Precalculus
by Paul Sisson
Precalculus begins with a comprehensive study of functions and their applications and then continues with more advanced material, all designed to prepare students for calculus. A full review of college algebra topics is integrated with a rigorous presentation of concepts that form the foundation of calculus, including a detailed coverage of trigonometry. Each chapter provides historical context, technology notes, and applications.
Updates to the third edition include a more streamlined table of contents, new chapters (Chapter 4: Working with Functions and Chapter 13: An Introduction to Limits, Continuity, and the Derivative), and more robust content.
New topics covered include:
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The difference quotient
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Constructing mathematical models
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Regression (linear, quadratic, exponential, logistic, and logarithmic)
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Interpolation and extrapolation
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Intervals of monotonicity
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Local extrema
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Average rate of change
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Stretching and compressing graphs horizontally
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Solving elementary logarithmic equations
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The Pythagorean Theorem
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The Unit Circle
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Simple Harmonic Motion
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Hyperbolic Functions
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Systems of linear inequalities
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Systems of nonlinear inequalities
Formats: Software, Textbook, Guided Notebook, eBook
Product | ISBN |
---|---|
Software + eBook | 978-1-642771-74-9 |
Software + eBook + Textbook | 978-1-64277-284-5 |
Software + eBook + Guided Notebook | 978-1-64277-345-3 |
Table of Contents
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Chapter 1: Algebraic Expressions, Equations, and Inequalities
- 1.1 Real Numbers and Algebraic Expressions
- 1.2 Properties of Exponents and Radicals
- 1.3 Polynomials and Factoring
- 1.4 Rational Expressions
- 1.5 Complex Numbers
- 1.6 Linear Equations in One Variable
- 1.7 Linear Inequalities in One Variable
- 1.8 Polynomial and Polynomial-Like Equations in One Variable
- 1.9 Rational and Radical Equations in One Variable
- Chapter 1 Review
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Chapter 2: Equations and Inequalities in Two Variables
- 2.1 The Cartesian Coordinate System
- 2.2 Circles
- 2.3 Linear Equations in Two Variables
- 2.4 Slope and Forms of Linear Equations
- 2.5 Parallel and Perpendicular Lines
- 2.6 Linear Inequalities in Two Variables
- Chapter 2 Review
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Chapter 3: Relations, Functions, and Their Graphs
- 3.1 Relations and Functions
- 3.2 Linear Functions
- 3.3 Quadratic Functions
- 3.4 Other Common Functions
- 3.5 Variation and Multivariable Functions
- 3.6 Mathematical Models
- Chapter 3 Review
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Chapter 4: Working with Functions
- 4.1 Transformations of Functions
- 4.2 Properties of Functions
- 4.3 Combining Functions
- 4.4 Inverses of Functions
- Chapter 4 Review
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Chapter 5: Polynomial and Rational Functions
- 5.1 Polynomial Functions and Polynomial Inequalities
- 5.2 Polynomial Division and the Division Algorithm
- 5.3 Locating Real Zeros of Polynomial Functions
- 5.4 The Fundamental Theorem of Algebra
- 5.5 Rational Functions and Rational Inequalities
- Chapter 5 Review
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Chapter 6: Exponential and Logarithmic Functions
- 6.1 Exponential Functions and Their Graphs
- 6.2 Exponential Models
- 6.3 Logarithmic Functions and Their Graphs
- 6.4 Logarithmic Properties and Models
- 6.5 Exponential and Logarithmic Equations
- Chapter 6 Review
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Chapter 7: Trigonometric Functions
- 7.1 Radian and Degree Measure
- 7.2 Trigonometric Functions and Right Triangles
- 7.3 Trigonometric Functions and the Unit Circle
- 7.4 Graphs of Sine and Cosine Functions
- 7.5 Graphs of Other Trigonometric Functions
- 7.6 Inverse Trigonometric Functions
- Chapter 7 Review
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Chapter 8: Trigonometric Identities and Equations
- 8.1 Fundamental Trigonometric Identities
- 8.2 Sum and Difference Identities
- 8.3 Product-Sum Identities
- 8.4 Trigonometric Equations
- Chapter 8 Review
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Chapter 9: Additional Topics in Trigonometry
- 9.1 The Law of Sines
- 9.2 The Law of Cosines
- 9.3 Polar Coordinates and Polar Equations
- 9.4 Parametric Equations
- 9.5 Trigonometric Form of Complex Numbers
- 9.6 Vectors in the Cartesian Plane
- 9.7 The Dot Product
- 9.8 Hyperbolic Functions
- Chapter 9 Review
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Chapter 10: Conic Sections
- 10.1 Ellipses
- 10.2 Parabolas
- 10.3 Hyperbolas
- 10.4 Rotation of Conic Sections
- 10.5 Polar Equations of Conic Sections
- Chapter 10 Review
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Chapter 11: Systems of Equations and Inequalities
- 11.1 Solving Systems of Linear Equations by Substitution and Elimination
- 11.2 Matrix Notation and Gauss-Jordan Elimination
- 11.3 Determinants and Cramer's Rule
- 11.4 Basic Matrix Operations
- 11.5 Inverses of Matrices
- 11.6 Partial Fraction Decomposition
- 11.7 Systems of Linear Inequalities and Linear Programming
- 11.8 Systems of Nonlinear Equations and Inequalities
- Chapter 11 Review
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Chapter 12: Sequences, Series, Combinatorics, and Probability
- 12.1 Sequences and Series
- 12.2 Arithmetic Sequences and Series
- 12.3 Geometric Sequences and Series
- 12.4 Mathematical Induction
- 12.5 Combinatorics
- 12.6 Probability
- Chapter 12 Review
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Chapter 13: An Introduction to Limits, Continuity, and the Derivative
- 13.1 Rates of Change and Tangents
- 13.2 Limits in the Plane
- 13.3 The Mathematical Definition of Limit
- 13.4 Determining Limits of Functions
- 13.5 Continuity
- 13.6 The Derivative
- Chapter 13 Review