Precalculus
A Right Triangle Approach
3rd Edition
Published on 21. March 2014
Book
Hardback
1104 pages
978-0-321-91276-3 (ISBN)
Description
Ratti and McWaters have combined years of lecture notes and classroom experience to bring you a series that connects concepts and maintains course rigor. An extensive array of exercises and learning aids further complements your instruction, which ultimately helps to improve student mathematical understanding and results in the course.
KEY TOPICS: Basic Concepts of Algebra; Equations and Inequalities; Graphs and Functions; Polynomial and Rational Functions; Exponential and Logarithmic Functions; Trigonometric Functions; Trigonometric Identities and Equations; Applications of Trigonometric Functions; Systems of Equations and Inequalities; Matrices and Determinants; Conic Sections; Further Topics in Algebra
MARKET: For all readers interested in precalculus.
KEY TOPICS: Basic Concepts of Algebra; Equations and Inequalities; Graphs and Functions; Polynomial and Rational Functions; Exponential and Logarithmic Functions; Trigonometric Functions; Trigonometric Identities and Equations; Applications of Trigonometric Functions; Systems of Equations and Inequalities; Matrices and Determinants; Conic Sections; Further Topics in Algebra
MARKET: For all readers interested in precalculus.
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Persons
J.S. Ratti has been teaching mathematics at all levels for over 35 years. He is currently a full professor of mathematics and director of the Center for Mathematical Services at the University of South Florida. Professor Ratti is the author of numerous research papers in analysis, graph theory, and probability. He has won several awards for excellence in undergraduate teaching at University of South Florida and is the coauthor of a successful finite mathematics textbook.
Marcus McWaters is currently the chair of the Mathematics Department at the University of South Florida, a position he has held for the last eleven years. Since receiving his PhD in mathematics from the University of Florida, he has taught all levels of undergraduate and graduate courses, with class sizes ranging from 3 to 250. As chair, he has worked intensively to structure a course delivery system for lower level courses that would improve the low retention rate these courses experience across the country. When not involved with mathematics or administrative activity, he enjoys playing racquetball, spending time with his two daughters, and traveling the world with his wife.
Marcus McWaters is currently the chair of the Mathematics Department at the University of South Florida, a position he has held for the last eleven years. Since receiving his PhD in mathematics from the University of Florida, he has taught all levels of undergraduate and graduate courses, with class sizes ranging from 3 to 250. As chair, he has worked intensively to structure a course delivery system for lower level courses that would improve the low retention rate these courses experience across the country. When not involved with mathematics or administrative activity, he enjoys playing racquetball, spending time with his two daughters, and traveling the world with his wife.
Content
P. Basic Concepts of Algebra
P.1 The Real Numbers and Their Properties
P.2 Integer Exponents and Scientific Notation
P.3 Polynomials
P.4 Factoring Polynomials
P.5 Rational Expressions
P.6 Rational Exponents and Radicals
Chapter P Summary
Chapter P Review Exercises
Chapter P Practice Test A
Chapter P Practice Test B
1. Equations and Inequalities
1.1 Linear Equations in One Variable
1.2 Quadratic Equations
1.3 Complex Numbers: Quadratic Equations with Complex Solutions
1.4 Solving Other Types of Equations
1.5 Inequalities
1.6 Equations and Inequalities Involving Absolute Value
Chapter 1 Summary
Chapter 1 Review Exercises
Chapter 1 Practice Test A
