Description
Book SynopsisThree 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, Coburnâs Precalculus uses narrative, extensive examples, and a range of exercises to connect seemingly disparate mathematical topics into a cohesive whole. Coburnâs hallmark applications are born out of the authorâs extensive experiences in and outside the classroom, and appeal to the vast diversity of students and teaching methods in this course area.
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Table of ContentsChapter 1: Equations and Inequalities1-1Linear Equations, Formulas, and Problem Solving1-2Linear Inequalities in One Variable1-3Absolute Value Equations and Inequalities1-4Complex Numbers1-5Solving Quadratic Equations1-6Solving Other Types of EquationsChapter 2: Relations, Functions and Graphs2-1Rectangular Coordinates; Graphing Circles and Relations2-2Graphs of Linear Equations2-3Linear Equations and Rates of Change2-4Functions, Notation, and Graphs of Functions2-5Analyzing the Graph of a Function2-6Toolbox Functions and Transformations2-7Piecewise-Defined Functions2-8The Algebra and Composition of FunctionsChapter 3: Polynomial and Rational Functions3-1Quadratic Functions and Applications3-2Synthetic Division; The Remainder and Factor Theorems3-3The Zeroes of Polynomial Functions3-4Graphing Polynomial Functions3-5Graphing Rational Functions3-6Additional Insights into Rational Functions3-7Polynomial and Rational Inequalities3-8Variation: Function Models in ActionChapter 4: Exponential and Logarithmic Functions4-1One-to-One and Inverse Functions4-2Exponential Functions4-3Logarithms and Logarithmic Functions4-4Properties of Logarithms; Solving Exponential and Logarithmic Equations4-5Applications from Business, Finance, and ScienceChapter 5: Introduction to Trigonometric Functions5-1Angle Measure, Special Triangles, and Special Angles5-2Unit Circles and the Trigonometry of Real Numbers5-3Graphs of Sine and Cosine Functions; Cosecant and Secant Functions 5-4Graphs of Tangent and Cotangent Functions 5-5Transformations and Applications of Trigonometric Graphs5-6The Trigonometry of Right Triangles 5-7Trigonometry and the Coordinate Plane Chapter 6: Trigonometric Identities, Inverses, and Equations6-1Fundamental Identities and Families of Identities 6-2Constructing and Verifying Identities 6-3The Sum and Difference Identities 6-4Double Angle, Half Angle & Product-to-Sum Identities6-5The Inverse Trigonometric Functions and Their Applications6-6Solving Basic Trigonometric Equations6-7General Trigonometric Equations and ApplicationsChapter 7: Applications of Trigonometry7-1Oblique Triangles and the Law of Sines 7-2The Law of Cosines; Area of a Triangle7-3Vectors and Vector Diagrams7-4Vector 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 Inequalities8-1Linear Systems in Two Variables with Applications8-2Linear Systems in Three Variables with Applications8-3Partial Fraction Decomposition8-4Systems of Inequalities and Linear Programming8-5Solving Systems Using Matrices and Row Operations8-6The Algebra of Matrices8-7Solving Linear Systems Using Matrix Equations8-8Applications of Matrices and Determinants: Cramer's Rule, Geometry, and MoreChapter 9: Analytical Geometry9-1Introduction to Analytic Geometry9-2The Circle and the Ellipse9-3The Hyperbola9-4The Analytic Parabola9-5Nonlinear Systems of Equations and Inequalities9-6Polar Coordinates, Equations, and Graphs9-7More on Conic Sections: Rotation of Axes and Polar Form9-8Parametric Equations and GraphsChapter 10: Additional Topics in Algebra10-1 Sequences and Series10-2 Arithmetic Sequences10-3 Geometric Sequences10-4 Mathematical Induction10-5 Counting Techniques10-6 Introduction to Probability10-7 The Binomial TheoremChapter 11: Bridges to Calculus - An Introduction to Limits11-1 Finding Limits Numerically and Graphically11-2 Algebraic Methods for Finding Limits; One-Sided Limits and Continuity11-3 Infinite Limits and Limits at Infinity11-4 Applications of Limits: Instantaneous Rates of Change and the Area Under a Curve
APPENDICESA-1A Review of Basic Concepts and SkillsA-2US Standard Units and the Metric SystemA-3Rational Expressions and the Least Common DenominatorA-4Deriving the Equation of a ConicA-5More on MatricesA-6Deriving the Equation of a Conic
