Three components contribute to a theme sustained throughout the Coburn/Herdlick Graphs and Models series: that of laying a firm foundation, building a solid framework, and providing strong connections. In the Graphs and Models texts, the authors combine their depth of experience with the conversational style and the wealth of applications that the Coburn/Herdlick texts have become known for. By combining a graphical approach to problem solving with algebraic methods, students learn how to relate their mathematical knowledge to the outside world. The authors use technology to solve the more…mehr
Three components contribute to a theme sustained throughout the Coburn/Herdlick Graphs and Models series: that of laying a firm foundation, building a solid framework, and providing strong connections. In the Graphs and Models texts, the authors combine their depth of experience with the conversational style and the wealth of applications that the Coburn/Herdlick texts have become known for. By combining a graphical approach to problem solving with algebraic methods, students learn how to relate their mathematical knowledge to the outside world. The authors use technology to solve the more true to life equations, to engage more applications, and to explore the more substantial questions involving graphical behavior. Benefiting from the feedback of hundreds of instructors and students across the country, Precalculus: Graphs & Models emphasizes connections in order to improve the level of student engagement in mathematics and increase their chances of success in precalculus and calculus. The launch of the Coburn/Herdlick Graphs and Models series provides a significant leap forward in terms of online course management with McGraw-Hill's new homework platform, Connect Math Hosted by ALEKS Corp. Math instructors served as digital contributors to choose the problems that will be available, authoring each algorithm and providing stepped out solutions that go into great detail and are focused on areas where students commonly make mistakes. From there, the ALEKS Corporation reviewed each algorithm to ensure accuracy. A unifying theme throughout the entire process was the involvement of the authors. Through each step, they provided feedback and guidance to the digital contributors to ensure that the content being developed digitally closely matched the textbook. The result is an online homework platform that provides superior content and feedback, allowing students to effectively learn the material being taught.
John Coburn grew up in the Hawaiian Islands, the seventh of sixteen children. He received his Associate of Arts degree in 1977 from Windward Community College, where he graduated with honors. In 1979 he received a Bachelor's Degree in Education from the University of Hawaii. After being lured into the business world for five years, he returned to his first love, accepting a teaching position in high school mathematics where he was recognized as Teacher of the Year in 1987. Soon afterward, the decision was made to seek a Masters Degree, which he received two years later from the University of Oklahoma. For the last fifteen years, he has been teaching mathematics at the Florissant Valley campus of St. Louis Community College, where he is now a full professor. During his tenure there he has received numerous nominations as an outstanding teacher by the local chapter of Phi Theta Kappa, two nominations to Who's Who Among America's Teachers and was recognized as Teacher of the year in 2004 by the Mathematics Educators of Greater St. Louis (MEGSL). He has made numerous presentations and local, state and national conferences on a wide variety of topics. His other loves include his family, music, athletics, games and all things beautiful, and hopes this love of life comes through in his writing, and serves to make the learning experience an interesting and engaging one for all students.
Inhaltsangabe
