Algebra And Trigonometry

Hardcover | January 29, 2007

byJudith A. Beecher, Judith A. Penna, Marvin L. Bittinger

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These authors have created a book to really help students visualize mathematics for better comprehension. By creating algebraic visual side-by-sides to solve various problems in the examples, the authors show students the relationship of the algebraic solution with the visual, often graphical, solution. In addition, the authors have added a variety of new tools to help students better use the book for maximum effectiveness to not only pass the course, but truly understand the material.

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These authors have created a book to really help students visualize mathematics for better comprehension. By creating algebraic visual side-by-sides to solve various problems in the examples, the authors show students the relationship of the algebraic solution with the visual, often graphical, solution. In addition, the authors have ad...

Judy Beecher has an undergraduate degree in mathematics from Indiana University and a graduate degree in mathematics from Purdue University. She has taught at both the high school and college levels with many years of developmental math and precalculus teaching experience at Indiana University - Purdue University Indianapolis. In addit...
Format:HardcoverDimensions:1072 pages, 10.3 × 8.14 × 1.57 inPublished:January 29, 2007Publisher:Pearson EducationLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0321466209

ISBN - 13:9780321466204

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Table of Contents

Chapter R  Basic Concepts of Algebra

R.1  The Real-Number System

R.2  Integer Exponents, Scientific Notation, and Order of Operations

R.3  Addition, Subtraction, and Multiplication of Polynomials

R.4  Factoring

R.5  Rational Expressions

R.6  Radical Notation and Rational Exponents

R.7  The Basics of Equation Solving

 

Chapter 1  Graphs, Functions, and Models

1.1  Introduction to Graphing

1.2  Functions and Graphs

1.3  Linear Functions, Slope, and Applications

1.4  Equations of Lines and Modeling

1.5  More on Functions

1.6  The Algebra of Functions

1.7  Symmetry and Transformations

 

Chapter 2  Functions, Equations, and Inequalities

2.1  Linear Equations, Functions, and Models

2.2  The Complex Numbers

2.3  Quadratic Equations, Functions, and Models

2.4  Analyzing Graphs of Quadratic Functions

2.5  More Equation Solving

2.6  Solving Linear Inequalities

 

Chapter 3  Polynomial And Rational Functions

3.1  Polynomial Functions and Models

3.2  Graphing Polynomial Functions

3.3  Polynomial Division; The Remainder and Factor Theorems

3.4  Theorems about Zeros of Polynomial Functions

3.5  Rational Functions

3.6  Polynomial and Rational Inequalities

3.7  Variation and Applications

 

Chapter 4  Exponential and Logarithmic Functions

4.1  Inverse Functions

4.2  Exponential Functions and Graphs

4.3  Logarithmic Functions and Graphs

4.4  Properties of Logarithmic Functions

4.5  Solving Exponential and Logarithmic Equations

4.6  Applications and Models:  Growth and Decay, and Compound Interest

 

Chapter 5  The Trigonometric Functions

5.1  Trigonometric Functions of Acute Angles

5.2  Applications of Right Triangles

5.3  Trigonometric Functions of Any Angle

5.4  Radians, Arc Length, and Angular Speed

5.5  Circular Functions:  Graphs and Properties

5.6  Graphs of Transformed Sine and Cosine Functions

 

Chapter 6  Trigonometric Identities, Inverse Functions, and Equations

6.1  Identities:  Pythagorean and Sum and Difference

6.2  Identities:  Cofunction, Double-Angle, and Half-Angle

6.3  Proving Trigonometric Identities

6.4  Inverses of the Trigonometric Functions

6.5  Solving Trigonometric Equations

 

Chapter 7  Applications of Trigonometry

7.1  The Law of Sines

7.2  The Law of Cosines

7.3  Complex Numbers:  Trigonometric Form

7.4  Polar Coordinates and Graphs

7.5  Vectors and Applications

7.6  Vector Operations

 

Chapter 8  Systems of Equations and Matrices

8.1  Systems of Equations in Two Variables

8.2  Systems of Equations in Three Variables

8.3  Matrices and Systems of Equations

8.4  Matrix Operations

8.5  Inverses of Matrices

8.6  Determinants and Cramer's Rule

8.7  Systems of Inequalities and Linear Programming

8.8  Partial Fractions

 

Chapter 9  Analytic Geometry Topics                                   

9.1  The Parabola

9.2  The Circle and the Eclipse

9.3  The Hyperbola

9.4  Nonlinear Systems of Equations and Inequalities

9.5  Rotation of Axes

9.6  Polar Equations of Conics

9.7  Parametric Equations

 

Chapter 10  Sequences, Series, and Combinatorics

10.1  Sequences and Series

10.2  Arithmetic Sequences and Series

10.3  Geometric Sequences and Series

10.4  Mathematical Induction

10.5  Combinatorics:  Permutations

10.6  Combinatorics:  Combinations

10.7  The Binomial Theorem

10.8  Probability

 

Appendix:  Basic Concepts from Geometry