Precalculus Metric Version 11th Edition by Ron Larson 147378817X ‎978-1473788176

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ISBN-10 ‏ : ‎ 147378817X

ISBN-13 ‏ : ‎ 978-1473788176

Author :  Ron Larson

Larson’s Precalculus is known for sound, consistently structured explanations of mathematical concepts and exercises to expertly prepare students for calculus. Engage your students and prepare them for success in your course and beyond with the student-focused approach of Ron Larson and WebAssign. Updated and refined through learning design principles, the 11th Metric Edition removes barriers to learning and offers a carefully planned and inclusive experience for all students. Larson presents concepts clearly and offers a wealth of learning support, addressing both readiness gaps and helping students take their understanding to the next level.

Precalculus Metric Version 11th Table of contents:

1. Functions and Their Graphs
1.1. Rectangular Coordinates
The Cartesian Plane
The Distance Formula
The Midpoint Formula
Application
1.1. Exercises
1.2. Graphs of Equations
The Graph of an Equation
Intercepts of a Graph
Symmetry
Circles
Application
1.2. Exercises
1.3. Linear Equations in Two Variables
Using Slope
Finding the Slope of a Line
Writing Linear Equations in Two Variables
Parallel and Perpendicular Lines
Applications
1.3. Exercises
1.4. Functions
Introduction to Functions and Function Notation
The Domain of a Function
Applications
1.4. Exercises
1.5. Analyzing Graphs of Functions
The Graph of a Function
Zeros of a Function
Increasing and Decreasing Functions
Relative Minimum and Relative Maximum Values
Average Rate of Change
Even and Odd Functions
1.5. Exercises
1.6. A Library of Parent Functions
Linear and Squaring Functions
Cubic, Square Root, and Reciprocal Functions
Step and Piecewise-Defined Functions
Commonly Used Parent Functions
1.6. Exercises
1.7. Transformations of Functions
Shifting Graphs
Reflecting Graphs
Nonrigid Transformations
1.7. Exercises
1.8. Combinations of Functions: Composite Functions
Arithmetic Combinations of Functions
Compositions of Functions
Application
1.8. Exercises
1.9. Inverse Functions
Inverse Functions
The Graph of an Inverse Function
One-to-One Functions
Finding Inverse Functions Algebraically
1.9. Exercises
1.10. Mathematical Modeling and Variation
Introduction
Least Squares Regression and Graphing Utilities
Direct Variation
Direct Variation as an n th Power
Inverse Variation
Combined Variation
Joint Variation
1.10. Exercises
Summary and Study Strategies
Review Exercises
Chapter Test
Proofs in Mathematics
P.S. Problem Solving
2. Polynomial and Rational Functions
2.1. Quadratic Functions and Models
The Graph of a Quadratic Function
The Standard Form of a Quadratic Function
Finding Minimum and Maximum Values
2.1. Exercises
2.2. Polynomial Functions of Higher Degree
Graphs of Polynomial Functions
The Leading Coefficient Test
Real Zeros of Polynomial Functions
The Intermediate Value Theorem
2.2. Exercises
2.3. Polynomial and Synthetic Division
Long Division of Polynomials
Synthetic Division
The Remainder and Factor Theorems
2.3. Exercises
2.4. Complex Numbers
The Imaginary Unit i
Operations with Complex Numbers
Complex Conjugates
Complex Solutions of Quadratic Equations
2.4. Exercises
2.5. Zeros of Polynomial Functions
The Fundamental Theorem of Algebra
The Rational Zero Test
Conjugate Pairs
Factoring a Polynomial
Other Tests for Zeros of Polynomials
Application
2.5. Exercises
2.6. Rational Functions
Introduction
Vertical and Horizontal Asymptotes
Sketching the Graph of a Rational Function
Slant Asymptotes
Applications
2.6. Exercises
2.7. Nonlinear Inequalities
Polynomial Inequalities
Rational Inequalities
Applications
2.7. Exercises
Summary and Study Strategies
Review Exercises
Chapter Test
Proofs in Mathematics