PreCalculus Concepts, Connections and ApplicationsChapter 1: Equations and Inequalities 1.1 Linear Equations, Formulas and Problem Solving 1.2 Linear Inequalities in One Variable with Applications 1.3 Solving Polynomial and Other Equations 1.4 Complex Numbers 1.5 Solving Non-Factorable Quadratic Equations Chapter 2: Functions and Graphs 2.1 Rectangular Coordinates and the Graph of a Line 2.2 Relations, Functions and Graphs 2.3 Linear Functions and Rates of Change 2.4 Quadratic and Other Toolbox Functions 2.5 Functions and Inequalities -- A Graphical View 2.6 Regression, Technology and Data Analysis Chapter 3: Operations on Functions and Analyzing Graphs 3.1 The Algebra and Composition of Functions 3.2 One-to-One and Inverse Functions 3.3 Toolbox Functions and Transformations 3.4 Graphing General Quadratic Functions 3.5 Asymptotes and Simple Rational Functions 3.6 Toolbox Applicaitons: Direct and Inverse Variation 3.7 Piecewise-Defined Functions 3.8 Analyzing the Graph of a Function Chapter 4: Polynomial and Rational Functions 4.1 Polynomial Long Division and Synthetic Division 4.2 The Remainder and Factor Theorems 4.3 Zeroes of Polynomial Functions 4.4 Graphing Polynomial Functions 4.5 Graphing Rational Functions 4.6 Additional Insights into Rational Functions 4.7 Polynomial and Rational Inequalities - Analytical View Chapter 5: Exponential and Logarithmic Functions 5.1 Exponential Functions 5.2 Logarithms and Logarithmic Functions 5.3 The Natural Logarithmic Function and Properties of Logarithms 5.4 Exponential/Logarithmic Equations and Applications 5.5 Applications from Investment, Finance and Physical Science 5.6 Exponential, Logarithmic and Logistic Regression Models Chapter 6: An Introduction to Trigonometric Functions 6.0 An Introduction to Cycles and Periodic Functions (on the Web) 6.1 Radian Measure and the Trigonometric Functionsand the Trigonometry of Real Numbers 6.3 Graphs of the Sine and Cosine Functions 6.4 Graphs of the Tangent and Cotangent Functions 6.5 Transformations and Applicaitons of Trigonometric Graphs 6.6 Angle Measure, Special Triangles and Special Angles 6.7 The Trigonmetry of Right Triangles 6.8 Trigonometry and the Coordinate Plane Chapter 7: Trigonometric Identities, Inverses and Equations 7.1 Fundamental Identities and Families of Identities 7.2 Constructing and Verifying Identities 7.3 The Sum and Difference Identities 7.4 Double Angle, Half Angle and Product-to-Sum Identities 7.5 The Inverse Trig Functions and their Application 7.6 Solving Basic Trig Equations 7.7 General Trig Equations and Applications 7.8 Trigonometric Models and Sinusoidal Regression Chapter 8: Applications of Trigonometry 8.1 Oblique Triangles and the Law of Sines 8.2 Law of Sines and the Ambiguous Case 8.3 the Law of Cosines 8.4 Vectors and Vector Diagrams 8.5 Vectors Applications and the Dot Product 8.6 Complex Numbers in Trigonometric Form; Products and Quotients 8.7 Demoivre's Theorem and the Nth Roots Theorem Chapter 9: Systems of Equations and Inequalities 9.1 Linear Systems in Two Variables with Applications 9.2 Linear Systems in Three Variables with Applications 9.3 Systems of Linear Inequalities and Linear Programming 9.4 Systems and Absolute Value Equations and Inequalities 9.5 Solving Linear Systems using Matrices and Row Operations 9.6 The Algebra of Matrices 9.7 Solving Linear Systems using Matrix Equations 9.8 Matrix Applications: Cramer's Rule, Partial Fractions and More Chapter 10: Topics From Analytical Geometry 10.0 An Introdcution to Analytical Geometry (on the Web) 10.1 The Circle and the Ellipse 10.2 The Hyperbola 10.3 Non-Linear Systems of Equations and Inequalities 10.4 Foci and the Analytic Ellipse and Hyperbola 10.5 The Analytic Parabola 10.6 Polar Coordinates, Equations and Graphs 10.7 More on the Conic Sections: Rotation of Axes and Polar Form 10.8 Parametric Equations of 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 Fundamentals of Quick-Counting 11.6 Counting Techniques: Permutations and Combinations 11.7 Introduction to Probability 11.8 The Binomial Theorem and Binomial Probabilities 11.9 Conditional Probability and Expected Value 11.10 Probability and the Normal Curve - Applications for TodayChapter R: 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, Polynomials and Operations on Polynomials R.4 Factoring Polynomials R.5 Rational Expressions R.6 Radicals and Rational Exponents R.7 Geometry Review with Unit Conversions R.8 Expressions, Tables and Graphing Calculators
