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Finite Mathematics & Applied Calculus 4e
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| You can get back here from anywhere by pressing the"Everything for Finite Math and Calculus" link. | ||
| Chapter 0 Algebra Review | |||
| 0.1 Real Numbers | On-line tutorial for Section 0.1 | ||
| 0.2 Exponents and Radicals | On-line tutorial for Section 0.2 | ||
| 0.3 Multiplying and Factoring Algebraic Equations | On-line tutorial for Section 0.3 | ||
| 0.4 Rational Expressions | On-line tutorial for Section 0.4 | ||
| 0.5 Solving Polynomial Equations | On-line tutorial for Section 0.5 | ||
| 0.6 Solving Miscellaneous Equations | |||
| Chapter 1 Functions and Linear 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 Regression | On-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 | |||
| Case Study: 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 | |||
| Function Evaluator & Grapher | Excel Grapher | Simple Regression Utility | Free Mac Grapher | |||
| Chapter 2 Systems of Linear Equations and Matrices | |||
| 2.1 Systems of Two Linear Equations in Two Unknowns | On-line tutorial for Section 2.1 | ||
| 2.2 Using Matrices to Solve Systems of Equations | On-line tutorial for Section 2.2 | ||
| 2.3 Applications of Systems of Linear Equations | On-line tutorial for Section 2.3 | ||
| Case Study: The Impact of Regulating Sulfur Emissions | |||
On-Line Resources for Chapter 2 | |||
| Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | Chapter Excel Tutorials | |||
Math Tools for Chapter 2 | |||
| Row Operation and Pivoting Utility | Excel Row Operation and Pivoting Utility | Graphing Calculator Pivot Program (TI-82/83/84/85/86) | Free Mac Gauss-Jordan Program | |||
| Chapter 3 Matrix Algebra | |||
| 3.1 Matrix Addition and Scalar Multiplication | On-line tutorial for Section 3.1 | ||
| 3.2 Matrix Multiplication | On-line tutorial for Section 3.2 | ||
| 3.3 Matrix Inversion | On-line tutorial for Section 3.3 | ||
| 3.4 Matrices in Practice: Game Theory | On-line tutorial for Section 3.4 | ||
| 3.5 Matrices in Practice: Input-Output Models | On-line tutorial for Section 3.5 | ||
| Case Study: The Japanese Economy | |||
On-Line Resources for Chapter 3 | |||
| Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | Chapter Excel Tutorials | |||
Math Tools for Chapter 3 | |||
| Matrix Algebra Tool | On-Line Game Theory Utility | Free Mac Matrix Algebra Program | |||
| Chapter 4 Linear Programming | |||
| 4.1 Graphing Linear Inequalities | |||
| 4.2 Solving Linear Programming Problems Graphically | |||
| 4.3 The Simplex Method: Solving Standard Maximization Problems | On-line tutorial for Section 4.3 | ||
| 4.4 The Simplex Method: Solving General Linear Programming Problems | On-line tutorial for Section 4.4 | ||
| 4.5 The Simplex Method and Duality (Optional) | |||
| Case Study: Airline Scheduling | |||
On-Line Resources for Chapter 4 | |||
| Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | Chapter Excel Tutorials | |||
Math Tools for Chapter 4 | |||
| Linear Programming Grapher | Excel Row Operation and Pivoting Utility | Simplex Method Tool | Row Operation and Pivoting Utility | Graphing Calculator Pivot Program (TI-82/83/84/85/86) | Free Mac Pivot Program | |||
| Chapter 5 Mathematics of Finance | |||
| 5.1 Simple Interest | |||
| 5.2 Compound Interest | |||
| 5.3 Annuities, Loans, and Bonds | |||
| Case Study: Saving for College | |||
On-Line Resources for Chapter 5 | |||
| Chapter Summary | Chapter True/False Quiz | Chapter Excel Tutorials | |||
Math Tools for Chapter 5 | |||
| Time Value of Money Utility | |||
| Chapter 6 Sets and Counting | |||
| 6.1 Set Operations | |||
| 6.2 Cardinality | |||
| 6.3 The Addition and Multiplication Principles | |||
| 6.4 Permutations and Combinations | |||
| Case Study: Designing a Puzzle | |||
On-Line Resources for Chapter 6 | |||
| Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | |||
| Chapter 7 Probability | |||
| 7.1 Sample Spaces and Events | On-line tutorial for Section 7.1 | ||
| 7.2 Estimated and Theoretical Probability | On-line tutorial for Section 7.2 | ||
| 7.3 Properties of Probability Distributions | On-line tutorial for Section 7.3 | ||
| 7.4* Probability and Counting Techniques | |||
