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Applied Calculus
Stefan Waner and Steven R. Costenoble

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Everything for Finite Math
Everything for Calculus
Everything for Finite Math & Calculus
Topic Summaries
On-Line Tutorials
On-Line Text
Topic Quizzes
Topic Review Exercises
On-Line Utilities
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Chapter 1 Functions and Models
1.1 Functions from the Numerical and Algebraic Viewpoints On-line tutorial for Section 1.1
1.2 Functions from the Graphical Viewpoint On-line tutorial for Section 1.2
1.3 Linear Functions On-line tutorial for Section 1.3
1.4 Linear Models On-line tutorial for Section 1.4
1.5 *Linear RegressionOn-line tutorial for Section 1.5
On-Line: New Functions from Old: Scaled and Shifted Functions
On-Line: Fitting Functions to Data: Linear and Exponential Regression
You're the Expert-- Modeling Spending on Internet Advertising

On-Line Resources for Chapter 1
Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | Chapter Excel Tutorials

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


Chapter 2 Nonlinear Models
2.1 Quadratic Functions and Models
2.2 Exponential Functions and Models
2.3 Logarithmic Functions and Models
2.4* Trigonometric Functions and Models
On-Line: Inverse Fuctions
On-Line: Fitting Functions to Data: Linear and Exponential Regression
On-Line: Using and Deriving Algebraic Properties of Logarithms
On-Line: Trigonometric Functions and Calculus
You're the Expert-- Epidemics

On-Line Resources for Chapter 2
Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | Chapter Excel Tutorials

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


Chapter 3 Introduction to the Derivative
3.1 Average Rate of Change On-line tutorial for Section 3.1
3.2 The Derivative as Rate of Change: A Numerical Approach On-line tutorial for Section 3.2
3.3 The Derivative as Slope: A Geometric Approach On-line tutorial for Section 3.3
3.4 The Derivative as a Function: An Algebraic Approach On-line tutorial for Section 3.4
3.5 A First Application: Marginal Analysis
3.6* Limits and Continuity: Numerical & Graphical Approaches On-line tutorial for Section 3.6
3.7* Limits and Continuity: Algebraic Approach On-line tutorial for Section 3.7
On-Line: Sketching the Graph of the Derivative
On-Line: Proof of the Power Rule
On-Line: Continuity and Differentiability
You're the Expert--Reducing Sulfur Emissions

On-Line Resources for Chapter 3
Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | Chapter Excel Tutorials

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


Chapter 4 Techniques of Differentiation
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 Derivatives of Trigonometric Functions On-line text for this topic
4.5 Implicit Differentiation
On-Line:Linear Approximation and Error Estimation
On-Line:Proof of the Quotient Rule
On-Line:Proof of the Chain Rule
On-Line: Proofs of Some Trigonometric Limits
You're the Expert -- Projecting Market Growth

On-Line Resources for Chapter 4
Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises


Chapter 5 Applications of the Derivative
5.1 Maxima and Minima On-line tutorial for Section 5.1
5.2 Applications of Maxima and Minima On-line tutorial for Section 5.2
5.3 The Second Derivative and Analyzing Graphs
5.4 Related Rates On-line tutorial for Section 5.4
5.5 Elasticity of Demand
You're the Expert--Production Lot Size Management

On-Line Resources for Chapter 5
Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | Chapter Excel Tutorials

Math Tools for Chapter 5
Java Graphing Utility | Function Evaluator & Grapher | Excel First- and Second-Derivative Graphing Utility | Free Mac Grapher


Chapter 6 The Integral
6.1 The Indefinite Integral On-line tutorial for Section 6.1
6.2 Substitution On-line tutorial for Section 6.2
6.3 The Definite Integral as a Sum: A Numerical Approach
6.4 The Definite Integral as Area: A Geometric Approach
6.5 The Definite Integral: An Algebraic Approach and the Fundamental Theorem of Calculus
On-Line: Numerical Integration
You're the Expert--Wage Inflation

On-Line Resources for Chapter 6
Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | Chapter Excel Tutorials

Math Tools for Chapter 6
Numerical Integration Utility | Graphing Calculator Programs for Numerical Integration | Excel Riemann Sum Grapher


Chapter 7 Further Techniques and Applications of the Integral
7.1 Integration by Parts
7.2 Area Between Two Curves and Applications
7.3 Averages and Moving Averages
7.4 Continuous Income Streams
7.5 Improper Integrals and Applications
7.6 Differential Equations and Applications
You're the Expert--Estimating Tax Revenues

On-Line Resources for Chapter 7
Chapter Summary | Chapter True/False Quiz | Chapter Excel Tutorials


Chapter 8 Functions of Several Variables
8.1 Functions of Several Variables from the Numerical and Algebraic Viewpoints
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 Also See On-Line Material on Regression
8.6 Double Integrals
You're the Expert--Constructing a Best Fit Demand Curve

On-Line Resources for Chapter 8
Chapter Summary | Chapter True/False Quiz

Math Tools for Chapter 8
Surface Graphing Utility | Excel Surface Graphing Utility | Linear Multiple Regression Utility


On-Line Chapter: Trigonometric Functions and Calculus
(Text and Complete Exercise Sets On-Line; brings together material in Chapters 2, 4, and 6)
Introduction
Modeling with the Sine Function
The Six Trigonometric Functions
Derivatives of Trigonometric Functions
Integrals of Trigonometric Functions


Chapter P: Calculus Applied to Probability and Statistics
(Text and Complete Exercise Sets On-Line; a complete text version of this chapter can be downloaded here in pdf format)
Introduction
CP.1 Continuous Random Variables and Histograms
CP.2 Probability Density Functions: Uniform, Exponential, Normal, and Beta
CP.3 Mean, Median, Variance and Standard Deviation
You're the Expert--Creating a Family Trust


Appendix A: Algebra Review
A.1 Real Numbers On-line tutorial for Section A.1
A.2 Exponents and Radicals On-line tutorial for Section A.2
A.3 Multiplying and Factoring Algebraic Equations On-line tutorial for Section A.3
A.4 Rational Expressions On-line tutorial for Section A.4
A.5 Solving Polynomial Equations On-line tutorial for Section A.5
A.6 Solving Miscellaneous Equations

Last Updated: March, 2002
On-Line Materials Copyright © 2001 Stefan Waner & Steven R. Costenoble

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