Chapter 1 Practice Test B
2. Graphs and Functions
2.1 The Coordinate Plane
2.2 Graphs of Equations
2.3 Lines
2.4 Functions
2.5 Properties of Functions
2.6 A Library of Functions
2.7 Transformations of Functions
2.8 Combining Functions; Composite Functions
2.9 Inverse Functions
Chapter 2 Summary
Chapter 2 Review Exercises
Chapter 2 Practice Test A
Chapter 2 Practice Test B
Cumulative Review Exercises- Chapters P-2
3. Polynomial and Rational Functions
3.1 Quadratic Functions
3.2 Polynomial Functions
3.3 Dividing Polynomials
3.4 The Real Zeros of a Polynomial Function
3.5 The Complex Zeros of a Polynomial Function
3.6 Rational Functions
3.7 Variation
Chapter 3 Summary
Chapter 3 Review Exercises
Chapter 3 Practice Test A
Chapter 3 Practice Test B
Cumulative Review Exercises- Chapters P-3
4. Exponential and Logarithmic Functions
4.1 Exponential Functions
4.2 Logarithmic Functions
4.3 Rules of Logarithms
4.4 Exponential and Logarithmic Equations and Inequalities
4.5 Logarithmic Scales
Chapter 4 Summary
Chapter 4 Review Exercises
Chapter 4 Practice Test A
Chapter 4 Practice Test B
Cumulative Review Exercises- Chapters P-4
5. Trigonometric Functions
5.1 Angles and Their Measure
5.2 Right-Triangle Trigonometry
5.3 Trigonometric Functions of Any Angle; The Unit Circle
5.4 Graphs of the Sine and Cosine Functions
5.5 Graphs of the Other Trigonometric Functions
5.6 Inverse Trigonometric Functions
Chapter 5 Summary
Chapter 5 Review Exercises
Chapter 5 Practice Test A
Chapter 5 Practice Test B
Cumulative Review Exercises- Chapters P-5
6. Trigonometric Identities and Equations
6.1 Verifying Identities
6.2 Sum and Difference Formulas
6.3 Double-Angle and Half-Angle Formulas
6.4 Product-to-Sum and Sum-to-Product Formulas
6.5 Trigonometric Equations I
6.6 Trigonometric Equations II
Chapter 6 Summary
Chapter 6 Review Exercises
Chapter 6 Practice Test A
Chapter 6 Practice Test B
Cumulative Review Exercises- Chapters P-6
7. Applications of Trigonometric Functions
7.1 The Law of Sines
7.2 The Law of Cosines
7.3 Areas of Polygons Using Trigonometry
7.4 Vectors
7.5 The Dot Product
7.6 Polar Coordinates
7.7 Polar Form of Complex Numbers; DeMoivre's Theorem
Chapter 7 Summary
Chapter 7 Review Exercises
Chapter 7 Practice Test A
Chapter 7 Practice Test B
Cumulative Review Exercises- Chapters P-7
8. Systems of Equations and Inequalities
8.1 Systems of Linear Equations in Two Variables
8.2 Systems of Linear Equations in Three Variables
8.3 Partial-Fraction Decomposition
8.4 Systems of Nonlinear Equations
8.5 Systems of Inequalities
8.6 Linear Programming
Chapter 8 Summary
Chapter 8 Review Exercises
Chapter 8 Practice Test A
Chapter 8 Practice Test B
Cumulative Review Exercises- Chapters P-8
9. Matrices and Determinants
9.1 Matrices and Systems of Equations
9.2 Matrix Algebra
9.3 The Matrix Inverse
9.4 Determinants and Cramer's Rule
Chapter 9 Summary
Chapter 9 Review Exercises
Chapter 9 Practice Test A
Chapter 9 Practice Test B
Cumulative Review Exercises- Chapters P-9
10. Conic Sections
10.1 Conic Sections: Overview
10.2 The Parabola
10.3 The Ellipse
10.4 The Hyperbola
Chapter 10 Summary
Chapter 10 Review Exercises
Chapter 10 Practice Test A
Chapter 10 Practice Test B
Cumulative Review Exercises- Chapters P-10
11. Further Topics in Algebra
11.1 Sequences and Series
11.2 Arithmetic Sequences; Partial Sums
11.3 Geometric Sequences and Series
11.4 Mathematical Induction
11.5 The Binomial Theorem
11.6 Counting Principles
11.7 Probability
Chapter 11 Summary
Chapter 11 Review Exercises
Chapter 11 Practice Test A
Chapter 11 Practice Test B
Cumulative Review Exercises- Chapters P-11
P.1 The Real Numbers and Their Properties
P.2 Integer Exponents and Scientific Notation
P.3 Polynomials
P.4 Factoring Polynomials
P.5 Rational Expressions
P.6 Rational Exponents and Radicals
Chapter P Summary
Chapter P Review Exercises
Chapter P Practice Test A
Chapter P Practice Test B
1. Equations and Inequalities
