Essentials of college algebra / / Margaret L. Lial [and three others]

• Autore: Lial Margaret L.
• Pubblicazione: Harlow, England : , : Pearson, , [2014]; ©2014
• Edizione: Eleventh edition, Global edition.
• Descrizione fisica: 1 online resource (512 pages) : illustrations (some color)
• Disciplina: 512.9
• Soggetto topico: Algebra; Mathematics
• Note generali: Includes indexes.
• Nota di contenuto: Cover -- Title -- Copyright -- Contents -- Preface -- Resources for Success -- R Review of Basic Concepts -- R.1 Sets -- Basic Definitions -- Operations on Sets -- R.2 Real Numbers and Their Properties -- Sets of Numbers and the Number Line -- Exponents -- Order of Operations -- Properties of Real Numbers -- Order on the Number Line -- Absolute Value -- R.3 Polynomials -- Rules for Exponents -- Polynomials -- Addition and Subtraction -- Multiplication -- Division -- R.4 Factoring Polynomials -- Factoring Out the Greatest Common Factor -- Factoring by Grouping -- Factoring Trinomials -- Factoring Binomials -- Factoring by Substitution -- R.5 Rational Expressions -- Rational Expressions -- Lowest Terms of a Rational Expression -- Multiplication and Division -- Addition and Subtraction -- Complex Fractions -- R.6 Rational Exponents -- Negative Exponents and the Quotient Rule -- Rational Exponents -- Complex Fractions Revisited -- R.7 Radical Expressions -- Radical Notation -- Simplified Radicals -- Operations with Radicals -- Rationalizing Denominators -- Test Prep -- Review Exercises -- Test -- 1 Equations and Inequalities -- 1.1 Linear Equations -- Basic Terminology of Equations -- Solving Linear Equations -- Identities, Conditional Equations, and Contradictions -- Solving for a Specified Variable (Literal Equations) -- 1.2 Applications and Modeling with Linear Equations -- Solving Applied Problems -- Geometry Problems -- Motion Problems -- Mixture Problems -- Modeling with Linear Equations -- 1.3 Complex Numbers -- Basic Concepts of Complex Numbers -- Operations on Complex Numbers -- 1.4 Quadratic Equations -- Solving a Quadratic Equation -- Completing the Square -- The Quadratic Formula -- Solving for a Specified Variable -- The Discriminant -- Chapter 1 Quiz (Sections 1.1-1.4) -- 1.5 Applications and Modeling with Quadratic Equations. ; Geometry Problems -- Using the Pythagorean Theorem -- Height of a Projected Object -- Modeling with Quadratic Equations -- 1.6 Other Types of Equations and Applications -- Rational Equations -- Work Rate Problems -- Equations with Radicals -- Equations with Rational Exponents -- Equations Quadratic in Form -- Summary Exercises on Solving Equations -- 1.7 Inequalities -- Linear Inequalities -- Three-Part Inequalities -- Quadratic Inequalities -- Rational Inequalities -- 1.8 Absolute Value Equations and Inequalities -- Basic Concepts -- Absolute Value Equations -- Absolute Value Inequalities -- Special Cases -- Absolute Value Models for Distance and Tolerance -- Test Prep -- Review Exercises -- Test -- 2 Graphs and Functions -- 2.1 Rectangular Coordinates and Graphs -- Ordered Pairs -- The Rectangular Coordinate System -- The Distance Formula -- The Midpoint Formula -- Graphing Equations in Two Variables -- 2.2 Circles -- Center-Radius Form -- General Form -- An Application -- 2.3 Functions -- Relations and Functions -- Domain and Range -- Determining Whether Relations Are Functions -- Function Notation -- Increasing, Decreasing, and Constant Functions -- 2.4 Linear Functions -- Graphing Linear Functions -- Standard Form Ax + By = C -- Slope -- Average Rate of Change -- Linear Models -- Chapter 2 Quiz (Sections 2.1-2.4) -- 2.5 Equations of Lines and Linear Models -- Point-Slope Form -- Slope-Intercept Form -- Vertical and Horizontal Lines -- Parallel and Perpendicular Lines -- Modeling Data -- Solving Linear Equations in One Variable by Graphing -- Summary Exercises on Graphs, Circles, Functions, and Equations -- 2.6 Graphs of Basic Functions -- Continuity -- The Identity, Squaring, and Cubing Functions -- The Square Root and Cube Root Functions -- The Absolute Value Function -- Piecewise-Defined Functions -- The Relation x = y2. ; 2.7 Graphing Techniques -- Stretching and Shrinking -- Reflecting -- Symmetry -- Even and Odd Functions -- Translations -- Chapter 2 Quiz (Sections 2.5-2.7) -- 2.8 Function Operations and Composition -- Arithmetic Operations on Functions -- The Difference Quotient -- Composition of Functions and Domain -- Test Prep -- Review Exercises -- Test -- 3 Polynomial and Rational Functions -- 3.1 Quadratic Functions and Models -- Quadratic Functions -- Graphing Techniques -- Completing the Square -- The Vertex Formula -- Quadratic Models -- 3.2 Synthetic Division -- Synthetic Division -- Evaluating Polynomial Functions Using the Remainder Theorem -- Testing Potential Zeros -- 3.3 Zeros of Polynomial Functions -- Factor Theorem -- Rational Zeros Theorem -- Number of Zeros -- Conjugate Zeros Theorem -- Finding Zeros of a Polynomial Function -- Descartes' Rule of Signs -- 3.4 Polynomial Functions: Graphs, Applications, and Models -- Graphs of f(x) = ax -- Graphs