Finite Mathematics and Calculus with Applications Book

R. Algebra Reference

R.1 Polynomials

R.2 Factoring

R.3 Rational Expressions

R.4 Equations

R.5 Inequalities

R.6 Exponents

R.7 Radicals

1. Linear Functions

1.1 Slopes and Equations of Lines

1.2 Linear Functions and Applications

1.3 The Least Squares Line

Chapter 1 Review

Extended Application: Using Extrapolation to Predict Life Expectancy

2. Systems of Linear Equations and Matrices

2.1 Solution of Linear Systems by the Echelon Method

2.2 Solution of Linear Systems by the Gauss-Jordan Method

2.3 Addition and Subtraction of Matrices

2.4 Multiplication of Matrices

2.5 Matrix Inverses

2.6 Input-Output Models

Chapter 2 Review

Extended Application: Contagion

3. Linear Programming: The Graphical Method

3.1 Graphing Linear Inequalities

3.2 Solving Linear Programming Problems Graphically

3.3 Applications of Linear Programming

Chapter 3 Review

Extended Application: Sensitivity Analysis

4. Linear Programming: The Simplex Method

4.1 Slack Variables and the Pivot

4.2 Maximization Problems

4.3 Minimization Problems; Duality

4.4 Nonstandard Problems

Chapter 4 Review

Extended Application: Using Integer Programming in the Stock-Cutting Problem

5. Mathematics of Finance

5.1 Simple and Compound Interest

5.2 Future Value of an Annuity

5.3 Present Value of an Annuity; Amortization

Chapter 5 Review

Extended Application: Time, Money, and Polynomials

6. Logic

6.1 Statements

6.2 Truth Tables and Equivalent Statements

6.3 The Conditional and Circuits

6.4 More on the Conditional

6.5 Analyzing Arguments and Proofs

6.6 Analyzing Arguments with Quantifiers

Chapter 6 Review

Extended Application: Logic Puzzles

7. Sets and Probability

7.1 Sets

7.2 Applications of Venn Diagrams

7.3 Introduction to Probability

7.4 Basic Concepts of Probability

7.5 Conditional Probability; Independent Events

7.6 Bayes' Theorem

Chapter 7 Review

Extended Application: Medical Diagnosis

8. Counting Principles; Further Probability Topics

8.1 The Multiplication Principle; Permutations

8.2 Combinations

8.3 Probability Applications of Counting Principles

8.4 Binomial Probability

8.5 Probability Distributions; Expected Value

Chapter 8 Review

Extended Application: Optimal Inventory for a Service Truck

9. Statistics

9.1 Frequency Distributions; Measures of Central Tendency

9.2 Measures of Variation

9.3 The Normal Distribution

9.4 Normal Approximation to the Binomial Distribution

Chapter 9 Review

Extended Application: Statistics in the Law - The Castaneda Decision

10. Nonlinear Functions

10.1 Properties of Functions

10.2 Quadratic Functions; Translation and Reflection

10.3 Polynomial and Rational Functions

10.4 Exponential Functions

10.5 Logarithmic Functions

10.6 Applications: Growth and Decay; Mathematics of Finance

Chapter 10 Review

Extended Application: Characteristics of the Monkeyface Prickleback

11. The Derivative

11.1 Limits

11.2 Continuity

11.3 Rates of Change

11.4 Definition of the Derivative

11.5 Graphical Differentiation

Chapter 11 Review

Extended Application: A Model for Drugs Administered Intravenously

12. Calculating the Derivative

12.1 Techniques for Finding Derivatives

12.2 Derivatives of Products and Quotients

12.3 The Chain Rule

12.4 Derivatives of Exponential Functions

12.5 Derivatives of Logarithmic Functions

Chapter 12 Review

Extended Application: Electrical Potential and Electric Field

13. Graphs and the Derivative

13.1 Increasing and Decreasing Functions

13.2 Relative Extrema

13.3 Higher Derivatives, Concavity, and the Second Derivative Test

13.4 Curve Sketching

Chapter 13 Review

Extended Application: A Drug Concentration Model for Orally Administered Medications

14. Applications of the Derivative

14.1 Absolute Extrema

14.2 Applications of Extrema

14.3 Further Business Applications: Economic Lot Size; Economic Order Quantity; Elasticity of Demand

14.4 Implicit Differentiation

14.5 Related Rates

14.6 Differentials: Linear Approximation

Chapter 14 Review

Extended Application: A Total Cost Model for a Training Program

15. Integration

15.1 Antiderivatives

15.2 Substitution

15.3 Area and the Definite Integral

15.4 The Fundamental Theorem of Calculus

15.5 The Area Between Two Curves

15.6 Numerical Integration

Chapter15 Review

Extended Application: Estimating Depletion Dates for Minerals

16. Further Techniques and Applications of Integration

16.1 Integraton by Parts

16.2 Volume and Average Value

16.3 Continuous Money Flow

16.4 Improper Integrals

Chapter 16 Review

Extended Application: Estimating Learning Curves in Manufacturing with Integrals

17. Multivariable Calculus

17.1 Functions of Several Variables

17.2 Partial Derivatives

17.3 Maxima and Minima

17.4 Lagrange Multipliers

17.5 Total Differentials and Approximations

17.6 Double Integrals

Chapter 17 Review

Extended Application: Using Multivariable Fitting to Create a Response Surface Design

18. Probability and Calculus

18.1 Continuous Probability Models

18.2 Expected Value and Variance of Continuous Random Variables

18.3 Special Probability Density Functions

Chapter 18 Review

Extended Application: Exponential Waiting Times