| 7.5 Conditional Probability and Independence | On-line tutorial for Section 7.5 | ||
| 7.6 Bayes' Theorem and Applications | On-line tutorial for Section 7.6 | ||
| 7.7 Probability in Practice: Markov Systems | |||
| Case Study: The Monty Hall Problem | On-line Monty Hall Simulation (Java) | ||
On-Line Resources for Chapter 7 | |||
| Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | |||
Math Tools for Chapter 7 | |||
| On-Line Markov System Simulation (Visual Simulation) | Matrix Algebra Tool | On-Line Markov System Computation Utility (Computes Powers of Transition Matrix) | |||
| Chapter 8 Random Variables and Statistics | |||
| 8.1 Random Variables and Distributions | On-line tutorial for Section 8.1 | ||
| 8.2 Bernoulli Trials and Binomial Random Variables | On-line tutorial for Section 8.2 | ||
| 8.3 Measures of Central Tendency | On-line tutorial for Section 8.3 | ||
| 8.4 Measures of Dispersion | On-line tutorial for Section 8.4 | ||
| 8.5 Normal Distributions | |||
| On-Line: Sampling Distributions and the Central Limit Theorem | |||
| On-Line: Confidence Intervals | |||
| On-Line: Calculus & Statistics | |||
| On-Line: Fitting Functions to Data: Regression | |||
| Case Study: Spotting Tax Fraud with Benford's Law | |||
On-Line Resources for Chapter 8 | |||
| Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | |||
Math Tools for Chapter 8 | |||
| Histogram and Probability Distribution Generator | Probability Distribution Generator and Grapher for Bernoulli Trials | Normal Distribution Utility | Normal Distribution Table | |||
| Chapter 9 Nonlinear Models | |||
| 9.1 Quadratic Functions and Models | On-line tutorial for Section 9.1 | ||
| 9.2 Exponential Functions and Models | On-line tutorial for Section 9.2 | ||
| 9.3 Logarithmic Functions and Models | On-line tutorial for Section 9.3 | ||
| 9.4 Logistic 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 | |||
| Case Study: Checking Up on Malthus | |||
On-Line Resources for Chapter 9 | |||
| Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | Chapter Excel Tutorials | |||
Math Tools for Chapter 9 | |||
| Function Evaluator & Grapher | Excel Grapher | Simple Regression Utility | Free Mac Grapher | |||
| Chapter 10 Introduction to the Derivative | |||
| 10.1 Limits: Numerical and Graphical Approaches | On-line tutorial for Section 10.1 | ||
| 10.2 Limits and Continuity | On-line tutorial for Section 10.2 | ||
| 10.3 Limits: Algebraic Approach | On-line tutorial for Section 10.3 | 10.4 Average Rate of Change | On-line tutorial for Section 10.4 Game version |
| 10.5 The Derivative: Numerical and Graphical Viewpoints | On-line tutorial for Section 10.5 Game version | ||
| 10.6 The Derivative: Algebraic Viewpoint | On-line tutorial for Section 10.6 Game version | ||
| 10.7 Derivatives of Powers, Sums, and Constant Multiples | On-line tutorial for Section 10.7 | ||
| 10.8 A First Application: Marginal Analysis | |||
| On-Line: Sketching the Graph of the Derivative | |||
| On-Line: Proof of the Power Rule | |||
| On-Line: Continuity and Differentiability | |||
| Case Study: Reducing Sulfur Emissions | |||
On-Line Resources for Chapter 10 | |||
| Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | Additional exercises for derivatives of powers, sums, and constant multiples | Chapter Excel Tutorials | |||
Math Tools for Chapter 10 | |||
| Function Evaluator & Grapher | Excel Grapher | Simple Regression Utility | Download Free Mac Grapher | |||
| Chapter 11 Techniques of Differentiation | |||
| 11.1 The Product and Quotient Rules | On-line tutorial for Section 11.1 | ||
| 11.2 The Chain Rule | On-line tutorial for Section 11.2 | ||
| 11.3 Derivatives of Logarithmic and Exponential Functions | On-line tutorial for Section 11.3 | ||
| 11.4 Implicit Differentiation | |||
| On-Line:Linear Approximation and Error Estimation | |||
| On-Line:Proof of the Quotient Rule | |||
| On-Line:Proof of the Chain Rule | |||
| Case Strudy: Projecting Market Growth | |||
On-Line Resources for Chapter 11 | |||
| Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | Additional exercises for product and quotient rules | |||
| Chapter 12 Applications of the Derivative | |||
| 12.1 Maxima and Minima | On-line tutorial for Section 12.1 | ||
| 12.2 Applications of Maxima and Minima | On-line tutorial for Section 12.2 | ||
