This text covers college-level algebra and trigonometry and is appropriate for a one-or two-term course in precalculus mathematics. Its approach is more interactive than most precalculus texts, and is designed to help students achieve a greater understanding of sophisticated mathematical concepts than they might be able to achieve with other texts. Our goal is to provide as much support and help for students as we can, in order to ease the difficult transition into their college-level mathematics course. At the same time, we want to give students solid preparation for calculus and maintain the appropriate topical coverage and level of presentation for a precalculus course.
The Real-Number System.
Exponential, Scientific, and Absolute-Value Notation.
Addition and Subtraction of Algebraic Expressions.
Multiplication of Algebraic Expressions.
Handling Dimension Symbols.
2. Equations, Inequalities, and Problem Solving.
Solving Equations and Inequalities.
Formulas and Problem Solving.
The Complex Numbers.
Formulas and Problem Solving.
Equations Reducible to Quadratic Variation.
3. Functions, Graphs, and Transformations.
Graphs of Equations.
The Distance Formula and Circles.
Lines and Linear Functions.
Graphs and Applications of Functions.
Combinations of Functions.
Transformations of Functions.
4. Polynomial and Rational Functions.
Sets, Sentences, and Inequalities.
Equations and Inequalities with Absolute Value.
Polynomial and Rational Inequalities.
Graphs of Polynomial Functions.
Division of Polynomials.
Theorems About Roots.
Further Help in Finding Roots.
5. Exponential and Logarithmic Functions.
Inverses of Relations and Functions.
Properties of Logarithmic Functions.
Finding Logarithmic Function Values on a Calculator.
Graphs of Exponential Functions with Base E, and Applications.
Solving Exponential and Logarithmic Equations.
Applications of Exponential and Logarithmic Functions.
Applications of Exponential and Natural Logarithmic Functions.
6. The Trigonometric Functions.
Trigonometric Functions of Acute Angles.
Applications of Right Triangles.
Trigonometric Functions of Any Angle.
Radians, Arc Length, and Angular Speed.
Graphs of Basic Circular Functions.
Graphs of Transformed Sine and Cosine Functions.
Transformed Graphs of Other Trigonometric Functions.
7. Trigonometric Identities, Inverse Functions, and Equations.
Trigonometric Manipulations and Identities.
Sum and Difference Identities.
Cofunction and Related Identities.
Some Important Identities.
Proving Trigonometric Identities.
Inverse of the Trigonometric Functions.
Composition of Trigonometric Functions and Their Inverses.
Identities in Solving Trigonometric Equations.
8. Triangles, Vectors, and Applications.
The Law of Sines.
The Law of Cosines.
Vectors and Applications.
Complex Numbers: DeMoivre's Theorem and nth Roots of Complex Numbers.
9. Systems and Matrices.
Systems of Equations in Two Variables.
Systems of Equations in Three or More Variables.
Special Cases of Systems.