Presents mathematical reform as the driving force behind this precalculus text. It's objectives are: to encourage students to investigate mathematical ideas and processes graphically and numerically, as well as algebraically; the development of a library of elementary functions, including their properties and uses; and more.
Presents mathematical reform as the driving force behind this precalculus text. It's objectives are: to encourage students to investigate mathematical ideas and processes graphically and numerically, as well as algebraically; the development of a library of elementary functions, including their properties and uses; and more.
1 Functions, Graphs, and Models 1.1 Using Graphing Utilities 1.2 Functions 1.3 Functions: Graphs and Properties 1.4 Functions: Graphs and Transformations 1.5 Operations on Functions; Composition 1.6 Inverse Functions 2 Modeling with Linear and Quadratic Functions 2.1 Linear Functions 2.2 Linear Equations and Models 2.3 Quadratic Functions 2.4 Complex Numbers 2.5 Quadratic Equations and Models 2.6 Additional Equation-Solving Techniques 2.7 Solving Inequalities 3 Polynomial and Rational Functions 3.1 Polynomial Functions and Models 3.2 Real Zeros and Polynomial Inequalities 3.3 Complex Zeros and Rational Zeros of Polynomials 3.4 Rational Functions and Inequalities 4 Exponential and Logarithmic Functions 4.1 Exponential Functions 4.2 Exponential Models 4.3 Logarithmic Functions 4.4 Logarithmic Models 4.5 Exponential and Logarithmic Equations 5 Modeling with Linear Systems 5.1 Systems of Linear Equations in Two Variables 5.2 Systems of Linear Equations and Augmented Matrices 5.3 Gauss-Jordan Elimination 5.4 Systems of Linear Inequalities 5.5 Linear Programming 6 Matrices and Determinants 6.1 Matrix Operations 6.2 Inverse of a Square Matrix 6.3 Matrix Equations and Systems of Linear Equations 6.4 Determinants 6.5 Properties of Determinants 6.6 Determinants and Cramer's Rule 7 Sequences, Induction, and Probability 7.1 Sequences and Series 7.2 Mathematical Induction 7.3 Arithmetic and Geometric Sequences 7.4 Multiplication Princple, Permutations, and Combinations 7.5 Sample Spaces and Probability 7.6 Binomial Formula 8 Additional Topics in Analytic Geometry 8.1 Conic Sections; Parabola 8.2 Ellipse 8.3 Hyperbola 8.4 Translation of Axes 8.5 Nonlinear Systems Appendix A Review of Equations and Graphing A.1 Linear Equations and Inequalities A.2 Cartesian Coordinate System A.3 Basic Formulas in Analytic Geometry Appendix B Special Topics B.1 Significant Digits B.2 Partial Fractions B.3 Descartes' Rule of Signs B.4 Parametric Equations Appendix C Geometric Formulas
1 Functions, Graphs, and Models 1.1 Using Graphing Utilities 1.2 Functions 1.3 Functions: Graphs and Properties 1.4 Functions: Graphs and Transformations 1.5 Operations on Functions; Composition 1.6 Inverse Functions 2 Modeling with Linear and Quadratic Functions 2.1 Linear Functions 2.2 Linear Equations and Models 2.3 Quadratic Functions 2.4 Complex Numbers 2.5 Quadratic Equations and Models 2.6 Additional Equation-Solving Techniques 2.7 Solving Inequalities 3 Polynomial and Rational Functions 3.1 Polynomial Functions and Models 3.2 Real Zeros and Polynomial Inequalities 3.3 Complex Zeros and Rational Zeros of Polynomials 3.4 Rational Functions and Inequalities 4 Exponential and Logarithmic Functions 4.1 Exponential Functions 4.2 Exponential Models 4.3 Logarithmic Functions 4.4 Logarithmic Models 4.5 Exponential and Logarithmic Equations 5 Modeling with Linear Systems 5.1 Systems of Linear Equations in Two Variables 5.2 Systems of Linear Equations and Augmented Matrices 5.3 Gauss-Jordan Elimination 5.4 Systems of Linear Inequalities 5.5 Linear Programming 6 Matrices and Determinants 6.1 Matrix Operations 6.2 Inverse of a Square Matrix 6.3 Matrix Equations and Systems of Linear Equations 6.4 Determinants 6.5 Properties of Determinants 6.6 Determinants and Cramer's Rule 7 Sequences, Induction, and Probability 7.1 Sequences and Series 7.2 Mathematical Induction 7.3 Arithmetic and Geometric Sequences 7.4 Multiplication Princple, Permutations, and Combinations 7.5 Sample Spaces and Probability 7.6 Binomial Formula 8 Additional Topics in Analytic Geometry 8.1 Conic Sections; Parabola 8.2 Ellipse 8.3 Hyperbola 8.4 Translation of Axes 8.5 Nonlinear Systems Appendix A Review of Equations and Graphing A.1 Linear Equations and Inequalities A.2 Cartesian Coordinate System A.3 Basic Formulas in Analytic Geometry Appendix B Special Topics B.1 Significant Digits B.2 Partial Fractions B.3 Descartes' Rule of Signs B.4 Parametric Equations Appendix C Geometric Formulas
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