of General Polynomial Functions -- Behavior at Zeros -- Turning Points and End Behavior -- Graphing Techniques -- Intermediate Value and Boundedness Theorems -- Approximating Real Zeros -- Polynomial Models -- Summary Exercises on Polynomial Functions, Zeros, and Graphs -- 3.5 Rational Functions: Graphs, Applications, and Models -- The Reciprocal Function f (x ) -- The Function f (x ) -- Asymptotes -- Steps for Graphing Rational Functions -- Rational Function Models -- Chapter 3 Quiz (Sections 3.1-3.5) -- Summary Exercises on Solving Equations and Inequalities -- 3.6 Variation -- Direct Variation -- Inverse Variation -- Combined and Joint Variation -- Test Prep -- Review Exercises -- Test -- 4 Inverse, Exponential, and Logarithmic Functions -- 4.1 Inverse Functions -- One-to-One Functions -- Inverse Functions -- Equations of Inverses -- An Application of Inverse Functions to Cryptography. ; 4.2 Exponential Functions -- Exponents and Properties -- Exponential Functions -- Exponential Equations -- Compound Interest -- The Number e and Continuous Compounding -- Exponential Models -- 4.3 Logarithmic Functions -- Logarithms -- Logarithmic Equations -- Logarithmic Functions -- Properties of Logarithms -- Summary Exercises on Inverse, Exponential, and Logarithmic Functions -- 4.4 Evaluating Logarithms and the Change-of-Base Theorem -- Common Logarithms -- Applications and Models with Common Logarithms -- Natural Logarithms -- Applications and Models with Natural Logarithms -- Logarithms with Other Bases -- Chapter 4 Quiz (Sections 4.1-4.4) -- 4.5 Exponential and Logarithmic Equations -- Exponential Equations -- Logarithmic Equations -- Applications and Models -- 4.6 Applications and Models of Exponential Growth and Decay -- The Exponential Growth or Decay Function -- Growth Function Models -- Decay Function Models -- Summary Exercises on Functions: Domains and Defining Equations -- Test Prep -- Review Exercises -- Test -- 5 Systems and Matrices -- 5.1 Systems of Linear Equations -- Linear Systems -- Substitution Method -- Elimination Method -- Special Systems -- Applying Systems of Equations -- Solving Linear Systems with Three Unknowns (Variables) -- Using Systems of Equations to Model Data -- 5.2 Matrix Solution of Linear Systems -- The Gauss-Jordan Method -- Special Systems -- 5.3 Determinant Solution of Linear Systems -- Determinants -- Cofactors -- Evaluating n x n Determinants -- Determinant Theorems -- Cramer's Rule -- 5.4 Partial Fractions -- Decomposition of Rational Expressions -- Distinct Linear Factors -- Repeated Linear Factors -- Distinct Linear and Quadratic Factors -- Repeated Quadratic Factors -- Chapter 5 Quiz (Sections 5.1-5.4) -- 5.5 Nonlinear Systems of Equations -- Solving Nonlinear Systems with Real Solutions. ; Solving Nonlinear Systems with Nonreal Complex Solutions -- Applying Nonlinear Systems -- Summary Exercises on Systems of Equations -- 5.6 Systems of Inequalities and Linear Programming -- Solving Linear Inequalities -- Solving Systems of Inequalities -- Linear Programming -- 5.7 Properties of Matrices -- Basic Definitions -- Adding Matrices -- Special Matrices -- Subtracting Matrices -- Multiplying Matrices -- Applying Matrix Algebra -- 5.8 Matrix Inverses -- Identity Matrices -- Multiplicative Inverses -- Solving Systems Using Inverse Matrices -- Test Prep -- Review Exercises -- Test -- Glossary -- Photo Credits.
• Sommario/riassunto: Steadfast Support for Your Evolving Course. Essentials of College Algebra, Eleventh Edition, by Lial, Hornsby, Schneider, and Daniels, develops both the conceptual understanding and the analytical skills necessary for success in mathematics. With the Eleventh Edition, the authors have adapted and updated the program for the evolving student, New co-author Callie Daniels brings her experience with traditional, hybrid, and online courses, to create a suite of resources to support today's learners. This program provides a better teaching and learning experience-for you and your students. Here's how: Support for learning concepts: a systematic approach is used to present each topic, and is designed to actively engage students in the learning process. The variety of exercise types promotes understanding of the concepts and reduces the opportunity for rote memorization. Support for review and test preparation: ample opportunities for review are interspersed throughout and at the end of chapters. MyMathLab® is not included. Students, if MyMathLab is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN. MyMathLab should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information. MyMathLab is an online homework, tutorial, and assessment product designed to personalize learning and improve results. With a wide range of interactive, engaging, and assignable activities, students are encouraged to actively learn and retain tough course concepts. &nbsp.
• Titolo autorizzato: Essentials of college algebra
• ISBN: 1-292-07581-3
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910154780603321
• Lo trovi qui: Univ. Federico II
• Serie: Always learning.