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David Cohen's PRECALCULUS: A PROBLEMS-ORIENTED APPROACH, Sixth Edition, focuses on teaching mathematics by using a graphical perspective throughout to provide a visual understanding of college algebra and trigonometry. The author is known for his clear writing style and the numerous quality exercises and applications he includes in his respected texts. In this new edition, graphs, visualization of data, and functions are now introduced much earlier and receive greater emphasis. Many sections now contain more examples and exercises involving applications and real-life data. While this edition takes the existence of the graphing calculator for granted, the material is arranged so that one can teach the course with as much or as little graphing utility work as he/she wishes.
1. FUNDAMENTALS.
Sets of Real Numbers. Absolute Value. Solving Equations (Review and Preview). Rectangular Coordinates. Visualizing Data. Graphs and Graphing Utilities. Equations of Lines. Symmetry and Graphs. Circles.
2. EQUATIONS AND INEQUALITIES.
Quadratic Equations: Theory and Examples. Other Types of Equations. Inequalities. More on Inequalities.
3. FUNCTIONS.
The Definition of a Function. The Graph of a Function. Shapes of Graphs. Average Rate of Change. Techniques in Graphing. Methods of Combining Function. Iteration. Inverse Functions.
4. POLYNOMIAL AND RATIONAL FUNCTIONS. APPLICATIONS TO OPTIMIZATION.
Linear Functions. Quadratic Functions. Using Iteration to Model Population Growth (Optional Section). Setting up Equations That Define Functions. Maximum and Minimum Problems. Polynomial Functions. Rational Functions.
5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions. The Exponential Function y = ex. Logarithmic Functions. Properties of Logarithms. Equations and Inequalities with Logs and Exponents. Compound Interest. Exponential Growth and Decay.
6. TRIGONOMETRIC FUNCTIONS OF ANGLES.
Trigonometric Functions of Acute Angles. Algebra and the Trigonometric Functions. Right-Triangle Applications. Trigonometric Functions of Angles. Trigonometric Identities.
7. TRIGONOMETRIC FUNCTIONS OF REAL NUMBERS.
Radian Measure. Radian Measure and Geometry. Trigonometric Functions of Real Numbers. Graphs of the Sine and the Cosine Functions. Graphs of y = A sin(Bx-C) and y = A cos(Bx - C). Simple Harmonic Motion. Graphs of the Tangent and the Reciprocal Functions.
8. ANALYTICAL TRIGONOMETRY.
The Addition Formulas. The Double-Angle Formulas. The Product-to-Sum and Sum-to-Product Formulas. Trigonometric Equations. The Inverse Trigonometric Functions.
9. ADDITIONAL TOPICS IN TRIGONOMETRY.
The Law of Sines and the Law of Cosines. Vectors in the Plane, a Geometric Approach. Vectors in the Plane, an Algebraic Approach. Parametric Equations. Introduction to Polar Coordinates. Curves in Polar Coordinates.
10. SYSTEMS OF EQUATIONS.
Systems of Two Linear Equations in Two Unknowns. Gaussian Elimination. Matrices. The Inverse of a Square Matrix. Determinants and Cramer's Rule. Nonlinear Systems of Equations. Systems of Inequalities.
11. ANALYTIC GEOMETRY.
The Basic Equations. The Parabola. Tangents to Parabolas (Optional). The Ellipse. The Hyperbola. The Focus-Directrix Property of Conics. The Conics in Polar Coordinates. Rotation of Axes.
12. ROOTS OF POLYNOMIAL EQUATIONS.
The Complex Number System. Division of Polynomials. Roots of Polynomial Equations: The Remainder Theorem and the Factor Theorem. The Fundamental Theorem of Algebra. Rational and Irrational Roots. Conjugate Roots and Descartes' Rule of Signs. Introduction to Partial Fractions. More About Partial Fractions.
13. ADDITIONAL TOPICS.
Mathematical Induction. The Binomial Theorem. Introduction to Sequences and Series. Arithmetic Sequences and Series. Geometric Sequences and Series. DeMoivre's Theorem.
Appendix 1: Using a Graphing Utility.
Appendix 2: Significant Digits and Calculators.
Tables.
Answers to Selected Exercises.
Index.
