Algebra & Trig

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P. PREREQUISITES.

Review of Real Numbers and Their Properties. Exponents and
Radicals. Polynomials and Special Products. Factoring Polynomials.
Rational Expressions. The Rectangular Coordinate System and Graphs.
Summary and Study Strategies. Review Exercises. Chapter Test.
Proofs in Mathematics. P.S. Problem Solving.

1. EQUATIONS, INEQUALITIES, AND MATHEMATICAL MODELING.

Graphs of Equations. Linear Equations in One Variable. Modeling
with Linear Equations. Quadratic Equations and Applications.
Complex Numbers. Other Types of Equations. Linear Inequalities in
One Variable. Other Types of Inequalities. Summary and Study
Strategies. Review Exercises. Chapter Test. Proofs in Mathematics.
P.S. Problem Solving.

2. FUNCTIONS AND THEIR GRAPHS.

Linear Equations in Two Variables. Functions. Analyzing Graphs of
Functions. A Library of Parent Functions. Transformations of
Functions. Combinations of Functions: Composite Functions. Inverse
Functions. Summary and Study Strategies. Review Exercises. Chapter
Test. Cumulative Test for Chapters P-2. Proofs in Mathematics. P.S.
Problem Solving.

3. POLYNOMIAL FUNCTIONS.

Quadratic Functions and Models. Polynomial Functions of Higher
Degree. Polynomial and Synthetic Division. Zeros of Polynomial
Functions. Mathematical Modeling and Variation. Summary and Study
Strategies. Review Exercises. Chapter Test. Proofs in Mathematics.
P.S. Problem Solving.

4. RATIONAL FUNCTIONS AND CONICS.

Rational Functions and Asymptotes. Graphs of Rational Functions.
Conics. Translations of Conics. Summary and Study Strategies.
Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem
Solving.

5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.

Exponential Functions and Their Graphs. Logarithmic Functions and
Their Graphs. Properties of Logarithms. Exponential and Logarithmic
Equations. Exponential and Logarithmic Models. Summary and Study
Strategies. Review Exercises. Chapter Test. Cumulative Test for
Chapters 3-5. Proofs in Mathematics. P.S. Problem Solving.

6. TRIGONOMETRY.

Angles and Their Measure. Right Triangle Trigonometry.
Trigonometric Functions of Any Angle. Graphs of Sine and Cosine
Functions. Graphs of Other Trigonometric Functions. Inverse
Trigonometric Functions. Applications and Models. Summary and Study
Strategies. Review Exercises. Chapter Test. Proofs in Mathematics.
P.S. Problem Solving.

7. ANALYTIC TRIGONOMETRY.

Using Fundamental Identities. Verifying Trigonometric Identities.
Solving Trigonometric Equations. Sum and Difference Formulas.
Multiple-Angle and Product-to-Sum Formulas. Summary and Study
Strategies. Review Exercises. Chapter Test. Proofs in Mathematics.
P.S. Problem Solving.

8. ADDITIONAL TOPICS IN TRIGONOMETRY.

Law of Sines. Law of Cosines. Vectors in the Plane. Vectors and Dot
Products. The Complex Plane. Trigonometric Form of a Complex
Number. Summary and Study Strategies. Review Exercises. Chapter
Test. Cumulative Test for Chapters 6-8. Proofs in Mathematics. P.S.
Problem Solving.

9. SYSTEMS OF EQUATIONS AND INEQUALITIES.

Linear and Nonlinear Systems of Equations. Two-Variable Linear
Systems. Multivariable Linear Systems. Partial Fractions. Systems
of Inequalities. Linear Programming. Summary and Study Strategies.
Review Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem
Solving.

10. MATRICES AND DETERMINANTS.

Matrices and Systems of Equations. Operations with Matrices. The
Inverse of a Square Matrix. The Determinant of a Square Matrix.
Applications of Matrices and Determinants. Summary and Study
Strategies. Review Exercises. Chapter Test. Proofs in Mathematics.
P.S. Problem Solving.

11. SEQUENCES, SERIES, AND PROBABILITY.

Sequences and Series. Arithmetic Sequences and Partial Sums.
Geometric Sequences and Series. Mathematical Induction. The
Binomial Theorem. Counting Principles. Probability. Summary and
Study Strategies. Review Exercises. Chapter Test. Cumulative Test
for Chapters 9-11. Proofs in Mathematics. P.S. Problem Solving.

APPENDIX A: Errors and the Algebra of Calculus.

APPENDIX B: Concepts in Statistics (Web).

B.1 Representing Data.

B.2 Analyzing Data.

B.3 Modeling Data.

Alternative Version of Chapter P (Web).

P.1. Operations with Real Numbers.

P.2. Properties of Real Numbers.

P.3. Algebraic Expressions.

P.4. Operations with Polynomials.

P.5. Factoring Polynomials.

P.6. Factoring Trinomials.

Dr. Ron Larson is a professor of mathematics at the Pennsylvania State University, where he has taught since 1970. He is considered the pioneer of using multimedia to enhance the learning of mathematics, having authored more than 30 software titles since 1990. Dr. Larson has also authored numerous acclaimed textbooks, including the best-selling calculus series coauthored with Dr. Bruce Edwards and published by Cengage. Dr. Larson received the 2017 William Holmes McGuffey Longevity Award for PRECALCULUS and for CALCULUS. He also received the 2018 Text and Academic Authors Association TEXTY Award for CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS. In addition, Dr. Larson received the 1996 Text and Academic Authors Association TEXTY Award for INTERACTIVE CALCULUS -- a complete text on CD-ROM that was the first mainstream college textbook to be offered on the internet.

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