Algebra and Trigonometry with Modeling and Visualization
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Algebra and Trigonometry with Modeling and Visualization

Algebra and Trigonometry with Modeling and Visualization

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About the Book

Gary Rockswold focuses on teaching algebra in context, answering the question, “Why am I learning this?” and ultimately motivating the students to succeed in this class. In addition, the author's understanding of what instructors need from a text (great 'real' examples and lots of exercises) makes this book fun and easy to teach from. Integrating this textbook into your course will be a worthwhile endeavor.

Table of Contents:
Chapter 1: INTRODUCTION TO FUNCTIONS AND GRAPHS    1.1 Numbers, Data, and Problem Solving         Sets of Numbers         Scientific Notation         Problem Solving 1.2 Visualization of Data         One-Variable Data         Two Variable Data         The Distance Formula         The Midpoint Formula         Graphing with a Calculator (Optional) Checking Basic Concepts for Sections 1.1 and 1.2    1.3 Functions and Their Representations         Basic Concepts         Representations of Functions         Formal Definition of a Function         Graphing Calculators and Functions (Optional)         Identifying Functions    1.4 Types of Functions and Their Rates of Change         Constant Functions         Linear Functions         Slope as a Rate of Change         Nonlinear Functions         Average Rate of Change         The Difference Quotient Checking Basic Concepts for Sections 1.3 and 1.4 Chapter 1 Summary  Chapter 1 Review Exercises Chapter 1 Extended and Discovery Exercises      Chapter 2: LINEAR FUNCTIONS AND EQUATIONS    2.1 Linear Functions and Models         Exact and Approximate Models         Representations of Linear Functions         Modeling with Linear Functions         Linear Regression (Optional) 2.2 Equations of Lines            Forms for Equations of Lines         Determining Intercepts         Horizontal, Vertical, Parallel, and Perpendicular Lines         Modeling Data (Optional)         Interpolation and Extrapolation         Direct Variation Checking Basic Concepts for Sections 2.1 and 2.2 2.3 Linear Equations         Equations         Symbolic Solutions         Graphical and Numerical Solutions         Problem-Solving Strategies   2.4 Linear Inequalities         Inequalities         Interval Notion         Techniques for Solving Inequalities         Compound Inequalities Checking Basic Concepts for Sections 2.3 and 2.4    2.5 Piecewise-Defined Functions         Evaluating and Graphing Piecewise-Defined Functions         The Greatest Integer Function         The Absolute Value Function         Equations and Inequalities Involving Absolute Values Checking Basic Concepts for Section 2.5    Chapter 2 Summary    Chapter 2 Review Exercises    Chapter 2 Extended and Discovery Exercises   Chapter 1-2 Cumulative Review Exercises   Chapter 3: QUADRATIC FUNCTIONS AND EQUATIONS 3.1 Quadratic Functions and Models         Basic Concepts         Completing the Square and the Vertex Formula         Applications and Models         Quadratic Regression (Optional) 3.2 Quadratic Equations and Problem Solving         Basic Concepts         Solving Quadratic Equations         Problem Solving Checking Basic Concepts for Sections 3.1 and 3.2  3.3 Quadratic Inequalities         Graphical Solutions         Symbolic Solutions 3.4 Transformations of Graphs            Vertical and Horizontal Translations         Stretching and Shrinking         Reflection of Graphs         Combining Transformations         Modeling with Transformations (Optional) Checking Basic Concepts for Sections 3.3 and 3.4 Chapter 3 Summary    Chapter 3 Review Exercises    Chapter 3 Extended and Discovery Exercises   Chapter 4: NONLINEAR FUNCTIONS AND EQUATIONS    4.1 Nonlinear Functions and Their Graphs            Polynomial Functions         Increasing and Decreasing Functions         Extrema of Nonlinear Functions         Symmetry 4.2 Polynomial Functions and