Precalculus / Margaret L. Lial , John Hornsby, David I. Schneider, Callie J. Daniels.

Includes index.

R. Review of basic concepts. Sets ; Real numbers and their properties ; Polynomials ; Factoring polynomials ; Rational expressions ; Rational exponents ; Radical expressions -- 1. Equations and inequalities. Linear equations ; Applications and modeling with linear equations ; Complex numbers ; Quadratic equations ; Applications and modeling with quadratic equations ; Other types of equations and applications ; Inequalities ; Absolute value equations and inequalities -- 2. Graphs and functions. Rectangular coordinates and graphs ; Circles ; Functions ; Linear functions ; Equations of lines and linear models ; Graphs of basic functions ; Graphing techniques ; Function operations and composition -- 3. Polynomial and rational functions. Quadratic functions and models ; Synthetic division ; Zeros of polynomial functions ; Polynomial functions: graphs, applications, and models ; Rational functions: graphs, applications, and models ; Variation -- 4. Inverse, exponential, and logarithmic functions. Inverse functions ; Exponential functions ; Logarithmic functions ; Evaluating logarithms and the change-of-base theorem ; Exponential and logarithmic equations ; Applications and models of exponential growth and decay -- 5. Trigonometric functions. Angles ; Trigonometric functions ; Trigonometric function values and angle measures ; Solutions and applications of right triangles -- 6. The circular functions and their graphs. Radian measure ; The unit circle and circular functions ; Graphs of the sine and cosine functions ; Translations of the graphs of the sine and cosine functions ; Graphs of the tangent and cotangent functions ; Graphs of the secant and cosecant functions ; Harmonic motion

7. Trigonometric identities and equations. Fundamental identities ; Verifying trigonometric identities ; Double-angle and half-angle identities ; Inverse circular functions ; Trigonometric equations ; Equations involving inverse trigonometric functions -- 8. Applications of trigonometry. The law of sines ; The law of cosines ; Geometrically defined vectors and applications ; Algebraically defined vectors and the dot product ; Trigonometric (polar) form of complex numbers: products and quotients ; De Moivre's Theorem; power and roots of complex numbers ; Polar equations and graphs ; Parametric equations, graphs, and applications -- 9. Systems and matrices. Systems of linear equations ; Matrix solution of linear systems ; Determinant solution of linear systems ; Partial fractions ; Nonlinear systems of equations ; Systems of inequalities and linear programming ; Properties of matrices ; Matrix inverses -- 10. Analytic geometry. Parabolas ; Ellipses ; Hyperbolas ; Summary of the conic sections -- 11. Further topics in algebra. Sequences and series ; Arithmetic sequences and series ; Geometric sequences and series ; The binomial theorem ; Mathematical induction ; Basics of counting theory ; Basics of probability -- Appendices. Appendix A. Polar form of conic sections -- Appendix B. Rotation of axes -- Appendix C. Geometry formulas.