David Cohen's PRECALCULUS: A PROBLEMS-ORIENTED APPROACH, Sixth Edition, focuses on teaching mathematics by using a graphical perspective throughout to provide a visual understanding of college algebra and trigonometry. The author is known for his clear writing style and the numerous quality exercises and applications he includes in his respected texts. In this new edition, graphs, visualization of data, and functions are now introduced much earlier and receive greater emphasis. Many sections now contain more examples and exercises involving applications and real-life data. While this edition takes the existence of the graphing calculator for granted, the material is arranged so that one can teach the course with as much or as little graphing utility work as he/she wishes.
Table of Contents
1. FUNDAMENTALS.
Sets of Real Numbers. Absolute Value. Solving Equations (Review and Preview). Rectangular Coordinates. Visualizing Data. Graphs and Graphing Utilities. Equations of Lines. Symmetry and Graphs. Circles.
2. EQUATIONS AND INEQUALITIES.
Quadratic Equations: Theory and Examples. Other Types of Equations. Inequalities. More on Inequalities.
3. FUNCTIONS.
The Definition of a Function. The Graph of a Function. Shapes of Graphs. Average Rate of Change. Techniques in Graphing. Methods of Combining Function. Iteration. Inverse Functions.
4. POLYNOMIAL AND RATIONAL FUNCTIONS. APPLICATIONS TO OPTIMIZATION.
Linear Functions. Quadratic Functions. Using Iteration to Model Population Growth (Optional Section). Setting up Equations That Define Functions. Maximum and Minimum Problems. Polynomial Functions. Rational Functions.
5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions. The Exponential Function y = ex. Logarithmic Functions. Properties of Logarithms. Equations and Inequalities with Logs and Exponents. Compound Interest. Exponential Growth and Decay.
6. TRIGONOMETRIC FUNCTIONS OF ANGLES.
Trigonometric Functions of Acute Angles. Algebra and the Trigonometric Functions. Right-Triangle Applications. Trigonometric Functions of Angles. Trigonometric Identities.
7. TRIGONOMETRIC FUNCTIONS OF REAL NUMBERS.
Radian Measure. Radian Measure and Geometry. Trigonometric Functions of Real Numbers. Graphs of the Sine and the Cosine Functions. Graphs of y = A sin(Bx-C) and y = A cos(Bx - C). Simple Harmonic Motion. Graphs of the Tangent and the Reciprocal Functions.
8. ANALYTICAL TRIGONOMETRY.
The Addition Formulas. The Double-Angle Formulas. The Product-to-Sum and Sum-to-Product Formulas. Trigonometric Equations. The Inverse Trigonometric Functions.
9. ADDITIONAL TOPICS IN TRIGONOMETRY.
The Law of Sines and the Law of Cosines. Vectors in the Plane, a Geometric Approach. Vectors in the Plane, an Algebraic Approach. Parametric Equations. Introduction to Polar Coordinates. Curves in Polar Coordinates.
10. SYSTEMS OF EQUATIONS.
Systems of Two Linear Equations in Two Unknowns. Gaussian Elimination. Matrices. The Inverse of a Square Matrix. Determinants and Cramer's Rule. Nonlinear Systems of Equations. Systems of Inequalities.
11. ANALYTIC GEOMETRY.
The Basic Equations. The Parabola. Tangents to Parabolas (Optional). The Ellipse. The Hyperbola. The Focus-Directrix Property of Conics. The Conics in Polar Coordinates. Rotation of Axes.
12. ROOTS OF POLYNOMIAL EQUATIONS.
The Complex Number System. Division of Polynomials. Roots of Polynomial Equations: The Remainder Theorem and the Factor Theorem. The Fundamental Theorem of Algebra. Rational and Irrational Roots. Conjugate Roots and Descartes' Rule of Signs. Introduction to Partial Fractions. More About Partial Fractions.
13. ADDITIONAL TOPICS.
Mathematical Induction. The Binomial Theorem. Introduction to Sequences and Series. Arithmetic Sequences and Series. Geometric Sequences and Series. DeMoivre's Theorem.
Appendix 1: Using a Graphing Utility.
Appendix 2: Significant Digits and Calculators.
Tables.
Answers to Selected Exercises.
Index.