Precalculus with Limits

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1. FUNCTIONS AND THEIR GRAPHS.

Rectangular Coordinates. Graphs of Equations. 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. Mathematical
Modeling and Variation. Summary and Study Strategies. Review
Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem
Solving.

2. POLYNOMIAL AND RATIONAL FUNCTIONS.

Quadratic Functions and Models. Polynomial Functions of Higher
Degree. Polynomial and Synthetic Division. Complex Numbers. Zeros
of Polynomial Functions. Rational Functions. Nonlinear
Inequalities. Summary and Study Strategies. Review Exercises.
Chapter Test. Proofs in Mathematics. P.S. Problem Solving.

3. 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 1-3. Proofs in Mathematics. P.S. Problem Solving.

4. TRIGONOMETRY.

Radian and Degree Measure. Trigonometric Functions: The Unit
Circle. 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.

5. 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.

6. 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 4-6. Proofs in Mathematics. P.S.
Problem Solving.

7. 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. Chapter Summary. Review
Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem
Solving.

8. 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. Chapter Summary. Review
Exercises. Chapter Test. Proofs in Mathematics. P.S. Problem
Solving.

9. 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 7-9. Proofs in Mathematics. P.S. Problem Solving.

10. TOPICS IN ANALYTIC GEOMETRY.

Lines. Introduction to Conics: Parabolas. Ellipses. Hyperbolas.
Rotation of Conics. Parametric Equations. Polar Coordinates. Graphs
of Polar Equations. Polar Equations of Conics. Summary and Study
Strategies. Review Exercises. Chapter Test. Proofs in Mathematics.
P.S. Problem Solving.

11. ANALYTIC GEOMETRY IN THREE DIMENSIONS.

The Three-Dimensional Coordinate System. Vectors in Space. The
Cross Product of Two Vectors. Lines and Planes in Space. Summary
and Study Strategies. Review Exercises. Chapter Test. Proofs in
Mathematics. P.S. Problem Solving.

12. LIMITS AND AN INTRODUCTION TO CALCULUS.

Introduction to Limits. Techniques for Evaluating Limits. The
Tangent Line Problem. Limits at Infinity and Limits of Sequences.
The Area Problem. Summary and Study Strategies. Review Exercises.
Chapter Test. Cumulative Test for Chapters. Proofs in Mathematics.
P.S. Problem Solving.

13. CONCEPTS IN STATISTICS.

Representing Data. Analyzing Data. Modeling Data. Summary and Study
Strategies. Review Exercises. Chapter Test. Cumulative Test for
Chapters. Proofs in Mathematics. P.S. Problem Solving.

APPENDIX A.

Review of Fundamental Concepts of Algebra.

A.1. Real Numbers and Their Properties.

A.2. Exponents and Radicals.

A.3. Polynomials and Factoring.

A.4. Rational Expressions.

A.5. Solving Equations.

A.6. Linear Inequalities in One Variable.

A.7. Errors and the Algebra of Calculus.

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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