P.S. Problem Solving
3. Exponential and Logarithmic Functions
3.1. Exponential Functions and Their Graphs
Exponential Functions
Graphs of Exponential Functions
The Natural Base e
Applications
3.1. Exercises
3.2. Logarithmic Functions and Their Graphs
Logarithmic Functions
Graphs of Logarithmic Functions
The Natural Logarithmic Function
Application
3.2. Exercises
3.3. Properties of Logarithms
Change of Base
Properties of Logarithms
Rewriting Logarithmic Expressions
Application
3.3. Exercises
3.4. Exponential and Logarithmic Functions
Introduction
Solving Exponential Equations
Solving Logarithmic Equations
Applications
3.4. Exercises
3.5. Exponential and Logarithmic Models
Introduction
Exponential Growth and Decay
Gaussian Models
Logistic Growth Models
Logarithmic Models
3.5. Exercises
Summary and Study Strategies
Review Exercises
Chapter Test
Cumulative Test for Chapters 1–3
Proofs in Mathematics
P.S. Problem Solving
4. Trigonometry
4.1. Radian and Degree Measure
Angles
Radian Measure
Degree Measure
Applications
4.1. Exercises
4.2. Trigonometric Functions: The Unit Circle
The Unit Circle
The Trigonometric Functions
Domain and Period of Sine and Cosine
4.2. Exercises
4.3. Right Triangle Trigonometry
The Six Trigonometric Functions
Trigonometric Identities
Applications Involving Right Triangles
4.3. Exercises
4.4. Trigonometric Functions of Any Angle
Introduction
Reference Angles
Trigonometric Functions of Real Numbers
4.4. Exercises
4.5. Graphs of Sine and Cosine Functions
Basic Sine and Cosine Curves
Amplitude and Period
Translations of Sine and Cosine Curves
Mathematical Modeling
4.5. Exercises
4.6. Graphs of Other Trigonometric Functions
Graph of the Tangent Function
Graph of the Cotangent Function
Graphs of the Reciprocal Functions
Damped Trigonometric Graphs
4.6. Exercises
4.7. Inverse Trigonometric Functions
Inverse Sine Function
Other Inverse Trigonometric Functions
Compositions with Inverse Trigonometric Functions
4.7. Exercises
4.8. Applications and Models
Applications Involving Right Triangles
Trigonometry and Bearings
Harmonic Motion
4.8. Exercises
Summary and Study Strategies
Review Exercises
Chapter Test
Proofs in Mathematics
P.S. Problem Solving
5. Analytic Trigonometry
5.1. Using Fundamental Identities
Introduction
Using the Fundamental Identities
5.1. Exercises
5.2. Verifying Trigonometric Identities
Verifying Trigonometric Identities
5.2. Exercises
5.3. Solving Trigonometric Equations
Introduction
Equations of Quadratic Type
Equations Involving Multiple Angles
Using Inverse Functions
5.3. Exercises
5.4. Sum and Difference Formulas
Using Sum and Difference Formulas
5.4. Exercises
5.5. Multiple-Angle and Product-to-Sum Formulas
Multiple-Angle Formulas
Power-Reducing Formulas
Half-Angle Formulas
Product-to-Sum and Sum-to-Product Formulas
Application
5.5. Exercises
Summary and Study Strategies
Review Exercises
Chapter Test
Proofs in Mathematics
P.S. Problem Solving
6. Additional Topics in Trigonometry
6.1. Law of Sines
Introduction
The Ambiguous Case (SSA)
Area of an Oblique Triangle
Application
6.1. Exercises
6.2. Law of Cosines
Introduction
Applications
Heron’s Area Formula
6.2. Exercises
6.3. Vectors in the Plane
Introduction
Component Form of a Vector
Vector Operations
Unit Vectors
Direction Angles
Applications
6.3. Exercises
6.4. Vectors and Dot Products
The Dot Product of Two Vectors
The Angle Between Two Vectors
Finding Vector Components
Work
6.4. Exercises
6.5. The Complex Plane
The Complex Plane
Operations with Complex Numbers in the Complex Plane
Distance and Midpoint Formulas in the Complex Plane
6.5. Exercises
6.6. Trigonometric Form of a Complex Number
Trigonometric Form of a Complex Number
Multiplication and Division of Complex Numbers
Powers of Complex Numbers
Roots of Complex Numbers
6.6. Exercises
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
