Ron Harshbarger got his BS from Shippensburg State, an MST from the University of New Hampshire, did graduate work at Penn State University, and received a PhD from the University of Pittsburgh. During a long and highly successful career at Penn State University, Dr. Harshbarger received both teaching and advising awards. At Georgia Southern University, he taught a wide variety of undergraduate and graduate courses in mathematics, developed five new mathematics courses, and created the mathematics component for a new doctoral degree.

At the University of South Carolina Beaufort, Dr. Harshbarger was named Professor of the year in 1999. In 2000, Professor Harshbarger was named the Governor’s Professor of the Year for the State of South Carolina. In 2001, the University of South Carolina Board of Trustees named him the Trustee Professor of the Year. In 2002, he received the Mathematical Association of America Southeastern Section Award for Distinguished University Teaching of Mathematics. He was nominated for the 2003 Haimo Award for Distinguished College or University Teaching of Mathematics, a national award given by the Mathematical Association of America. In 2003, he was also named Professor of the Year at the University of South Carolina Beaufort and given the Governor’s Distinguished Professor Award for the state of South Carolina.

1. Functions, Graphs, and Models; Linear Functions

            INTEGRATED REVIEW TOPICS:

            1. Write sets of numbers using descriptions or elements

            2. Identify sets of real numbers as being integers, rational numbers, and/or irrational numbers

            3. Graph numbers on a number line

            4.  Work with set operations

            5. Find absolute values

            6. Calculate with real numbers

            7. Use properties of real numbers

            8. Express inequalities as intervals and graph inequalities

            9. Identify the coefficients of terms and constants in algebraic expressions

            10. Combine like terms

            11. Removing parentheses

            12. Evaluate algebraic expressions

            13. Plot points on a coordinate system

            14. Use subscripts to represent fixed points

1.1 Functions and Models

1.2 Graphs of Functions

1.3 Linear Functions

1.4 Equations of Lines

2. Linear Models, Equations, and Inequalities

            INTEGRATED REVIEW TOPICS:

            1. Rounding and significant digits

            2. Write fractions in lowest terms

            3. Multiply and divide fractions

            4. Add and subtract fractions

            5. Identify expressions and equations

            6. Solve basic linear equations using the addition or multiplication property

            7. Use the multiplication or division properties of equations to solve linear equations

            8. Solve more linear equations

            9. Determine if a linear equation is a conditional equation, and identity, or a contradiction

            10. Evaluate formulas for given values

            11. Use properties of inequalities to solve linear inequalities

2.1 Algebraic and Graphical Solution of Linear Equations

2.2 Fitting Lines to Data Points: Modeling Linear Functions

2.3 Systems of Linear Equations in Two Variables

2.4 Solutions of Linear Inequalities

3. Quadratic, Piecewise-Defined, and Power Functions

            INTEGRATED REVIEW TOPICS:

            1. Use the properties of exponents with integers

            2. Understand terminology related to polynomials

            3. Add and subtract monomials and polynomials

            4. Multiply monomials and polynomials

            5. Factor out common factors

            6. Factor by grouping

            7. Factor polynomials

            8. Factor trinomials

            9. Radicals

            10.  Simplify radicals

            11. Multiply and divide radicals

            12. Add and subtract radicals

            13. Convert between exponential and radical form

3.1 Quadratic Functions; Parabolas

3.2 Solving Quadratic Equations

3.3 Piecewise-Defined Functions and Power Functions

3.4 Quadratic and Power Models

4. Additional Topics with Functions

            INTEGRATED REVIEW TOPICS:

            1. Write rational expressions in lowest terms

            2. Multiply and divide rational expressions

            3. Add and subtract rational expressions with the same denominator

            4. Find the least common denominator

            5. Add and subtract rational expressions with the unlike denominators

            6. Simplify complex fractions

            7. Work with the complex number i

            8. Add and subtract complex numbers

            9. Multiply and divide complex numbers

4.1 Transformations of Graphs and Symmetry

4.2 Combining Functions; Composite Functions

4.3 One-to-One and Inverse Functions

4.4 Additional Equations and Inequalities

5. Exponential and Logarithmic Functions

            INTEGRATED REVIEW TOPICS:

            1. Use properties of exponents with real numbers

            2. Simplify exponential expressions

            3. Convert between standard notation and scientific notation

            4. Simplify expressions involving scientific notation

            5. Simplify expressions involving rational exponents

            6. Divide polynomials

5.1 Exponential Functions

5.2 Logarithmic Functions; Properties of Logarithms

5.3 Exponential and Logarithmic Equations

5.4 Exponential and Logarithmic Models

5.5 Exponential Functions and Investing

5.6 Annuities; Loan Repayment

5.7 Logistic and Gompertz Functions

6. Higher-Degree Polynomial and Rational Functions

6.1 Higher-Degree Polynomial Functions

6.2 Modeling with Cubic and Quartic Functions

6.3 Solution of Polynomial Equations

6.4 Polynomial Equations Continued; Fundamental Theorem of Algebra

6.5 Rational Functions and Rational Equations

6.6 Polynomial and Rational Inequalities

7. Systems of Equations and Matrices

7.1 Systems of Linear Equations in Three Variables

7.2 Matrix Solution of Systems of Linear Equations

7.3 Matrix Operations

7.4 Inverse Matrices; Matrix Equations

7.5 Systems of/onlinear Equations

8. Special Topics: Systems of Inequalities and Linear Programming; Sequences and Series; Preparing for Calculus

8.1 Systems of Inequalities

8.2 Linear Programming: Graphical Methods

8.3 Sequences and Discrete Functions

8.4 Series

8.5 Preparing for Calculus

Appendix A: Basic Calculator Guide

Appendix B: Basic Guide to Excel 2003 and Excel 2010

Answers to Selected Exercises

Index

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.