Functions, Data and Models : An Applied Approach to College Algebra.
Gordon, Sheldon P.
Functions, Data and Models : An Applied Approach to College Algebra. - 1st ed. - 1 online resource (509 pages)
cover -- copyright page -- title page -- Contents -- Preface -- To the Student -- To the Instructor -- Philosophy of the Book -- The Intended Audiences -- Suggested Courses Based on the Book -- Acknowledgments -- 1 Data Everywhere -- 1.1 Data in the Real World -- Measuring the Center of a Set of Data -- Measuring the Spread in a Set of Data -- How the Standard Deviation Formula Arises -- Quartiles -- Problems -- 1.2 Displaying Data -- Normally Distributed Data -- Box-and-Whisker Plots -- Problems -- 1.3 Two-Variable Data -- Simple Patterns in Data -- Problems -- Virtual Laboratory 1 -- 2 Functions Everywhere -- 2.1 Functions in the Real World -- Representing Functions with Formulas and Equations -- Representing Functions with Graphs -- Representing Functions with Tables -- Representing Functions with Words -- Why Study Functions? -- Connecting Between the Different Representations -- Problems -- 2.2 Describing the Behavior of Functions -- Increasing and Decreasing Functions -- Concavity: How A Function Bends -- Periodic Behavior -- Problems -- 2.3 Representing Functions Symbolically -- Domain and Range of a Function -- Proportionality -- Problems -- 2.4 Mathematical Models -- Parameters and Mathematical Models -- Problems -- 3 Linear Functions -- 3.1 Fundamental Concepts of Linear Functions -- Linear Functions That Pass Through the Origin -- The Graph of a Linear Function That Passes Through the Origin -- Lines That Don't Pass Through the Origin -- The Point-Slope Formula -- Problems -- Exercising Your Algebra Skills -- 3.2 Modeling With Linear Functions -- Problems -- 3.3 Linear Functions and Data -- Determining Whether a Set of Data Is Linear -- Capturing a Linear Pattern in Data -- z-Values -- Problems -- Exercising Your Algebra Skills -- 3.4 Linear Regression: Finding the Best Line -- The Least Squares Criterion. Additional Examples of Linear Regression -- The Correlation Coefficient -- Variation among Samples -- Problems -- Virtual Laboratory 3.1: Biology -- Bradford Analysis for Protein Concentrations -- Virtual Laboratory 3.2: Physics -- Hooke's Law on the Elongation of a Spring -- 4 More about Linear Functions -- 4.1 Systems of Linear Equations -- Solving Systems of Linear Equations Geometrically -- Solving Systems of Linear Equations Algebraically -- Solving Systems of Linear Equations Using Matrices -- Problems -- 4.2 Applications of Linear Equations -- Solving the Regression Equations -- Balancing Chemical Equations -- Not Every System of Equations has a Solution -- Some Systems of Equations have Multiple Solutions -- Problems -- 4.3 Matrix Products and their Applications -- Two Competing Populations -- Comparing Successive Vectors -- How the Product of a Matrix and a Vector is Defined -- How the Product of Two Matrices is Defined -- What is the Inverse Matrix? -- Problems -- 4.4 Linear Models with Several Variables -- The Multiple Correlation Coefficient -- Performing Multivariate Regression in Excel -- Problems -- 5 Families of Nonlinear Functions -- 5.1 Exponential Growth Functions -- Comparing Linear and Exponential Growth -- Applications of Exponential Growth -- Doubling Time -- Predicting with Exponential Growth Functions -- Finding an Exponential Function Through Two Points -- Rules for Exponents -- Problems -- Exercising Your Algebra Skills -- 5.2 Exponential Decay Functions -- Half-life -- Radioactive Decay -- DeterminingWhether a Set of Data Is Exponential -- Comparing Linear and Exponential Functions -- Problems -- Exercising Your Algebra Skills -- 5.3 Fitting Exponential Functions to Data -- The Base e -- Problems -- 5.4 Logarithmic Functions -- How the Exponential Regression Function is Calculated. Exponential Regression and the Correlation Coefficient -- Comparing Exponential and Logarithmic Functions -- Problems -- Exercising Your Algebra Skills -- 5.5 Modeling with Logarithmic Functions -- pH Values -- Intensity of Earthquakes and the Richter Scale -- Measuring the Intensity of Sounds -- Changing Bases -- Fitting Logarithmic Functions to Data -- How the