1.1 Linear Equations in One Variable
1.2 Quadratic Equations
1.3 Complex Numbers: Quadratic Equations with Complex Solutions
1.4 Solving Other Types of Equations
1.5 Inequalities
1.6 Equations and Inequalities Involving Absolute Value
Chapter 1 Summary
Chapter 1 Review Exercises
Chapter 1 Practice Test A
Chapter 1 Practice Test B
2. Graphs and Functions
2.1 The Coordinate Plane
2.2 Graphs of Equations
2.3 Lines
2.4 Functions
2.5 Properties of Functions
2.6 A Library of Functions
2.7 Transformations of Functions
2.8 Combining Functions; Composite Functions
2.9 Inverse Functions
Chapter 2 Summary
Chapter 2 Review Exercises
Chapter 2 Practice Test A
Chapter 2 Practice Test B
Cumulative Review Exercises- Chapters P-2
3. Polynomial and Rational Functions
3.1 Quadratic Functions
3.2 Polynomial Functions
3.3 Dividing Polynomials
3.4 The Real Zeros of a Polynomial Function
3.5 The Complex Zeros of a Polynomial Function
3.6 Rational Functions
3.7 Variation
Chapter 3 Summary
Chapter 3 Review Exercises
Chapter 3 Practice Test A
Chapter 3 Practice Test B
Cumulative Review Exercises- Chapters P-3
4. Exponential and Logarithmic Functions
4.1 Exponential Functions
4.2 Logarithmic Functions
4.3 Rules of Logarithms
4.4 Exponential and Logarithmic Equations and Inequalities
4.5 Logarithmic Scales
Chapter 4 Summary
Chapter 4 Review Exercises
Chapter 4 Practice Test A
Chapter 4 Practice Test B
Cumulative Review Exercises- Chapters P-4
5. Trigonometric Functions
5.1 Angles and Their Measure
5.2 Right-Triangle Trigonometry
5.3 Trigonometric Functions of Any Angle; The Unit Circle
5.4 Graphs of the Sine and Cosine Functions
5.5 Graphs of the Other Trigonometric Functions
5.6 Inverse Trigonometric Functions
Chapter 5 Summary
Chapter 5 Review Exercises
Chapter 5 Practice Test A
Chapter 5 Practice Test B
Cumulative Review Exercises- Chapters P-5
6. Trigonometric Identities and Equations
6.1 Verifying Identities
6.2 Sum and Difference Formulas
6.3 Double-Angle and Half-Angle Formulas
6.4 Product-to-Sum and Sum-to-Product Formulas
6.5 Trigonometric Equations I
6.6 Trigonometric Equations II
Chapter 6 Summary
Chapter 6 Review Exercises
Chapter 6 Practice Test A
Chapter 6 Practice Test B
Cumulative Review Exercises- Chapters P-6
7. Applications of Trigonometric Functions
7.1 The Law of Sines
7.2 The Law of Cosines
7.3 Areas of Polygons Using Trigonometry
7.4 Vectors
7.5 The Dot Product
7.6 Polar Coordinates
7.7 Polar Form of Complex Numbers; DeMoivre's Theorem
Chapter 7 Summary
Chapter 7 Review Exercises
Chapter 7 Practice Test A
Chapter 7 Practice Test B
Cumulative Review Exercises- Chapters P-7
8. Systems of Equations and Inequalities
8.1 Systems of Linear Equations in Two Variables
8.2 Systems of Linear Equations in Three Variables
8.3 Partial-Fraction Decomposition
8.4 Systems of Nonlinear Equations
8.5 Systems of Inequalities
8.6 Linear Programming
Chapter 8 Summary
Chapter 8 Review Exercises
Chapter 8 Practice Test A
Chapter 8 Practice Test B
Cumulative Review Exercises- Chapters P-8
9. Matrices and Determinants
9.1 Matrices and Systems of Equations
9.2 Matrix Algebra
9.3 The Matrix Inverse
9.4 Determinants and Cramer's Rule
Chapter 9 Summary
Chapter 9 Review Exercises
Chapter 9 Practice Test A
Chapter 9 Practice Test B
Cumulative Review Exercises- Chapters P-9
10. Conic Sections
10.1 Conic Sections: Overview
10.2 The Parabola
10.3 The Ellipse
10.4 The Hyperbola
Chapter 10 Summary
Chapter 10 Review Exercises
Chapter 10 Practice Test A
Chapter 10 Practice Test B
Cumulative Review Exercises- Chapters P-10
11. Further Topics in Algebra
11.1 Sequences and Series
11.2 Arithmetic Sequences; Partial Sums
11.3 Geometric Sequences and Series
11.4 Mathematical Induction
11.5 The Binomial Theorem
11.6 Counting Principles
11.7 Probability
Chapter 11 Summary
Chapter 11 Review Exercises
Chapter 11 Practice Test A
Chapter 11 Practice Test B
Cumulative Review Exercises- Chapters P-11