College Algebra and Trigonometry

Mark Dugopolski was born in Menominee, Michigan. After receiving a B.S. from Michigan State University, he taught high school for four years, and then went on to receive an M.S. in mathematics from Northern Illinois University. He also received a Ph.D. in the area of topology from the University of Illinois at Champaign-Urbana, and ever since, Mark has been teaching at Southeastern Louisiana in Hammond, LA. He has been writing textbooks for about fifteen years. He is married and has two daughters, and enjoys playing tennis, jogging, and riding his bicycle in his spare time. Despite the presence of sailboats both on and in his precalculus textbooks, Mark does not sail-- it's his passion for showing students how mathematics is used in the real world that led him to the world of sailing.

P. Prerequisites.


Real Numbers and Their Properties.



Integral Exponents and Scientific Notation.



Rational Exponents and Radicals.



Polynomials.



Factoring Polynomials.



Rational Expressions.



1. Equations, Inequalities, and Modeling.


Equations in One Variable.



Constructing Models to Solve Problems.



Equations and Graphs in Two Variables.



Linear Equations in Two Variables.



Scatter Diagrams and Curve Fitting.



Quadratic Equations.



Linear and Absolute Value Inequalities.



2. Functions and Graphs.


Functions.



Graphs of Relations and Functions.



Families of Functions, Transformations, and Symmetry.



Operations with Functions.



Inverse Functions.



Constructing Functions with Variation.



3. Polynomial and Rational Functions.


Quadratic Functions and Inequalities.



Complex Numbers.



Zeros of Polynomial Functions.



The Theory of Equations.



Miscellaneous Equations.



Graphs of Polynomial Functions.



Rational Functions and Inequalities.



4. Exponential and Logarithmic Functions.


Exponential Functions and Their Applications.



Logarithmic Functions and Their Applications.



Rules of Logarithms.



More Equations and Applications.



5. The Trigonometric Functions.


Angles and Their Measurements.



The Sine and Cosine Functions.



The Graphs of the Sine and Cosine Functions.



The Other Trigonometric Functions and Their Graphs.



The Inverse Trigonometric Functions.



Right Triangle Trigonometry.



6. Trigonometric Identities and Conditional Equations.


Basic Identities.



Verifying Identities.



Sum and Difference Identities.



Double-Angle and Half-Angle Identities.



Product and Sum Identities.



Conditional Trigonometric Equations.



7. Applications of Trigonometry.


The Law of Sines.



The Law of Cosines.



Vectors.



Trigonometric Form of Complex Numbers.



Powers and Roots of Complex Numbers.



Polar Equations.



Parametric Equations.



8. Systems of Equations and Inequalities.


Systems of Linear Equations in Two Variables.



Systems of Linear Equations in Three Variables.



Nonlinear Systems of Equations.



Partial Fractions.



Inequalities and Systems of Inequalities in Two Variables.



The Linear Programming Model.



9. Matrices and Determinants.


Solving Linear Systems Using Matrices.



Operations with Matrices.



Multiplication of Matrices.



Inverses of Matrices.



Solution of Linear Systems in Two Variables Using Determinants.



Solution of Linear Systems in Three Variables Using Determinants.



10. The Conic Sections.


The Parabola.



The Ellipse and the Circle.



The Hyperbola.



11. Sequences, Series, and Probability.


Sequences.



Series.



Geometric Sequences and Series.



Counting and Permutations.



Combinations, Labeling, and the Binomial Theorem.



Probability.



Mathematical Induction.