Models            Graphs of Polynomial Functions         Piecewise-Defined Polynomial Functions         Polynomial Regression (Optional) Checking Basic Concepts for Sections 4.1 and 4.2    4.3 Real Zeros of Polynomial Functions            Division of Polynomials         Factoring Polynomials         Graphs and Multiple Zeros         Rational Zeros         Polynomial Equations  4.4 The Fundamental Theorem of Algebra            Complex Numbers         Quadratic Equations with Complex Solutions         Fundamental Theorem of Algebra         Polynomial Equations with Complex Solutions Checking Basic Concepts for Sections 4.3 and 4.4    4.5 Rational Functions and Models            Rational Functions         Vertical Asymptotes         Horizontal Asymptotes         Identifying Asymptotes         Rational Equations         Variation 4.6 Polynomial and Rational Inequalities            Polynomial Inequalities         Rational Inequalities Checking Basic Concepts for Sections 4.5 and 4.6    4.7 Power Functions and Radical Equations            Rational Exponents and Radical Notation         Power Functions and Models         Equations Involving Rational Exponents         Equations Involving Radicals         Power Regression (Optional) Checking Basic Concepts for Section 4.7    Chapter 4 Summary Chapter 4 Review Exercises    Chapter 4 Extended and Discovery Exercises      Chapters 1-4 Cumulative Review Exercises   Chapter 5: EXPONENTIAL AND LOGARITHMIC FUNCTIONS    5.1 Combining Functions            Arithmetic Operations on Functions         Composition of Functions 5.2 Inverse Functions and Their Representations            Inverse Operations         One-to-One Functions         Symbolic Representations of Inverse Functions         Other Representations of Inverse Functions Checking Basic Concepts for Sections 5.1 and 5.2     5.3 Exponential Functions and Models            Linear and Exponential Growth         Exponential Models         Compound Interest         The Natural Exponential Function 5.4 Logarithmic Functions and Models            The Common Logarithmic Function         Basic Equations         Logarithms with Other Bases         General Logarithmic Equations Checking Basic Concepts for Sections 5.3 and 5.4    5.5 Properties of Logarithms            Basic Properties of Logarithms         Change of Base Formula 5.6 Exponential and Logarithmic Equations            Exponential Equations         Logarithmic Equations Checking Basic Concepts for 5.5 and 5.6    5.7 Constructing Nonlinear Models            Exponential Model         Logarithmic Model         Logistic Model Checking Basic Concepts for Section 5.7    Chapter 5 Summary    Chapter 5 Review Exercises    Chapter 5 Extended and Discovery Exercises   Chapter 6: TRIGONOMETRIC FUNCTIONS    6.1 Angles and Their Measure            Angles         Degree Measure         Radian Measure         Arc Length         Area of a Sector 6.2 Right Triangle Trigonometry            Basic Concepts of Trigonometric Functions         Applications of Right Triangle Trigonometry         Complementary Angles and Cofunctions Checking Basic Concepts for 6.1 and 6.2    6.3 The Sine and Cosine Functions and Their Graphs           Definitions         The Unit Circle         Representations of the Sine and the Cosine Functions         Applications of the Sine and Cosine Functions         Modeling with the Sine Function (Optional) 6.4 Other Trigonometric Functions and Their Graphs            Definitions and Basic Identities         Representations of Other Trigonometric Functions         Applications of Trigonometric Functions Checking Basic Concepts for Sections 6.3 and 6.4    6.5 Graphing Trigonometric Functions         Transformations of Trigonometric Graphs         Graphing Trigonometric Functions by Hand         Simple Harmonic Motion         Models Involving Trigonometric Functions (Optional) 6.6 Inverse Trigonometric Functions            Review of Inverses         The Inverse Sine Function         The Inverse Cosine Function         The Inverse Tangent Function         Solving Triangles and Equations Checking Basic Concepts