College Algebra and Trigonometry

Mark Dugopolski was born in Menominee, Michigan. After receiving a B.S. from Michigan State University, he taught high school in Illinois for four years. He received an M.S. in mathematics from Northern Illinois University at DeKalb. He then received a Ph.D. in the area of topology and an M.S. in statistics from the University of Illinois at Champaign-Urbana. Mark taught mathematics at Southeastern Louisiana University in Hammond for 25 years and now holds the rank of Professor Emeritus of Mathematics. He has been writing textbooks since 1988. He is married and has two daughters. In his spare time he enjoys tennis, jogging, bicycling, fishing, kayaking, gardening, bridge, and motorcycling.

Chapter P   Prerequisites

P.1       Real Numbers and Their Properties

P.2       Integral Exponents and Scientific Notation

P.3       Rational Exponents and Radicals

P.4       Complex Numbers

P.5       Polynomials

P.6       Factoring Polynomials

P.7       Rational Expressions

 

Chapter 1  Equations, Inequalities, and Modeling

1.1       Equations in One Variable

1.2       Constructing Models to Solve Problems

1.3       Equations and Graphs in Two Variables

1.4       Linear Equations in Two Variables

1.5       Scatter Diagrams and Curve Fitting 

1.6       Quadratic Equations

1.7       Linear and Absolute Value and Inequalities

 

Chapter 2  Functions and Graphs

2.1       Functions

2.2       Graphs of Relations and Functions

2.3       Families of Functions, Transformations, and Symmetry

2.4       Operations with Functions

2.5       Inverse Functions

2.6       Constructing Functions with Variation

 

Chapter 3  Polynomial and Rational Functions

3.1       Quadratic Functions and Inequalities

3.2       Zeros of Polynomial Functions

3.3       The Theory of Equations

3.4       Miscellaneous Equations

3.5       Graphs of Polynomial Functions

3.6       Rational Functions and Inequalities

 

Chapter 4  Exponential and Logarithmic Functions

4.1       Exponential Functions and Their Applications

4.2       Logarithmic Functions and Their Applications

4.3       Rules of Logarithms

4.4       More Equations and Applications

 

Chapter 5  The Trigonometric Functions

5.1       Angles and Their Measurements

5.2       The Sine and Cosine Functions

5.3       The Graphs of the Sine and Cosine Functions

5.4       The Other Trigonometric Functions and Their Graphs

5.5       The Inverse Trigonometric Functions

5.6       Right Triangle Trigonometry

 

Chapter 6  Trigonometric Identities and Conditional Equations

6.1       Basic Identities

6.2       Verifying Identities

6.3       Sum and Difference Identities

6.4       Double-Angle and Half-Angle Identities

6.5       Product and Sum Identities

6.6       Conditional Trigonometric Equations

 

Chapter 7  Applications of Trigonometry

7.1       The Law of Sines

7.2       The Law of Cosines

7.3       Vectors

7.4       Trigonometric Form of Complex Numbers

7.5       Powers and Roots of Complex Numbers

7.6       Polar Equations

7.7       Parametric Equations

 

Chapter 8  Systems of Equations and Inequalities

8.1       Systems of Linear Equations in Two Variables

8.2       Systems of Linear Equations in Three Variables

8.3       Nonlinear Systems of Equations

8.4       Partial Fractions

8.5       Inequalities and Systems of Inequalities in Two Variables

8.6       The Linear Programming Model

 

Chapter 9  Matrices and Determinants

9.1       Solving Linear Systems Using Matrices

9.2       Operations with Matrices

9.3       Multiplication of Matrices

9.4       Inverses of Matrices

9.5       Solution of Linear Systems in Two Variables Using Determinants

9.6       Solution of Linear Systems in Three Variables Using Determinants 

 

Chapter 10  The Conic Sections

10.1     The Parabola

10.2     The Ellipse and the Circle

10.3     The Hyperbola

 

Chapter 11  Sequences, Series, and Probability

11.1     Sequences

11.2     Series

11.3     Geometric Sequences and Series

11.4     Counting and Permutations

11.5     Combinations, Labeling, and the Binomial Theorem

11.6     Probability

11.7     Mathematical Induction