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Marge Lial was always interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, is now affiliated with American River College.
Marge is an avid reader and traveler. Her travel experiences often find their way into her books as applications, exercise sets, and feature sets. She is particularly interested in archeology. Trips to various digs and ruin sites have produced some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.
Raymond N. Greenwell earned a B.A. in Mathematics and Physics from the University of San Diego, and an M.S. in Statistics, an M.S. in Applied Mathematics, and a Ph.D. in Applied Mathematics from Michigan State University, where he earned the graduate student teaching award in 1979. After teaching at Albion College in Michigan for four years, he moved to Hofstra University in1983, where he currently is Professor of Mathematics.
Raymond has published articles on fluid mechanics, mathematical biology, genetic algorithms, combinatorics, statistics, and undergraduate mathematics education. He is a member of MAA, AMS, SIAM, NCTM, and AMATYC. He is currently (2002-2005) governor of the Metropolitan New York Section of the MAA, as well as webmaster and liaison coordinator, and he received a distinguished service award from the Section in 2003. He is an outdoor enthusiast and leads trips in the Sierra Club’s Inner City Outings program.
Nathan P. Ritchey earned a B.A. in Mathematics with a minor in Music from Mansfield University of Pennsylvania. He earned a M.S. in Applied Mathematics and a Ph.D. in Mathematics from Carnegie Mellon University. He is currently a Professor of Mathematics and Chair of the Department of Mathematics and Statistics at Youngstown State University. He has published articles in economics, honors education, medicine, mathematics, operations research, and student recruitment. Nate is a Consultant/Evaluator for the North Central Association's Higher Learning Commission and regularly participates in program evaluations.
In recognition of his numerous activities, Nate has received the Distinguished Professor Award for University Service, the Youngstown Vindicator's "People Who Make a Difference Award," the Watson Merit Award for Department Chairs, the Spirit in Education Award from the SunTex corporation, and the Provost's Merit Award for significant contributions to the Honors Program.
A father of four children, Nate enthusiastically coaches soccer and softball. He also loves music, playing several instruments, and is a tenor in the Shenango Valley Chorale. More information about Nate Ritchey can be found at: http://www.as.ysu.edu/~nate/
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