for Sections 6.5 and 6.6 Chapter 6 Summary    Chapter 6 Review Exercises    Chapter 6 Extended and Discovery Exercises   Chapters 1-6 Cumulative Review Exercises   Chapter 7: TRIGONOMETRIC IDENTITIES AND EQUATIONS    7.1 Fundamental Identities            Reciprocal and Quotient Identities         Pythagorean Identities         Negative-Angle Identities 7.2 Verifying Identities            Simplifying Trigonometric Expressions         Verification of Identities Checking Basic Concepts for Section 7.1 and 7.2 7.3 Trigonometric Equations         Reference Angles         Solving Trigonometric Equations         Solving Inverse Trigonometric Equations 7.4 Sum and Difference Identities            Sum and Difference Identities for Cosine         Other Sum and Difference Identities Checking Basic Concepts for Section 7.3 and 7.4    7.5 Multiple-Angle Identities            Double-Angle Identities         Half-Angle Formulas         Solving Equations         Product-to-Sum and Sum-to-Product Identities Checking Basic Concepts for Section 7.5 Chapter 7 Summary    Chapter 7 Review Exercises    Chapter 7 Extended and Discovery Exercises   Chapter 8: FURTHER TOPICS IN TRIGONOMETRY 8.1 Law of Sines         Oblique Triangles         Solving Triangles         The Ambiguous Case 8.2 Law of Cosines            Derivation of the Law of Cosines         Solving Triangles         Area Formulas Checking Basic Concepts for Sections 8.1 and 8.2    8.3 Vectors            Basic Concepts         Operations on Vectors         The Dot Product         Work 8.4 Parametric Equations            Basic Concepts         Applications of Parametric Equations Checking Basic Concepts for Sections 8.3 and 8.4    8.5 Polar Equations         The Polar Coordinate System         Graphs of Polar Equations         Graphing Calculators and Polar Equations (Optional)         Solving Polar Equations 8.6 Trigonometric Form and Roots of Complex Numbers            Trigonometric Form         Products and Quotients of Complex Numbers         De Moivre’s Theorem         Roots of Complex Numbers Checking Basic Concepts for Sections 8.5 and 8.6    Chapter 8 Summary    Chapter 8 Review Exercises    Chapter 8 Extended and Discovery Exercises   Chapters 1-8 Cumulative Review Exercises             Chapter 9: SYSTEMS OF EQUATIONS AND INEQUALITIES    9.1 Functions and Equations in Two Variables            Functions of Two Variables         Systems of Equations         The Method of Substitution         Graphical and Numerical Methods         Joint Variation 9.2 Systems of Equations and Inequalities in Two Variables            Types of Linear Systems in Two Variables         The Elimination Method         Systems of Linear and Nonlinear Inequalities         Linear Programming Checking Basic Concepts for 9.1 and 9.2    9.3 Systems of Linear Equations in Three Variables            Basic Concepts         Solving with Elimination and Substitution         Systems with No Solutions         Systems with Infinitely Many Solutions 9.4 Solutions to Linear Systems Using Matrices            Representing Systems of Linear Equations with Matrices         Row-Echelon Form         Gaussian Elimination         Solving Systems of Linear Equations with Technology (Optional) Checking Basic Concepts for Sections 9.3 and 9.4    9.5 Properties and Applications of Matrices            Matrix Notation         Sums, Differences, and Scalar Multiples of Matrices         Matrix Products         Technology and Matrices (Optional) 9.6 Inverses of Matrices            Matrix Inverses         Finding Inverses Symbolically         Representing Linear Systems with Matrix Equations         Solving Linear Systems with Inverses Checking Basic Concepts for Sections 9.5 and 9.6     9.7 Determinants            Definition and Calculation of Determinants         Area of Regions         Cramer’s Rule         Limitations on the Method of Cofactors and Cramer’s Rule Checking Basic Concepts for Section 9.7 Chapter 9 Summary    Chapter 9 Review Exercises    Chapter 9 Extended and Discovery Exercise   Chapter 10: CONIC SECTIONS    10.1 Parabolas            