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Summary
Mathematical reform is the driving force behind the organization and development of this new precalculus text. The use of technology, primarily graphing utilities, is assumed throughout the text. The development of each topic proceeds from the concrete to the abstract and takes full advantage of technology, wherever appropriate.The first major objective of this book is to encourage students to investigate mathematical ideas and processes graphically and numerically, as well as algebraically. Proceeding in this way, students gain a broader, deeper, and more useful understanding of a concept or process. Even though concept development and technology are emphasized, manipulative skills are not ignored, and plenty of opportunities to practice basic skills are present. A brief look at the table of contents will reveal the importance of the function concept as a unifying theme.The second major objective of this book is the development of a library of elementary functions, including their important properties and uses. Having this library of elementary functions as a basic working tool in their mathematical tool boxes, students will be able to move into calculus with greater confidence and understanding. In addition, a concise review of basic algebraic concepts is included in Appendix A for easy reference, or systematic review. The third major objective of this book is to give the student substantial experience in solving and modeling real world problems. Enough applications are included to convince even the most skeptical student that mathematics is really useful. Most of the applications are simplified versions of actual real-world problems taken from professional journals and professional books. No specialized experience is required to solve any of the applications.
Table of Contents
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 Trigonometric Functions: A Unit Circle Approach
5.3 Solving Right Triangles
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