Aims to encourage students to investigate mathematical ideas and processes graphically, numerically, and algebraically. This title focuses on the development of a library of elementary functions, including their important properties and uses. Many applications are real-world problems taken from professional journals and professional books.
Aims to encourage students to investigate mathematical ideas and processes graphically, numerically, and algebraically. This title focuses on the development of a library of elementary functions, including their important properties and uses. Many applications are real-world problems taken from professional journals and professional books.
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 Trigonometric Functions 5.1 Angles and Their Measure 5.2 Right Triangle Trigonometry 5.3 Trigonometric Functions: A Unit Circle Approach 5.4 Properties of Trigonometric Functions 5.5 More General Trigonometric Functions and Models 5.6 Inverse Trigonometric Functions 6 Trigonometric Identities and Conditional Equations 6.1 Basic Identities and Their Use 6.2 Sum, Difference, and Cofunction Identities 6.3 Double-Angle and Half-Angle Identities 6.4 Product-Sum and Sum-Product Identities 6.5 Trigonometric Equations 7 Additional Topics in Trigonometry 7.1 Law of Sines 7.2 Law of Cosines 7.3 Geometric Vectors 7.4 Algebraic Vectors 7.5 Polar Coordinates and Graphs 7.6 Complex Numbers in Rectangular and Polar Forms 7.7 De Moivre's Theorem 8 Modeling with Linear Systems 8.1 Systems of Linear Equations in Two Variables 8.2 Systems of Linear Equations and Augmented Matrices 8.3 Gauss-Jordan Elimination 8.4 Systems of Linear Inequalities 8.5 Linear Programming 9 Matrices and Determinants 9.1 Matrix Operations 9.2 Inverse of a Square Matrix 9.3 Matrix Equations and Systems of Linear Equations 9.4 Determinants 9.5 Properties of Determinants 9.6 Determinants and Cramer's Rule 10 Sequences, Induction, and Probability 10.1 Sequences and Series 10.2 Mathematical Induction 10.3 Arithmetic and Geometric Sequences 10.4 Multiplication Principle, Permutations, and Combinations 10.5 Sample Spaces and Probability 10.6 Binomial Formula 11 Additional Topics in Analytic Geometry 11.1 Conic Sections; Parabola 11.2 Ellipse 11.3 Hyperbola 11.4 Translation of Axes 11.5 Rotation of Axes 11.6 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 Trigonometric Functions 5.1 Angles and Their Measure 5.2 Right Triangle Trigonometry 5.3 Trigonometric Functions: A Unit Circle Approach 5.4 Properties of Trigonometric Functions 5.5 More General Trigonometric Functions and Models 5.6 Inverse Trigonometric Functions 6 Trigonometric Identities and Conditional Equations 6.1 Basic Identities and Their Use 6.2 Sum, Difference, and Cofunction Identities 6.3 Double-Angle and Half-Angle Identities 6.4 Product-Sum and Sum-Product Identities 6.5 Trigonometric Equations 7 Additional Topics in Trigonometry 7.1 Law of Sines 7.2 Law of Cosines 7.3 Geometric Vectors 7.4 Algebraic Vectors 7.5 Polar Coordinates and Graphs 7.6 Complex Numbers in Rectangular and Polar Forms 7.7 De Moivre's Theorem 8 Modeling with Linear Systems 8.1 Systems of Linear Equations in Two Variables 8.2 Systems of Linear Equations and Augmented Matrices 8.3 Gauss-Jordan Elimination 8.4 Systems of Linear Inequalities 8.5 Linear Programming 9 Matrices and Determinants 9.1 Matrix Operations 9.2 Inverse of a Square Matrix 9.3 Matrix Equations and Systems of Linear Equations 9.4 Determinants 9.5 Properties of Determinants 9.6 Determinants and Cramer's Rule 10 Sequences, Induction, and Probability 10.1 Sequences and Series 10.2 Mathematical Induction 10.3 Arithmetic and Geometric Sequences 10.4 Multiplication Principle, Permutations, and Combinations 10.5 Sample Spaces and Probability 10.6 Binomial Formula 11 Additional Topics in Analytic Geometry 11.1 Conic Sections; Parabola 11.2 Ellipse 11.3 Hyperbola 11.4 Translation of Axes 11.5 Rotation of Axes 11.6 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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