Equations and Graphs of Parabolas         Reflective Property of Parabolas         Translations of Parabolas 10.2 Ellipses            Equations and Graphs of Ellipses         Reflective Property of Ellipses         Translations of Ellipses         Circles         Solving Systems of Equations and Inequalities Checking Basic Concepts for Section 10.1 and 10.2    10.3 Hyperbolas            Equations and Graphs of Hyperbolas         Reflective Property of Hyperbolas         Translations of Hyperbolas         Solving Systems of Nonlinear Equations Checking Basic Concepts for Section 10.3 Chapter 10 Summary Chapter 10 Review Exercises    Chapter 10 Extended and Discovery Exercises   Chapter 11: FURTHER TOPICS IN ALGEBRA     11.1 Sequences            Basic Concepts         Representations of Sequences         Arithmetic Sequences         Geometric Sequences 11.2 Series            Basic Concepts         Arithmetic Series         Geometric Series         Summation Notation Checking Basic Concepts for Sections 11.1 and 11.2    11.3 Counting            Fundamental Counting Principle         Permutations         Combinations 11.4 The Binomial Theorem            Derivation of the Binomial Theorem         Pascal’s Triangle Checking Basic Concepts for Sections 11.3 and 11.4    11.5 Mathematical Induction            Mathematical Induction         Proving Statements         Generalized Principle of Mathematical Induction 11.6 Probability            Definition of Probability         Compound Events         Independent and Dependent Events Checking Basic Concepts for Sections 11.5 and 11.6    Chapter 11 Summary    Chapter 11 Review Exercises    Chapter 11 Extended and Discovery Exercises   Chapters 1-11 Cumulative Review Exercises             Chapter R: REFERENCE- BASIC CONCEPTS FROM ALGEBRA AND GEOMETRY R.1 Formulas from Geometry            Geometric Shapes in a Plane         The Pythagorean Theorem         Three-Dimensional Objects         Similar Triangles         A Summary of Geometric Formulas R.2 Circles            Equations and Graphs of Circles         Finding the Center and Radius of a Circle R.3 Integer Exponents            Bases and Positive Exponents         Zero and Negative Exponents         Product, Quotient, and Power Rules R.4 Polynomial Expressions            Addition and Subtraction of Monomials         Addition and Subtraction of Polynomials         Distributive Properties         Multiplying Polynomials         Some Special Products R.5 Factoring Polynomials            Common Factors         Factoring by Grouping         Factoring x2 + bx + c         Factoring Trinomials by Grouping         Factoring Trinomials with FOIL         Difference of Two Squares         Perfect Square Trinomials         Sum and Difference of Two Cubes R.6 Rational Expressions            Simplifying Rational Expressions         Multiplication and Division of Rational Expressions         Least Common Multiples         Common Denominators         Addition and Subtraction of Rational Expressions         Clearing Fractions         Complex Fractions R.7 Radical Notation and Rational Exponents            Radical Notation         Rational Exponents         Properties of Rational Exponents  R.8 Radical Expressions            Product Rule for Radical Expressions         Quotient Rule for Radical Expressions         Addition and Subtraction         Multiplication         Rationalizing the Denominator   APPENDIX A: A Library of Functions    APPENDIX B: Using the Graphing Calculator   APPENDIX C: Partial Fractions APPENDIX D: Rotation of Axes   Bibliography Answers to Selected Exercises Index of Applications Index


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Product Details
  • ISBN-13: 9780321279101
  • Publisher: Pearson Education (US)
  • Publisher Imprint: Pearson
  • Language: English
  • Weight: 2175 gr
  • ISBN-10: 0321279107
  • Publisher Date: 11 Apr 2005
  • Binding: Hardback
  • No of Pages: 1216


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Algebra and Trigonometry with Modeling and Visualization
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