Algebra & Trigonometry

Hardcover | February 13, 2009

byJohn Coburn

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Three components contribute to a theme sustained throughout the Coburn Series: that of laying a firm foundation, building a solid framework, and providing strong connections. Not only does Coburn present a sound problem-solving process to teach students to recognize a problem, organize a procedure, and formulate a solution, the text encourages students to see beyond procedures in an effort to gain a greater understanding of the big ideas behind mathematical concepts.

Written in a readable, yet mathematically mature manner appropriate for college algebra level students, Coburn’s Algebra & Trigonometry uses narrative, extensive examples, and a range of exercises to connect seemingly disparate mathematical topics into a cohesive whole. Coburn’s hallmark applications are born out of the author’s extensive experiences in and outside the classroom, and appeal to the vast diversity of students and teaching methods in this course area.

Benefiting from the feedback of hundreds of instructors and students across the country, Algebra & Trigonometry second edition, continues to emphasize connections in order to improve the level of student engagement in mathematics and increase their chances of success in college algebra.

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Three components contribute to a theme sustained throughout the Coburn Series: that of laying a firm foundation, building a solid framework, and providing strong connections. Not only does Coburn present a sound problem-solving process to teach students to recognize a problem, organize a procedure, and formulate a solution, the text e...

Format:HardcoverDimensions:11.1 × 8.7 × 1.7 inPublished:February 13, 2009Publisher:McGraw-Hill EducationLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0077276515

ISBN - 13:9780077276515

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Table of Contents

Chapter R: A Review of Basic Concepts and Skills

R-1The Language, Notation, and Numbers of Mathematics

R-2Algebraic Expressions and the Properties of Real Numbers

R-3Exponents, Scientific Notation, and a Review of Polynomials

R-4Factoring Polynomials

R-5Rational Expressions

R-6Radicals and Rational Exponents

Chapter 1: Equations and Inequalities

1-1Linear Equations, Formulas, and Problem Solving

1-2Linear Inequalities in One Variable

1-3Absolute Value Equations and Inequalities

1-4Complex Numbers

1-5Solving Quadratic Equations

1-6Solving Other Types of Equations

Chapter 2: Relations, Functions and Graphs

2-1Rectangular Coordinates; Graphing Circles and Relations

2-2Graphs of Linear Equations

2-3Linear Equations and Rates of Change

2-4Functions, Notation, and Graphs of Functions

2-5Analyzing the Graph of a Function

2-6Toolbox Functions and Transformations

2-7Piecewise-Defined Functions

2-8The Algebra and Composition of Functions

Chapter 3: Polynomial and Rational Functions

3-1Quadratic Functions and Applications

3-2Synthetic Division; The Remainder and Factor Theorems

3-3The Zeroes of Polynomial Functions

3-4Graphing Polynomial Functions

3-5Graphing Rational Functions

3-6Additional Insights into Rational Functions

3-7Polynomial and Rational Inequalities

3-8Variation: Function Models in Action

Chapter 4: Exponential and Logarithmic Functions

4-1One-to-One and Inverse Functions

4-2Exponential Functions

4-3Logarithms and Logarithmic Functions

4-4Properties of Logarithms; Solving Exponential and Logarithmic Equations

4-5Applications from Business, Finance, and Science

Chapter 5: Introduction to Trigonometric Functions

5-1Angle Measure, Special Triangles, and Special Angles

5-2The Trigonometry of Right Triangles

5-3Trigonometry and the Coordinate Plane

5-4Unit Circles and the Trigonometric of Real Numbers

5-5Graphs of Sine and Cosine Functions; Cosecant and Secant Functions

5-6Graphs of Tangent and Cotangent Functions

5-7Transformations and Applications of Trigonometric Graphs

Chapter 6: Trigonometric Identities, Inverses, and Equations

6-1Fundamental Identities and Families of Identities

6-2Constructing and Verifying Identities

6-3The Sum and Difference Identities

6-4Double Angle, Half Angle & Product-to-Sum Identities

6-5The Inverse Trigonometric Functions and Their Applications

6-6Solving Basic Trigonometric Equations

6-7General Trigonometric Equations and Applications

Chapter 7: Applications of Trigonometry

7-1Oblique Triangles and the Law of Sines

7-2The Law of Cosines; Area of a Triangle

7-3Vectors and Vector Diagrams

7-4Vector Applications and the Dot Product

7-5Complex Numbers in Trigonometric Form

7-6Demoivre's Theorem and the Theorem on nth Roots

Chapter 8: Systems of Equations and Inequalities

8-1Linear Systems in Two Variables with Applications

8-2Linear Systems in Three Variables with Applications

8-3Nonlinear Systems of Equations and Inequalities

8-4Systems of Inequalities and Linear Programming

Chapter 9: Matrices and Matrix Applications

9-1Solving Systems Using Matrices and Row Operations

9-2The Algebra of Matrices

9-3Solving Linear Systems Using Matrix Equations

9-4Applications of Matrices and Determinants: Cramer's Rule, Partial Fractions, and More

Chapter 10: Analytical Geometry and Conic Sections

10-1 Introduction to Analytic Geometry

10-2 The Circle and the Ellipse

10-3 The Hyperbola

10-4 The Analytic Parabola

10-5 Polar Coordinates, Equations, and Graphs

10-6 More on Conic Sections: Rotation of Axes and Polar Form

10-7 Parametric Equations and Graphs

Chapter 11: Additional Topics in Algebra

11-1 Sequences and Series

11-2 Arithmetic Sequences

11-3 Geometric Sequences

11-4 Mathematical Induction

11-5 Counting Techniques

11-6 Introduction to Probability

11-7 The Binomial TheoremSummary and Concept Review

APPENDICES

A-1More on Synthetic Division
A-2More on Matrices
A-3Deriving the Equation of a Conic
A-4Proof Positive - A Selection of Proofs from Algebra and Trigonometry