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Full Description
This book, intended for a graphing calculator optional precalculus course that introduces limits, offers students the content and tools they will need to be successful in learning precalculus concepts. The authors have attempted to address the needs of students who will continue their study of mathematics, as well as those who are taking precalculus as their final mathematics course. Emphasis is placed on exploring mathematics by using current applications, real data, and technology.
Contents
1. Equations and Inequalities. Linear Equations.Linear Applications and Modeling.Complex Numbers.Quadratic Equations.Quadratic Applications and Modeling.Other Types of Equations.Inequalities.Absolute Value Equations and Inequalities.2. Relations, Functions, and Graphs. Relations and the Rectangular Coordinate System; Circles.Functions.Linear Functions.Equations of Lines; Curve Fitting.Graphs of Relations and Functions.Graphing Techniques; Transformations.Operations and Composition.3. Polynomial and Rational Functions. Quadratic Functions; Curve Fitting.Synthetic Division.Zeros of Polynomial Functions.Polynomial Functions: Graphs, Applications, and Models.Rational Functions: Graphs, Applications, and Models.Variation.4. 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 and Their Measures.The Unit Circle and Circular Functions.Right Triangles and Trigonometric Functions.Finding Trigonometric Function Values.Solving Right Triangles.Graphs of the Sine and Cosine Functions.Graphs of the Other Circular Functions.6. Trigonometric Identities and Equations. Fundamental Identities.Verifying Trigonometric Identities.Sum and Difference Identities.Double-Angle Identities and Half-Angle Identities.Inverse Trigonometric Functions.Trigonometric Equations.Equations Involving Inverse Trigonometric Functions.7. Applications of Trigonometry. Oblique Triangles and the Law of Sines.The Law of Cosines.Vectors and the Dot Product.Applications of Vectors.Vectors in Space.Products and Quotients of Complex Numbers.DeMoiure's Theorem; Powers and Roots of Complex Numbers.Polar Equations and Graphs.Parametric Equations, Graphs and Applications.8. Systems of Equations and Inequalities. Linear Systems of 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.9. Analytic Geometry. Parabolas.Ellipses.Hyperbolas.Summary of the Conic Sections; Rectangular and Polar Forms.Rotation of Axes.10. Further Topics in Algebra. Sequences and Series.Arithmetic Sequences and Series.Geometric Sequences and Series.The Binomial Theorem.Mathematical Induction.Counting Theory.Basics of Probability.11. An Introduction to Calculus: Limits and Derivatives. An Introduction to Limits.Techniques for Calculating Limits.One-Sided Limits; Limits Involving Infinity.Tangent Lines and Derivatives.R Reference: Algebraic Expressions. Review of Exponents and Polynomials.Review of Factoring.Review of Rational Expressions.Review of Negative and Rational Exponents.Review of Radical Expressions.