| 12.3 The Second Derivative and Analyzing Graphs | On-line tutorial for Section 12.3 | ||
| 12.4 Related Rates | On-line tutorial for Section 12.4 | ||
| 12.5 Elasticity of Demand | |||
| Case Study: Production Lot Size Management | |||
On-Line Resources for Chapter 12 | |||
| Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | Chapter Excel Tutorials | |||
Math Tools for Chapter 12 | |||
| Function Evaluator & Grapher | Excel First- and Second-Derivative Graphing Utility | Free Mac Grapher | |||
| Chapter 13 The Integral | |||
| 13.1 The Indefinite Integral | On-line tutorial for Section 13.1 | ||
| 13.2 Substitution | On-line tutorial for Section 13.2 | ||
| 13.3 The Definite Integral: Numerical and Graphical Approaches | On-line tutorial for Section 13.3 | ||
| 13.4 The Definite Integral: Algebraic Approach and the Fundamental Theorem of Calculus | On-line tutorial for Section 13.4 | ||
| On-Line: Numerical Integration | |||
| Case Study: Wage Inflation | |||
On-Line Resources for Chapter 13 | |||
| Chapter Summary | Chapter True/False Quiz | Chapter Review Exercises | Chapter Excel Tutorials | |||
Math Tools for Chapter 13 | |||
| Numerical Integration Utility | Graphing Calculator Programs for Numerical Integration | Excel Riemann Sum Grapher | |||
| Chapter 14 Further Techniques and Applications of the Integral | |||
| 14.1 Integration by Parts | |||
| 14.2 Area Between Two Curves and Applications | |||
| 14.3 Averages and Moving Averages | |||
| 14.4 Applications to Business and Economics: Consumers' and Producers' Surplus and Continuous Income Streams | |||
| 14.5 Improper Integrals and Applications | |||
| 14.6 Differential Equations and Applications | |||
| Case Study: Estimating Tax Revenues | |||
On-Line Resources for Chapter 14 | |||
| Chapter Summary | Chapter True/False Quiz | Chapter Excel Tutorials | |||
| Chapter 15 Functions of Several Variables | |||
| 15.1 Functions of Several Variables from the Numerical and Algebraic Viewpoints | |||
| 15.2 Three Dimensional Space and the Graph of a Function of Two Variables | |||
| 15.3 Partial Derivatives | |||
| 15.4 Maxima and Minima | |||
| 15.5 Constrained Maxima and Minima Applications | Also See On-Line Material on Regression | ||
| 15.6 Double Integrals | |||
| Case Study: Constructing a Best Fit Demand Curve | |||
On-Line Resources for Chapter 15 | |||
| Chapter Summary | Chapter True/False Quiz | |||
Math Tools for Chapter 15 | |||
| Surface Graphing Utility | Excel Surface Graphing Utility | Linear Multiple Regression Utility | |||
| Chapter 16 Trigonometric Models | |||
| 16.1 Trigonometric Functions, Models, and Regression | |||
| 16.2 Derivatives of Trigonometric Functions and Applications | |||
| 16.3 Integrals of Trigonometric Functions and Applications | |||
| On-Line: Proofs of Some Trigonometric Limits | |||
| On-Line: New Functions from Old: Scaled and Shifted Functions | |||
| Case Study: Predicting Cocoa Inventories | |||
On-Line Resources for Chapter 16 | |||
| Chapter Summary | On-line version of this chapter | |||
Math Tools for Chapter 16 | |||
| Function Evaluator & Grapher | Excel Grapher | Excel Derivative Grapher | |||
| On-Line Chapter: Trigonometric Functions and Calculus (Text and Complete Exercise Sets On-Line; brings together material in Chapters 10, 12, and 14) |
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| 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) |
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| 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 | |||
| Case Study: Creating a Family Trust | |||
| Appendix A: Logic (Also see on-line full chapter version below.) | |||
| Appendix B: Table: Area Under a Normal Curve | |||
| Chapter L: Introduction to Logic (Text and Complete Exercise Sets On-Line; a complete text version of this chapter can be downloaded here in pdf format) |
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| Introduction | |||
| L.1 Statements and Logical Operators | |||
| L.2 Logical Equivalence, Tautologies and Contradictions | |||
| L.3 The Conditional and the Biconditional | |||
| L.4 Tautological Implications and Tautological Equivalences | |||
| L.5 Rules of Inference | |||
| L.6 Arguments and Proofs | |||
| L.7 Predicate Calculus | |||