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Appropriate for freshman-/sophomore-level courses in Algebra and Trigonometry or Precalculus. This second in a series of three texts covers the traditional topics for Algebra and Trigonometry with a unique emphasis on concepts that are valuable to other courses or other applications, especially those that can be explored and illustrated on a graphics calculator. It de-emphasizes the more manipulative skills in favor of visualization, graphing, data analysis, and modeling of problems from the physical world.
1. Numbers, Calculations and Basic Algebra. The Integers and the Rational Numbers. Real Numbers and their Properties. Order and Averages. Exponents and their Properties. Polynomials and their Factors. Rational Expressions. The Complex Numbers. 2. Equations and Inequalities. Solving Equations Algebraically. Equations and Applications. Displaying Equations Geometrically. Graphs with Graphics Calculators. Inequalities and Absolute Values. Lines. Some Important Quadratic Curves. Linear Regression. 3. Functions and Their Graphs. The Function Concept. Linear Functions. Quadratic Functions. More on Graphics Calculators. Polynomial Functions. Rational Functions. Combinations of Functions. Inverse Functions. Special Functions. 4. Exponential and Logarithmic Functions. Exponential Functions. Logarithms and Logarithmic Functions. Scientific Applications. Business Applications. Nonlinear Regression. 5. The Trigonometric Functions. Right Triangle Trigonometry. General Angles and Arcs. The Sine and Cosine Functions. Graphs of the Sine and Cosine Functions. Four More Trigonometric Functions. Inverse Trigonometric Functions. 6. Trigonometric Identities, Equations and Laws. Basic Trigonometric Identities. Addition Identities. More Identities. Trigonometric Equations. The Law of Sines. The Law of Cosines. Vectors. 7. Systems of Equations and Inequalities. Equivalent Systems of Equations. Solving Systems Using Matrices. The Algebra of Matrices. Inverses of Matrices. Determinants. Systems of Inequalities. 8. Analytic Geometry. Parabolas. Ellipses. Hyperbolas. Rotations. Parametric Equations. Polar Coordinates. Polar Equations of Conics. 9. Sequences, Counting and Probability. Arithmetic Sequences and Sums. Geometric Sequences and Sums. General Sequences and Programming. Mathematical Induction. The Binomial Formula. Counting Ordered Arrangements. Counting Unordered Collections. Introduction to Probablility. Independence in Probability Problems. Answers to Selected Problems. Index.
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- ID: 9780133815757
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