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Summary
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 College Algebra Essentials 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, College Algebra Essentials 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.
Table of Contents
Chapter R: A Review of Basic Concepts and Skills
R-1 The Language, Notation, and Numbers of Mathematics
R-2 Algebraic Expressions and the Properties of Real Numbers
R-3 Exponents, Scientific Notation, and a Review of Polynomials
R-4 Factoring Polynomials
R-5 Rational Expressions
R-6 Radicals and Rational Exponents
Chapter 1: Equations and Inequalities
1-1 Linear Equations, Formulas, and Problem Solving
1-2 Linear Inequalities in One Variable
1-3 Absolute Value Equations and Inequalities
1-4 Complex Numbers
1-5 Solving Quadratic Equations
1-6 Solving Other Types of Equation
Chapter 2: Relations, Functions and Graphs
2-1 Rectangular Coordinates; Graphing Circles and Relations
2-2 Graphs of Linear Equations
2-3 Linear Equations and Rates of Change
2-4 Functions, Notation, and Graphs of Functions
2-5 Analyzing the Graph of a Function
2-6 Toolbox Functions and Transformations
2-7 Piecewise-Defined Functions
2-8 The Algebra and Composition of Functions
Chapter 3: Polynomial and Rational Functions
3-1 Quadratic Functions and Applications
3-2 Synthetic Division; The Remainder and Factor Theorems
3-3 The Zeroes of Polynomial Functions
3-4 Graphing Polynomial Functions
3-5 Graphing Rational Functions
3-6 Additional Insights into Rational Functions
3-7 Polynomial and Rational Inequalities
3-8 Variation: Function Models in Action
Chapter 4: Exponential and Logarithmic Functions
4-1 One-to-One and Inverse Functions
4-2 Exponential Functions
4-3 Logarithms and Logarithmic Functions
4-4 Properties of Logarithms; Solving Exponential and Logarithmic Equations
4-5 Applications from Business, Finance, and Science
Chapter 5: Systems of Equations and Inequalities
5-1 Linear Systems in Two Variables with Applications
5-2 Linear Systems in Three Variables with Applications
5-3 Nonlinear Systems of Equations and Inequalities
5-4 Systems of Inequalities and Linear Programming
Chapter 6: Matrices and Matrix Applications
6-1 Solving Systems Using Matrices and Row Operations
6-2 The Algebra of Matrices
6-3 Solving Linear Systems Using Matrix Equations
6-4 Applications of Matrices and Determinants:
Chapter 7: Analytical Geometry and Conic Sections
7-1 Introduction to Analytic Geometry
7-2 The Circle and the Ellipse
7-3 The Hyperbola
7-4 The Analytic Parabola
Chapter 8: Additional Topics in Algebra
8-1 Sequences and Series
8-2 Arithmetic Sequences
8-3 Geometric Sequences
8-4 Mathematical Induction
8-5 Counting Techniques
8-6 Introduction to Probability
8-7 The Binomial Theorem
APPENDICES
A-1 More on Synthetic Division
A-2 More on Matrices
A-3 Deriving the Equation of a Conic
A-4 Proof Positive - A Selection of Proofs from College Algebra