7.1. Linear and Nonlinear Systems of Equations
The Method of Substitution
Nonlinear Systems of Equations
Graphical Method for Finding Solutions
Applications
7.1. Exercises
7.2. Two-Variable Linear Systems
The Method of Elimination
Graphical Interpretation of Solutions
Applications
7.2. Exercises
7.3. Multivariable Linear Systems
Row-Echelon Form and Back-Substitution
Gaussian Elimination
Nonsquare Systems
Applications
7.3. Exercises
7.4. Partial Fractions
Introduction
Partial Fraction Decomposition
7.4. Exercises
7.5. Systems of Inequalities
The Graph of an Inequality
Systems of Inequalities
Applications
7.5. Exercises
7.6. Linear Programming
Linear Programming: A Graphical Approach
Applications
7.6. Exercises
Summary and Study Strategies
Review Exercises
Chapter Test
Proofs in Mathematics
P.S. Problem Solving
8. Matrices and Determinants
8.1. Matrices and Systems of Equations
Matrices
Elementary Row Operations
Gaussian Elimination with Back-Substitution
Gauss-Jordan Elimination
8.1. Exercises
8.2. Operations with Matrices
Equality of Matrices
Matrix Addition and Scalar Multiplication
Matrix Multiplication
Using Matrices to Transform Vectors
Applications
8.2. Exercises
8.3. The Inverse of a Square Matrix
The Inverse of a Matrix
Finding Inverse Matrices
The Inverse of a 2 × 2 Matrix
Systems of Linear Equations
8.3. Exercises
8.4. The Determinant of a Square Matrix
The Determinant of a 2 × 2 Matrix
Minors and Cofactors
The Determinant of a Square Matrix
8.4. Exercises
8.5. Applications of Matrices and Determinants
Cramer’s Rule
Area of a Triangle
Lines in a Plane
Further Applications of 2 × 2 Matrices
Cryptography
8.5. Exercises
Summary and Study Strategies
Review Exercises
Chapter Test
Proofs in Mathematics
P.S. Problem Solving
9. Sequences, Series, and Probability
9.1. Sequences and Series
Sequences
Factorial Notation
Summation Notation
Series
Application
9.1. Exercises
9.2. Arithmetic Sequences and Partial Sums
Arithmetic Sequences
The Sum of a Finite Arithmetic Sequence
Application
9.2. Exercises
9.3. Geometric Sequences and Series
Geometric Sequences
The Sum of a Finite Geometric Sequence
Geometric Series
Application
9.3. Exercises
9.4. Mathematical Induction
Introduction
Pattern Recognition
Sums of Powers of Integers
Finite Differences
9.4. Exercises
9.5. The Binomial Theorem
Binomial Coefficients
Pascal’s Triangle
Binomial Expansions
9.5. Exercises
9.6. Counting Principles
Simple Counting Problems
The Fundamental Counting Principle
Permutations
Combinations
9.6. Exercises
9.7. Probability
The Probability of an Event
Mutually Exclusive Events
Independent Events
The Complement of an Event
9.7. Exercises
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
10.1. Lines
Inclination of a Line
The Angle Between Two Lines
The Distance Between a Point and a Line
10.1. Exercises
10.2. Introduction to Conics: Parabolas
Conics
Parabolas
The Reflective Property of Parabolas
10.2. Exercises
10.3. Ellipses
Introduction
Application
Eccentricity
10.3. Exercises
10.4. Hyperbolas
Introduction
Asymptotes of a Hyperbola
Applications
General Equations of Conics
10.4. Exercises
10.5. Rotation of Conics
Rotation
Invariants under Rotation and the Discriminant
10.5. Exercises
10.6. Parametric Equations
Plane Curves
Sketching a Plane Curve
Eliminating the Parameter
Finding Parametric Equations for a Graph
10.6. Exercises
10.7. Polar Coordinates
Introduction
Coordinate Conversion
Equation Conversion
10.7. Exercises
10.8. Graphs of Polar Equations
Introduction
Symmetry, Zeros, and Maximum Values of | r |
Special Polar Graphs
10.8. Exercises
10.9. Polar Equations of Conics
Alternative Definition and Polar Equations of Conics
Application
10.9. Exercises
Summary and Study Strategies
Review Exercises
Chapter Test
Proofs in Mathematics

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