Logarithmic Regression Function is Calculated -- Problems -- 5.6 Power Functions -- Behavior of Power Functions for x > -- 0 -- Behavior of Power Functions for x > -- 1 -- Applications of Power Functions -- The Power Function Through Two Points -- Problems -- Exercising Your Algebra Skills -- 5.7 Fitting Power Functions to Data -- How the Power Regression Equation is Calculated -- Some Applications -- Potential Problems when Fitting Power Functions to Data -- Problems -- 5.8 How Good Is the Fit? -- Interpreting the Graphs -- Interpreting the Correlation Coefficient -- Interpreting the Sum of the Squares -- may have measurements on the growth of bacteria in a test tube that might suggest exponential growth,but you know that such growth cannot continue indefinitely, so an exponential function will model thepopulation only for a short while.Other Measures -- Problems -- Virtual Laboratory 5.1: Kepler's Third Law of Planetary Motion -- Virtual Laboratory 5.2: Running Speed and Length of the Body -- 6 Polynomial Functions -- 6.1 Introduction to Polynomial Functions -- Polynomials of Degree 1: Linear Functions -- Polynomials of Degree 2: Quadratic Functions -- Polynomials of Degree 3: Cubic Functions -- Polynomials of Degree 4: Quartic Functions -- The Zeros of a Polynomial and the Roots of An Equation -- Problems -- Exercising Your Algebra Skills -- 6.2 The Behavior of Polynomial Functions -- Quadratic Polynomials -- Cubic Polynomials -- Polynomials of Degree n. The End Behavior of a Polynomial -- Problems -- Exercising Your Algebra Skills -- 6.3 Modeling with Polynomial Functions -- The Path of a Projectile -- Fitting Polynomials to Data -- Deriving the Regression Equations -- Problems -- Virtual Laboratory 6.1: Biosciences and Social Sciences -- Virtual Laboratory 6.2: Physics -- 7 Extended Families of Functions -- 7.1 Building New Functions from Old: Shifting, Stretching, and Shrinking -- Shifting Functions -- Stretching and Shrinking Functions -- Problems -- Exercising Your Algebra Skills -- 7.2 Using Shifting and Stretching With Data -- Analyzing a Cooling Experiment -- Terminal Velocity in Skydiving -- Repeated Dosages of a Medication -- Using Shifts -- Using Stretches -- Modeling Normal Distributions -- Problems -- 7.3 The Central Limit Theorem and Confidence Intervals -- The Distribution of Sample Means -- Samples from the Normal Population -- Samples from the U-Shaped Population -- Estimating the Mean of a Population -- Exploring Confidence Intervals -- Problems -- 7.4 Functions of Several Variables: Tables, Contours, Formulas -- Functions of Several Variables via Tables -- Functions of Several Variables via Graphs -- Functions of Several Variables via Formulas -- Problems -- Virtual Laboratory 7: Chemistry -- 8 Modeling Periodic Phenomena -- 8.1 The Sinusoidal Functions Sine and Cosine -- The Sine Function -- The Cosine Function -- Problems -- 8.2 Modeling Periodic Behavior with the Sine and Cosine -- The Vertical Shift or Midline -- The Amplitude -- The Frequency and the Period -- Fitting Sinusoidal Functions to Data -- Problems -- 8.3 Solving Equations with Sine and Cosine -- Problems -- 8.4 Approximating the Sine and Cosine with Polynomials -- Approximating the Sine Function -- Using Linear Regression -- Improving on the Linear Approximation to the Sine -- Patterns in the Approximation Formulas. Improving the Approximation Using the Behavior of sin x -- Approximating the Cosine Function -- Problems -- Virtual Laboratory 8: Meteorology -- Appendices -- Appendix A: Some Mathematical Momentsto Remember -- Appendix B: Statistical Calculations on TI Calculators -- Using the STAT Features of the TI-84 Family -- Using the STAT Features of the TI-89 -- Appendix C: Statistical Calculations In Excel -- Using Excel 2003 and Earlier Versions -- Using Excel 2007 -- Appendix D: The Algebra of Linear Functions -- The Distributive Law -- Converting between the slope-intercept form and the point-slope form of a line -- Predictions with linear functions based on values of the independent variable -- Predicting with linear functions based on values of the dependent variable-solving linear equations -- The normal form for the equation of a line -- Appendix E: Solving Equations Graphically: Zoom-and-Trace -- Appendix F: Linear Regression on TI Calculators -- Using the STAT Features of the TI-83/84 Family -- Using the STAT Features of the TI-89 -- Appendix G: Linear Regression Using Excel -- To Draw a Scatterplot of Data in Excel 2003 -- To Add the Regression Line or Curve to a Scatterplot -- To Draw a Scatterplot of Data in Excel 2007 -- To Add the Regression Line or Curve to a Scatterplot -- Appendix H: Where the Correlation Coefficient Formula Comes From -- Appendix I: Solving Systems of Linear Equations Algebraically -- Appendix J: Curve Fitting in Excel -- Using Excel 2003 and Earlier Versions -- Using Excel 2007 -- Appendix K: Symmetry -- Appendix L: The Arithmetic of Complex Numbers -- M World Population Data for 2009 -- Selected Short Answers -- Chapter 1 -- Section 1.1 -- Section 1.2 -- Section 1.3 -- Chapter 2 -- Section 2.1 -- Section 2.2 -- Section 2.3 -- Section 2.4 -- Chapter 3 -- Section 3.1 -- Section 3.2 -- Section 3.3 -- Section 3.4. Chapter 4.
This is a college algebra-level textbook written to provide the kind of mathematical knowledge and experiences that students will need for courses in other fields, such as biology, chemistry, business, finance, economics, and other areas that are heavily dependent on data either from laboratory experiments or from other studies. The focus is on the fundamental mathematical concepts and the realistic problem-solving via mathematical modeling rather than the development of algebraic skills that might be needed in calculus.Functions, Data, and Models presents college algebra in a way that differs from almost all college algebra books available today. Rather than going over material covered in high school courses the Gordons teach something new. Students are given an introduction to data analysis and mathematical modeling presented at a level that students with limited algebraic skills can understand. The book contains a rich set of exercises, many of which use real data. Also included are thought experiments or what if questions that are meant to stretch the student's mathematical thinking.
9781614446095
Algebra -- Textbooks.
Electronic books.
QA154.3.G67 2010eb
512.9
Functions, Data and Models : An Applied Approach to College Algebra. - 1st ed. - 1 online resource (509 pages)
cover -- copyright page -- title page -- Contents -- Preface -- To the Student -- To the Instructor -- Philosophy of the Book -- The Intended Audiences -- Suggested Courses Based on the Book -- Acknowledgments -- 1 Data Everywhere -- 1.1 Data in the Real World -- Measuring the Center of a Set of Data -- Measuring the Spread in a Set of Data -- How the Standard Deviation Formula Arises -- Quartiles -- Problems -- 1.2 Displaying Data -- Normally Distributed Data -- Box-and-Whisker Plots -- Problems -- 1.3 Two-Variable Data -- Simple Patterns in Data -- Problems -- Virtual Laboratory 1 -- 2 Functions Everywhere -- 2.1 Functions in the Real World -- Representing Functions with Formulas and Equations -- Representing Functions with Graphs -- Representing Functions with Tables -- Representing Functions with Words -- Why Study Functions? -- Connecting Between the Different Representations -- Problems -- 2.2 Describing the Behavior of Functions -- Increasing and Decreasing Functions -- Concavity: How A Function Bends -- Periodic Behavior -- Problems -- 2.3 Representing Functions Symbolically -- Domain and Range of a Function -- Proportionality -- Problems -- 2.4 Mathematical Models -- Parameters and Mathematical Models -- Problems -- 3 Linear Functions -- 3.1 Fundamental Concepts of Linear Functions -- Linear Functions That Pass Through the Origin -- The Graph of a Linear Function That Passes Through the Origin -- Lines That Don't Pass Through the Origin -- The Point-Slope Formula -- Problems -- Exercising Your Algebra Skills -- 3.2 Modeling With Linear Functions -- Problems -- 3.3 Linear Functions and Data -- Determining Whether a Set of Data Is Linear -- Capturing a Linear Pattern in Data -- z-Values -- Problems -- Exercising Your Algebra Skills -- 3.4 Linear Regression: Finding the Best Line -- The Least Squares Criterion. Additional Examples of Linear Regression -- The Correlation Coefficient -- Variation among Samples -- Problems -- Virtual