PreCalculus Concepts, Connections and ApplicationsChapter 1: Equations and Inequalities 1.1 Linear Equations, Formulas and Problem Solving 1.2 Linear Inequalities in One Variable with Applications 1.3 Solving Polynomial and Other Equations 1.4 Complex Numbers 1.5 Solving Non-Factorable Quadratic Equations Chapter 2: Functions and Graphs 2.1 Rectangular Coordinates and the Graph of a Line 2.2 Relations, Functions and Graphs 2.3 Linear Functions and Rates of Change 2.4 Quadratic and Other Toolbox Functions 2.5 Functions and Inequalities -- A Graphical View 2.6 Regression, Technology and Data Analysis Chapter 3: Operations on Functions and Analyzing Graphs 3.1 The Algebra and Composition of Functions 3.2 One-to-One and Inverse Functions 3.3 Toolbox Functions and Transformations 3.4 Graphing General Quadratic Functions 3.5 Asymptotes and Simple Rational Functions 3.6 Toolbox Applicaitons: Direct and Inverse Variation 3.7 Piecewise-Defined Functions 3.8 Analyzing the Graph of a Function Chapter 4: Polynomial and Rational Functions 4.1 Polynomial Long Division and Synthetic Division 4.2 The Remainder and Factor Theorems 4.3 Zeroes of Polynomial Functions 4.4 Graphing Polynomial Functions 4.5 Graphing Rational Functions 4.6 Additional Insights into Rational Functions 4.7 Polynomial and Rational Inequalities - Analytical View Chapter 5: Exponential and Logarithmic Functions 5.1 Exponential Functions 5.2 Logarithms and Logarithmic Functions 5.3 The Natural Logarithmic Function and Properties of Logarithms 5.4 Exponential/Logarithmic Equations and Applications 5.5 Applications from Investment, Finance and Physical Science 5.6 Exponential, Logarithmic and Logistic Regression Models Chapter 6: An Introduction to Trigonometric Functions 6.0 An Introduction to Cycles and Periodic Functions (on the Web) 6.1 Radian Measure and the Trigonometric Functionsand the Trigonometry of Real Numbers 6.3 Graphs of the Sine and Cosine Functions 6.4 Graphs of the Tangent and Cotangent Functions 6.5 Transformations and Applicaitons of Trigonometric Graphs 6.6 Angle Measure, Special Triangles and Special Angles 6.7 The Trigonmetry of Right Triangles 6.8 Trigonometry and the Coordinate Plane Chapter 7: Trigonometric Identities, Inverses and Equations 7.1 Fundamental Identities and Families of Identities 7.2 Constructing and Verifying Identities 7.3 The Sum and Difference Identities 7.4 Double Angle, Half Angle and Product-to-Sum Identities 7.5 The Inverse Trig Functions and their Application 7.6 Solving Basic Trig Equations 7.7 General Trig Equations and Applications 7.8 Trigonometric Models and Sinusoidal Regression Chapter 8: Applications of Trigonometry 8.1 Oblique Triangles and the Law of Sines 8.2 Law of Sines and the Ambiguous Case 8.3 the Law of Cosines 8.4 Vectors and Vector Diagrams 8.5 Vectors Applications and the Dot Product 8.6 Complex Numbers in Trigonometric Form; Products and Quotients 8.7 Demoivre's Theorem and the Nth Roots Theorem Chapter 9: Systems of Equations and Inequalities 9.1 Linear Systems in Two Variables with Applications 9.2 Linear Systems in Three Variables with Applications 9.3 Systems of Linear Inequalities and Linear Programming 9.4 Systems and Absolute Value Equations and Inequalities 9.5 Solving Linear Systems using Matrices and Row Operations 9.6 The Algebra of Matrices 9.7 Solving Linear Systems using Matrix Equations 9.8 Matrix Applications: Cramer's Rule, Partial Fractions and More Chapter 10: Topics From Analytical Geometry 10.0 An Introdcution to Analytical Geometry (on the Web) 10.1 The Circle and the Ellipse 10.2 The Hyperbola 10.3 Non-Linear Systems of Equations and Inequalities 10.4 Foci and the Analytic Ellipse and Hyperbola 10.5 The Analytic Parabola 10.6 Polar Coordinates, Equations and Graphs 10.7 More on the Conic Sections: Rotation of Axes and Polar Form 10.8 Parametric Equations of 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 Fundamentals of Quick-Counting 11.6 Counting Techniques: Permutations and Combinations 11.7 Introduction to Probability 11.8 The Binomial Theorem and Binomial Probabilities 11.9 Conditional Probability and Expected Value 11.10 Probability and the Normal Curve - Applications for TodayChapter R: 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, Polynomials and Operations on Polynomials R.4 Factoring Polynomials R.5 Rational Expressions R.6 Radicals and Rational Exponents R.7 Geometry Review with Unit Conversions R.8 Expressions, Tables and Graphing Calculators
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