analyzing Graphs
5.4. Exercises
5.5. Related Rates
5.5. Exercises
5.6. Elasticity
Price Elasticity of Demand
Income Elasticity of Demand
5.6. Exercises
Key Concepts
Review Exercises
Case Study: Production Lot Size Management
Technology Guide. TI-83/84 Plus
Technology Guide. Spreadsheet
6. The Integral
6.1. The Indefinite Integral
Antiderivatives and the Indefinite Integral
Calculating Indefinite Integrals
Applications
Motion in a Straight Line
6.1. Exercises
6.2. Substitution
The Technique of Substitution
Application
Shortcuts
6.2. Exercises
6.3. The Definite Integral: Numerical and Graphical Viewpoints
Riemann Sums
Calculating Riemann Sums
The Definite Integral
Calculating Definite Integrals
6.3. Exercises
6.4. The Definite Integral: Algebraic Viewpoint and the Fundamental Theorem of Calculus
Connection between Definite and Indefinite Integrals
Statement of the Fundamental Theorem of Calculus
Applications
6.4. Exercises
Key Concepts
Review Exercises
Case Study: Spending on Housing Construction
Technology Guide. TI-83/84 Plus
Technology Guide. Spreadsheet
7. Further Integration Techniques and Applications of the Integral
7.1. Integration by Parts
Integration-by-Parts Formula
The Tabular Method
7.1. Exercises
7.2. Area between Two Curves and Applications
7.2. Exercises
7.3. Averages and Moving Averages
Averages
Interpreting the Average of a Function Geometrically
7.3. Exercises
7.4. Applications to Business and Economics: Consumers’ and Producers’ Surplus and Continuous Income Streams
Consumers’ Surplus
Consumers’ Willingness to Spend
Consumers’ Expenditure
Producers’ Surplus
Continuous Income Streams
7.4. Exercises
7.5. Improper Integrals and Applications
Integrals in Which a Limit of Integration Is Infinite
Integrals in Which the Integrand Becomes Infinite
7.5. Exercises
7.6. Differential Equations and Applications
Differential Equations and Their Solutions
Simple Differential Equations
Separable Differential Equations
7.6. Exercises
Key Concepts
Review Exercises
Case Study. Estimating Tax Revenues
Technology Guide. TI-83/84 Plus
Technology Guide. Spreadsheet
8. Functions of Several Variables
8.1. Functions of Several Variables from the Numerical, Algebraic, and Graphical Viewpoints
Numerical and Algebraic Viewpoints
Geometric Viewpoint: Three-Dimensional Space and the Graph of a Function of Two Variables
8.1. Exercises
8.2. Partial Derivatives
Calculating and Interpreting Partial Derivatives
Geometric Interpretation of Partial Derivatives
Second-Order Partial Derivatives
8.2. Exercises
8.3. Maxima and Minima
Relative and Absolute Maxima and Minima
Second Derivative Test
Application: Deriving the Formulas for Linear Regression
8.3. Exercises
8.4. Constrained Maxima and Minima and Applications
Substitution Method
The Method of Lagrange Multipliers
Applications
8.4. Exercises
8.5. Double Integrals and Applications
Applications
8.5. Exercises
Key Concepts
Review Exercises
Case Study: Modeling College Population
Technology Guide. TI-83/84 Plus
Technology Guide. Spreadsheet
9. Trigonometric Models
9.1. Trigonometric Functions, Models, and Regression
The Sine Function
The Cosine Function
The Other Trigonometric Functions
Trigonometric Regression
9.1. Exercises
9.2. Derivatives of Trigonometric Functions and Applications
Derivatives of Sine and Cosine
Derivation of Formulas for Derivatives of the Sine and Cosine Functions
Derivatives of Other Trigonometric Functions
9.2. Exercises
9.3. Integrals of Trigonometric Functions and Applications
Integrals of Sine and Cosine
Integrals of the Six Trigonometric Functions
Derivations of Formulas for Integrals of Trigonometic Functions
Shortcuts
Using Integration by Parts with Trigonometric Functions
9.3. Exercises
Key Concepts
Review Exercises
Case Study: Predicting Airline Empty Seat Volume
Technology Guide. TI-83/84 Plus
Technology Guide. Spreadsheet
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Tags: Stefan Waner, Steven Costenoble, Applied Calculus