Calculus Applied to the Real World

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Calculus Applied to the Real World

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Finite Mathematics
Applied to the Real World

Finite Mathematics & Calculus
Applied to the Real World

Chapter 1 Functions and Graphs
Introduction
1.1 Coordinates and Graphs
1.2 Functions and their Graphs
1.3 Linear Functions
1.4 Linear Models
1.5 Quadratic Functions and Models
1.6 Solving Equations Using Graphing Calculators or Computers
You're the Expert--Modeling the Demand for Poultry
Review Exercises
On-Line Chapter Summary
On-Line Chapter True/False Quiz
On-Line Chapter Review Exercises

Additional On-Line Topics
New Functions from Old: Scaled and Shifted Functions
Fitting Functions to Data: Regression

Math Tools for Chapter 1
Java Graphing Utility | Function Evaluator & Grapher & Grapher | Simple Regression Utility | Free Mac Grapher


Chapter 2 Exponential and Logarithmic Functions
Introduction
2.1 Exponential Functions and Applications
2.2 Continuous Growth and Decay and the Number e
2.3 Logarithmic Functions
2.4 Applications of Logarithms
You're the Expert--Epidemics
Review Exercises
On-Line Chapter Summary
On-Line Chapter True/False Quiz

Math Tools for Chapter 2
Java Graphing Utility | Function Evaluator & Grapher | Simple Regression Utility | Free Mac Grapher


Chapter 3 Introduction to the Derivative
Introduction
3.1 Rates of Change and the Derivative On-line tutorial for Section 3.1
3.2 Geometric Interpretation of the Derivative On-line tutorial for Section 3.2
3.3 Limits and Continuity On-line tutorial for Section 3.3
3.4 Derivatives of Powers and Polynomials On-line tutorial for Section 3.4
3.5 Marginal Analysis
3.6 More on Limits, Continuity and Differentiability
You're the Expert--Reducing Sulfur Emissions
Review Exercises
On-Line Chapter Summary
On-Line Chapter True/False Quiz

Additional On-Line Topics
Sketching the Graph of the Derivative
Proof of the Power Rule

Math Tools for Chapter 3
Java Graphing Utility | Function Evaluator & Grapher | Simple Regression Utility | Free Mac Grapher


Chapter 4 Techniques of Differentiation
Introduction
4.1 The Product and Quotient Rules On-line tutorial for Section 4.1
4.2 The Chain Rule On-line tutorial for Section 4.2
4.3 Derivatives of Logarithmic and Exponential Functions On-line tutorial for Section 4.3
4.4 Implicit Differentiation
4.5 Linear Approximation and Error Estimation
You're the Expert --Estimating Mortgage Rates
Review Exercises
On-Line Chapter Summary
On-Line Chapter True/False Quiz
On-Line Chapter Review Exercises

Additional On-Line Topics
Proof of the Quotient Rule
Proof of the ChainRule
Proofs of some Trigonometric Limits


Chapter 5 Applications of the Derivative
Introduction
5.1 Maxima and Minima
5.2 Applications of Maxima and Minima
5.3 The Second Derivative: Acceleration and Concavity
5.4 Curve Sketching
5.5 Related Rates On-line tutorial for Section 5.5
5.6 Elasticity of Demand
You're the Expert--Production Lot Size Management
Review Exercises
On-Line Chapter Summary
On-Line Chapter True/False Quiz
On-Line Review Exercises on Maxima & Minima
On-Line Review Exercises onElasticity of Demand

Math Tools for Chapter 5
Java Graphing Utility | Function Evaluator & Grapher | Free Mac Grapher


Chapter 6 The Integral
Introduction
6.1 The Indefinite Integral On-line tutorial for Section 6.1
6.2 Substitution On-line tutorial for Section 6.2
6.3 Applications of the Indefinite Integral
6.4 Geometric Definition of the Definite Integral
6.5 Algebraic Definition of the Definite Integral
6.6 The Fundamental Theorem of Calculus
6.7 Numerical Integration
You're the Expert--The Cost of Issuing a Warranty
Review Exercises
On-Line Chapter Summary
On-Line Chapter True/False Quiz
On-Line Review Exercises for Chapter 6

Math Tools for Chapter 10
Numerical Integration Utility | Graphing Calculator Programs for Numerical Integration


Chapter 7 Further Techniques and Applications of the Integral
Introduction
7.1 Integration by Parts
7.2 Integration Using Tables
7.3 Area Between Two Curves and Applications
7.4 Averages and Moving Averages
7.5 Improper Integrals and Applications
You're the Expert--Estimating Tax Revenues
Review Exercises
On-Line Chapter Summary
On-Line Chapter True/False Quiz


Chapter 8 Functions of Several Variables
Introduction
8.1 Functions of Two or More Variables
8.2 Three Dimensional Space and the Graph of a Function of Two Variables
8.3 Partial Derivatives
8.4 Maxima and Minima
8.5 Constrained Maxima and Minima Applications
8.6 Least Squares Fit Also See On-Line Material on Regression
You're the Expert--Constructing a Best Fit Demand Curve
Review Exercises
On-Line Chapter Summary
On-Line Chapter True/False Quiz

Math Tools for Chapter 8
Linear Multiple Regression Utility


On-Line Chapter: Calculus and Probability
(Text and Complete Exercise Sets On-Line)
Introduction
Continuous Random Variables and Histograms
Probability Density Functions: Uniform, Exponential, Normal, and Beta
Mean, Median, Variance and Standard Deviation
You're the Expert--Creating a Family Trust


On-Line Chapter: Trigonometric Functions and Calculus
(Text and Complete Exercise Sets On-Line)
Introduction
Modeling with the Sine Function
The Six Trigonometric Functions
Derivatives of Trigonometric Functions
Integrals of Trigonometric Functions


Appendix A: Algebra Review
Introduction
Operations on the Real Numbers On-line tutorial for Section A.1
Integer Exponents On-line tutorial for Section A.2
Radicals and Rational Exponents On-line tutorial for Section A.3
The Distributive Law: Multiplying Algebraic Expressions On-line tutorial for Section A.4
Factoring Algebraic Expressions On-line tutorial for Section A.5
Rational Expressions On-line tutorial for Section A.6
Equations On-line tutorial for Section A.7
Solving Polynomial Equations
Solving Miscellaneous Equations


Appendix B: Using a Graphing Calculator


Appendix C: Using a Computer Spreadsheet


Appendix D: A Table of Integrals

Last Updated: February, 1998
Copyright © 1995-1996 HarperCollins Publishers
On-Line Materials Copyright © 1997-1998 Stefan Waner & Steven R. Costenoble