In the name of of Allah the Merciful

Precalculus: Graphical, Numerical, Algebraic

Gregory D. Foley; David E. Bock; Franklin D. Demana; Daniel Kennedy; Bert K. Waits, 9781292438962, 1292438967, 978-1292438962

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English | 2023 | PDF

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About The Authors
Chapter P. Prerequisites
P.1 Real Numbers
P.2 Cartesian Coordinate System
P.3 Linear Equations and Inequalities
P.4 Lines in the Plane
P.5 Solving Equations Graphically, Numerically, and Algebraically
P.6 Complex Numbers
P.7 Solving Inequalities Algebraically and Graphically
Key Ideas
Review Exercises
Chapter 1. Functions and Graphs
1.1 Modeling and Equation Solving
1.2 Functions and Their Properties
1.3 Twelve Basic Functions
1.4 Building Functions from Functions
1.5 Parametric Relations and Inverses
1.6 Graphical Transformations
1.7 Modeling with Functions
Key Ideas
Review Exercises
Modeling Project
Chapter 2. Polynomial, Power, and Rational Functions
2.1 Linear and Quadratic Functions and Modeling
2.2 Modeling with Power Functions
2.3 Polynomial Functions of Higher Degree with Modeling
2.4 Real Zeros of Polynomial Functions
2.5 Complex Zeros and the Fundamental Theorem of Algebra
2.6 Graphs of Rational Functions
2.7 Solving Equations in One Variable
2.8 Solving Inequalities in One Variable
Key Ideas
Review Exercises
Modeling Project
Chapter 3. Exponential, Logistic, and Logarithmic Functions
3.1 Exponential and Logistic Functions
3.2 Exponential and Logistic Modeling
3.3 Logarithmic Functions and Their Graphs
3.4 Properties of Logarithmic Functions
3.5 Equation Solving and Modeling
3.6 Mathematics of Finance
Key Ideas
Review Exercises
Modeling Project
Chapter 4. Trigonometric Functions
4.1 Angles and Their Measures
4.2 Trigonometric Functions of Acute Angles
4.3 Trigonometry Extended: The Circular Functions
4.4 Graphs of Sine and Cosine: Sinusoids
4.5 Graphs of Tangent, Cotangent, Secant, and Cosecant
4.6 Graphs of Composite Trigonometric Functions
4.7 Inverse Trigonometric Functions
4.8 Solving Problems with Trigonometry
Key Ideas
Review Exercises
Modeling Project
Chapter 5. Analytic Trigonometry
5.1 Fundamental Identities
5.2 Proving Trigonometric Identities
5.3 Sum and Difference Identities
5.4 Multiple-Angle Identities
5.5 The Law of Sines
5.6 The Law of Cosines
Key Ideas
Review Exercises
Modeling Project
Chapter 6. Applications of Trigonometry
6.1 Vectors in the Plane
6.2 Dot Product of Vectors
6.3 Parametric Equations and Motion
6.4 Polar Coordinates
6.5 Graphs of Polar Equations
6.6 De Moivre’s Theorem and nth Roots
Key Ideas
Review Exercises
Modeling Project
Chapter 7. Systems and Matrices
7.1 Solving Systems of Two Equations
7.2 Matrix Algebra
7.3 Multivariate Linear Systems and Row Operations
7.4 Systems of Inequalities in Two Variables
Key Ideas
Review Exercises
Modeling Project
Chapter 8. Analytic Geometry in Two and Three Dimensions
8.1 Conic Sections and a New Look at Parabolas
8.2 Circles and Ellipses
8.3 Hyperbolas
8.4 Quadratic Equations with xy Terms
8.5 Polar Equations of Conics
8.6 Three-Dimensional Cartesian Coordinate System
Key Ideas
Review Exercises
Modeling Project
Chapter 9. Discrete Mathematics
9.1 Basic Combinatorics
9.2 Binomial Theorem
9.3 Sequences
9.4 Series
9.5 Mathematical Induction
Key Ideas
Review Exercises
Modeling Project
Chapter 10. Statistics and Probability
10.1 Probability
10.2 Statistics (Graphical)
10.3 Statistics (Numerical)
10.4 Random Variables and Probability Models
10.5 Statistical Literacy
Key Ideas
Review Exercises
Modeling Project
Chapter 11. An Introduction to Calculus: Limits, Derivatives, and Integrals
11.1 Limits and Motion: The Tangent Problem
11.2 Limits and Motion: The Area Problem
11.3 More on Limits
11.4 Numerical Derivatives and Integrals
Key Ideas
Review Exercises
Modeling Project
Appendix A. Algebra Review
A.1 Radicals and Rational Exponents
A.2 Polynomials and Factoring
A.3 Fractional Expressions
Appendix B. Logic
B.1 Logic: An Introduction
B.2 Conditionals and Biconditionals
Appendix C. Key Formulas
C.1 Formulas from Algebra
C.2 Formulas from Geometry
C.3 Formulas from Trigonometry
C.4 Formulas from Analytic Geometry
C.5 Gallery of Basic Functions
Selected Answers
Applications Index