# Calculus Applied to the Real World

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 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