The 12th edition of Larsons Algebra & Trig provides you with clear explanations of math concepts, engaging examples and exercises that relate to everyday life and helpful digital resources to help you study and practice when and where you want. Getting Ready for the Chapter sections prepare you to learn new concepts and Checkpoint problems, reinforcing your understanding of important skills. Summary and Study Strategies for each chapter include explanations and examples of the key objectives and essential study skills to help you succeed in the course.
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. 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. 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. 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. Proofs in Mathematics. P.S. Problem Solving.
APPENDIX A: ERRORS AND THE ALGEBRA OF CALCULUS.
APPENDIX B: CONCEPTS IN STATISTICS (ONLINE).
Representing Data. Analyzing Data. Modeling Data.
ALTERNATIVE VERSION OF CHAPTER P (ONLINE
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.