Laboratory 3.1: Biology -- Bradford Analysis for Protein Concentrations -- Virtual Laboratory 3.2: Physics -- Hooke's Law on the Elongation of a Spring -- 4 More about Linear Functions -- 4.1 Systems of Linear Equations -- Solving Systems of Linear Equations Geometrically -- Solving Systems of Linear Equations Algebraically -- Solving Systems of Linear Equations Using Matrices -- Problems -- 4.2 Applications of Linear Equations -- Solving the Regression Equations -- Balancing Chemical Equations -- Not Every System of Equations has a Solution -- Some Systems of Equations have Multiple Solutions -- Problems -- 4.3 Matrix Products and their Applications -- Two Competing Populations -- Comparing Successive Vectors -- How the Product of a Matrix and a Vector is Defined -- How the Product of Two Matrices is Defined -- What is the Inverse Matrix? -- Problems -- 4.4 Linear Models with Several Variables -- The Multiple Correlation Coefficient -- Performing Multivariate Regression in Excel -- Problems -- 5 Families of Nonlinear Functions -- 5.1 Exponential Growth Functions -- Comparing Linear and Exponential Growth -- Applications of Exponential Growth -- Doubling Time -- Predicting with Exponential Growth Functions -- Finding an Exponential Function Through Two Points -- Rules for Exponents -- Problems -- Exercising Your Algebra Skills -- 5.2 Exponential Decay Functions -- Half-life -- Radioactive Decay -- DeterminingWhether a Set of Data Is Exponential -- Comparing Linear and Exponential Functions -- Problems -- Exercising Your Algebra Skills -- 5.3 Fitting Exponential Functions to Data -- The Base e -- Problems -- 5.4 Logarithmic Functions -- How the Exponential Regression Function is Calculated. Exponential Regression and the Correlation Coefficient -- Comparing Exponential and Logarithmic Functions -- Problems -- Exercising Your Algebra Skills -- 5.5 Modeling with Logarithmic Functions -- pH Values -- Intensity of Earthquakes and the Richter Scale -- Measuring the Intensity of Sounds -- Changing Bases -- Fitting Logarithmic Functions to Data -- How the Logarithmic Regression Function is Calculated -- Problems -- 5.6 Power Functions -- Behavior of Power Functions for x > -- 0 -- Behavior of Power Functions for x > -- 1 -- Applications of Power Functions -- The Power Function Through Two Points -- Problems -- Exercising Your Algebra Skills -- 5.7 Fitting Power Functions to Data -- How the Power Regression Equation is Calculated -- Some Applications -- Potential Problems when Fitting Power Functions to Data -- Problems -- 5.8 How Good Is the Fit? -- Interpreting the Graphs -- Interpreting the Correlation Coefficient -- Interpreting the Sum of the Squares -- may have measurements on the growth of bacteria in a test tube that might suggest exponential growth,but you know that such growth cannot continue indefinitely, so an exponential function will model thepopulation only for a short while.Other Measures -- Problems -- Virtual Laboratory 5.1: Kepler's Third Law of Planetary Motion -- Virtual Laboratory 5.2: Running Speed and Length of the Body -- 6 Polynomial Functions -- 6.1 Introduction to Polynomial Functions -- Polynomials of Degree 1: Linear Functions -- Polynomials of Degree 2: Quadratic Functions -- Polynomials of Degree 3: Cubic Functions -- Polynomials of Degree 4: Quartic Functions -- The Zeros of a Polynomial and the Roots of An Equation -- Problems -- Exercising Your Algebra Skills -- 6.2 The Behavior of Polynomial Functions -- Quadratic Polynomials -- Cubic Polynomials -- Polynomials of Degree n. The End Behavior of a Polynomial -- Problems -- Exercising Your Algebra Skills -- 6.3 Modeling with Polynomial Functions -- The Path of a Projectile -- Fitting Polynomials to Data -- Deriving the Regression Equations -- Problems -- Virtual Laboratory 6.1: Biosciences and Social Sciences -- Virtual Laboratory 6.2: Physics -- 7 Extended Families of Functions -- 7.1 Building New Functions from Old: Shifting, Stretching, and Shrinking -- Shifting Functions -- Stretching and Shrinking Functions -- Problems -- Exercising Your Algebra Skills -- 7.2 Using Shifting and Stretching With Data -- Analyzing a Cooling Experiment -- Terminal Velocity in Skydiving -- Repeated Dosages of a Medication -- Using Shifts -- Using Stretches -- Modeling Normal Distributions -- Problems -- 7.3 The Central Limit Theorem and Confidence Intervals -- The Distribution of Sample Means -- Samples from the Normal Population -- Samples from the U-Shaped Population -- Estimating the Mean of a Population -- Exploring Confidence Intervals -- Problems -- 7.4 Functions of Several Variables: Tables, Contours, Formulas -- Functions of Several Variables via Tables -- Functions of Several Variables via Graphs -- Functions of Several Variables via Formulas -- Problems -- Virtual Laboratory 7: Chemistry -- 8 Modeling Periodic Phenomena -- 8.1 The Sinusoidal Functions Sine and Cosine -- The Sine Function -- The Cosine Function -- Problems -- 8.2 Modeling Periodic Behavior with the Sine and Cosine -- The Vertical Shift or Midline -- The Amplitude -- The Frequency and the Period -- Fitting Sinusoidal Functions to Data -- Problems -- 8.3 Solving Equations with Sine and Cosine -- Problems -- 8.4 Approximating the Sine and Cosine with Polynomials -- Approximating the Sine Function -- Using Linear Regression -- Improving on the Linear Approximation to the Sine -- Patterns in the Approximation Formulas. Improving the Approximation Using the Behavior of sin x -- Approximating the Cosine Function -- Problems -- Virtual Laboratory 8: Meteorology -- Appendices -- Appendix A: Some Mathematical Momentsto Remember -- Appendix B: Statistical Calculations on TI Calculators -- Using the STAT Features of the TI-84 Family -- Using the STAT Features of the TI-89 -- Appendix C: Statistical Calculations In Excel -- Using Excel 2003 and Earlier Versions -- Using Excel 2007 -- Appendix D: The Algebra of Linear Functions -- The Distributive Law -- Converting between the slope-intercept form and the point-slope form of a line -- Predictions with linear functions based on values of the independent variable -- Predicting with linear functions based on values of the dependent variable-solving linear equations -- The normal form for the equation of a line -- Appendix E: Solving Equations Graphically: Zoom-and-Trace -- Appendix F: Linear Regression on TI Calculators -- Using the STAT Features of the TI-83/84 Family -- Using the STAT Features of the TI-89 -- Appendix G: Linear Regression Using Excel -- To Draw a Scatterplot of Data in Excel 2003 -- To Add the Regression Line or Curve to a Scatterplot -- To Draw a Scatterplot of Data in Excel 2007 -- To Add the Regression Line or Curve to a Scatterplot -- Appendix H: Where the Correlation Coefficient Formula Comes From -- Appendix I: Solving Systems of Linear Equations Algebraically -- Appendix J: Curve Fitting in Excel -- Using Excel 2003 and Earlier Versions -- Using Excel 2007 -- Appendix K: Symmetry -- Appendix L: The Arithmetic of Complex Numbers -- M World Population Data for 2009 -- Selected Short Answers -- Chapter 1 -- Section 1.1 -- Section 1.2 -- Section 1.3 -- Chapter 2 -- Section 2.1 -- Section 2.2 -- Section 2.3 -- Section 2.4 -- Chapter 3 -- Section 3.1 -- Section 3.2 -- Section 3.3 -- Section 3.4. Chapter 4.
This is a college algebra-level textbook written to provide the kind of mathematical knowledge and experiences that students will need for courses in other fields, such as biology, chemistry, business, finance, economics, and other areas that are heavily dependent on data either from laboratory experiments or from other studies. The focus is on the fundamental mathematical concepts and the realistic problem-solving via mathematical modeling rather than the development of algebraic skills that might be needed in calculus.Functions, Data, and Models presents college algebra in a way that differs from almost all college algebra books available today. Rather than going over material covered in high school courses the Gordons teach something new. Students are given an introduction to data analysis and mathematical modeling presented at a level that students with limited algebraic skills can understand. The book contains a rich set of exercises, many of which use real data. Also included are thought experiments or what if questions that are meant to stretch the student's mathematical thinking.
9781614446095
Algebra -- Textbooks.
Electronic books.
QA154.3.G67 2010eb
512.9