Table Of ContentP. Prerequisites. Real Numbers and Their Properties. Integral Exponents and Scientific Notation. Rational Exponents and Radicals. Polynomials. Factoring Polynomials. Rational Expressions. 1. Equations, Inequalities, and Modeling. Equations in One Variable. Constructing Models to Solve Problems. Equations and Graphs in Two Variables. Linear Equations in Two Variables. Scatter Diagrams and Curve Fitting. Quadratic Equations. Linear and Absolute Value Inequalities. 2. Functions and Graphs. Functions. Graphs of Relations and Functions. Families of Functions, Transformations, and Symmetry. Operations with Functions. Inverse Functions. Constructing Functions with Variation. 3. Polynomial and Rational Functions. Quadratic Functions and Inequalities. Complex Numbers. Zeros of Polynomial Functions. The Theory of Equations. Miscellaneous Equations. Graphs of Polynomial Functions. Rational Functions and Inequalities. 4. Exponential and Logarithmic Functions. Exponential Functions and Their Applications. Logarithmic Functions and Their Applications. Rules of Logarithms. More Equations and Applications. 5. Systems of Equations and Inequalities. Systems of Linear Equations in Two Variables. Systems of Linear Equations in Three Variables. Nonlinear Systems of Equations. Partial Fractions. Inequalities and Systems of Inequalities in Two Variables. The Linear Programming Model. 6. Matrices and Determinants. Solving Linear Systems Using Matrices. Operations with Matrices. Multiplication of Matrices. Inverses of Matrices. Solution of Linear Systems in Two Variables Using Determinants. Solution of Linear Systems in Three Variables Using Determinants. 7. The Conic Sections. The Parabola. The Ellipse and the Circle. The Hyperbola. 8. Sequences, Series, and Probability. Sequences. Series. Geometric Sequences and Series. Counting and Permutations. Combinations, Labeling, and the Binomial Theorem. Probability. Mathematical Induction.
SynopsisThis text is designed for a variety of students with different mathematical needs. For those students who will take additional mathematics, the text will provide the proper foundation of skills, understanding, and insights necessary for success in further courses. For those students who will not pursue further mathematics, the extensive emphasis on applications and modeling will demonstrate the usefulness and applicability of mathematics in the world today. Many of the applied problems in this text are actually real problems that people have had to solve on the job. With an emphasis on problem solving, this text provides students with an excellent opportunity to sharpen their reasoning and thinking skills. With increased critical thinking skills, students will have the confidence they need to tackle whatever future problems they may encounter inside and outside the classroom.This text is technology optional. With this approach, teachers will be able to offer either a technology-oriented course or a course that does not make use of technology. For departments requiring both options, this text provides the advantage of flexibility., This text is designed for a variety of students with different mathematical needs. For those students who will take additional mathematics, the text will provide the proper foundation of skills, understanding, and insights necessary for success in further courses. For those students who will not pursue further mathematics, the extensive emphasis on applications and modeling will demonstrate the usefulness and applicability of mathematics in the world today. Many of the applied problems in this text are actually real problems that people have had to solve on the job. With an emphasis on problem solving, this text provides students with an excellent opportunity to sharpen their reasoning and thinking skills. With increased critical thinking skills, students will have the confidence they need to tackle whatever future problems they may encounter inside and outside the classroom. This text is technology optional. With this approach, teachers will be able to offer either a technology-oriented course or a course that does not make use of technology. For departments requiring both options, this text provides the advantage of flexibility.