College Algebra with Trigonometry: Graphs and Models with MathZone

Mathematical reform is the driving force behind the organization and development of this new text in college algebra and trigonometry. 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 Models1.1 Using Graphing Utilities1.2 Functions1.3 Functions: Graphs and Properties1.4 Functions: Graphs and Transformations1.5 Operations on Functions; Composition1.6 Inverse Functions2 Modeling with Linear and Quadratic Functions2.1 Linear Functions2.2 Linear Equations and Models2.3 Quadratic Functions2.4 Complex Numbers2.5 Quadratic Equations and Models2.6 Additional Equation-Solving Techniques2.7 Solving Inequalities3 Polynomial and Rational Functions3.1 Polynomial Functions and Models3.2 Real Zeros and Polynomial Inequalities3.3 Complex Zeros and Rational Zeros of Polynomials3.4 Rational Functions and Inequalities4 Exponential and Logarithmic Functions4.1 Exponential Functions4.2 Exponential Models4.3 Logarithmic Functions4.4 Logarithmic Models4.5 Exponential and Logarithmic Equations5 Trigonometric Functions5.1 Angles and Their Measure5.2 Right Triangle Trigonometry5.3 Trigonometric Functions: A Unit Circle Approach5.4 Properties of Trigonometric Functions5.5 More General Trigonometric Functions and Models5.6 Inverse Trigonometric Functions6 Trigonometric Identities and Conditional Equations6.1 Basic Identities and Their Use6.2 Sum, Difference, and Cofunction Identities6.3 Double-Angle and Half-Angle Identities6.4 Product-Sum and Sum-Product Identities6.5 Trigonometric Equations7 Additional Topics in Trigonometry7.1 Law of Sines7.2 Law of Cosines7.3 Geometric Vectors7.4 Algebraic Vectors7.5 Polar Coordinates and Graphs7.6 Complex Numbers in Rectangular and Polar Forms7.7 De Moivre's Theorem8 Modeling with Linear Systems8.1 Systems of Linear Equations in Two Variables8.2 Systems of Linear Equations and Augmented Matrices8.3 Gauss-Jordan Elimination8.4 Systems of Linear Inequalities8.5 Linear Programming9 Matrices and Determinants9.1 Matrix Operations9.2 Inverse of a Square Matrix9.3 Matrix Equations and Systems of Linear Equations9.4 Determinants9.5 Properties of Determinants9.6 Determinants and Cramer's Rule10 Sequences, Induction, and Probability10.1 Sequences and Series10.2 Mathematical Induction10.3 Arithmetic and Geometric Sequences10.4 Multiplication Principle, Permutations, and Combinations10.5 Sample Spaces and Probability10.6 Binomial Formula11 Additional Topics in Analytic Geometry11.1 Conic Sections; Parabola11.2 Ellipse11.3 Hyperbola11.4 Translation of Axes11.5 Rotation of Axes11.6 Nonlinear SystemsAppendix A Review of Equations and GraphingA.1 Linear Equations and InequalitiesA.2 Cartesian Coordinate SystemA.3 Basic Formulas in Analytic GeometryAppendix B Special TopicsB.1 Significant DigitsB.2 Partial FractionsB.3 Descartes' Rule of SignsB.4 Parametric EquationsAppendix C Geometric Formulas