Functioning in the Real World
A Precalculus Experience
2nd Edition
Published on 16. December 2003
Book
Hardback
800 pages
978-0-201-38389-8 (ISBN)
Description
This text, which grew out of a NSF grant, takes a fresh approach with a focus on the underlying concepts of precalculus, rather than sheer algebraic manipulation. It effectively prepares students for a new generation of calculus courses and allows instructors to become actively involved in the teaching process. The authors make extensive use of real world applications, showing students how mathematics relates to their field of study, as well as including a thorough integration of technology. Additionally, the authors have incorporated a number of learning features designed to ready students for a more positive calculus experience.
More details
Other editions
Previous edition
Sheldon P. Gordon | Florence S. Gordon | B. A. Fusaro
Functioning in the Real World
A Precalculus Experience
Book
01/2001
Pearson
€105.85
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Content
(Each Chapter ends with a Summary and Review.)
1. Functions in the Real World.
Functions are all around us.
Describing the behavior of functions.
Representing functions symbolically.
Connecting geometric and symbolic representations.
Mathematical models.
2. Families of Functions.
Introduction.
Linear functions.
Linear functions and Data.
Exponential growth functions.
Exponential decay functions.
Logarithmic functions.
Power functions.
Comparing Rates of Growth and Decay.
Inverse functions.
3. Fitting Functions to Data.
Introduction to Data Analysis.
Linear regression analysis.
Fitting nonlinear functions to data.
How to fit exponential and logarithmic functions to data.
How to fit power functions to data.
How good is the fit?
Linear models with several variables.
4. Extended Families of Functions.
Introduction to polynomial functions.
The behavior of polynomial functions.
Modeling with polynomial functions.
The roots of polynomial equations: Real or complex?
Finding polynomial patterns.
Building new functions from old: Operations on Functions.
Building new functions from old: Shifting, stretching, and shrinking.
Using shifting and stretching to analyze data.
The logistic and surge functions.
5. Modeling with Difference Equations.
Eliminating drugs from the body.
Modeling with difference equations.
The logistic or inhibited growth model.
Newton's Laws of Cooling and Heating.
Geometric sequences and their sums.
6. Introduction to Trigonometry.
The tangent of an angle.
The sine and cosine of an angle.
The sine, cosine and tangent in general.
Relationships among trigonometric functions.
The law of sines and the law of cosnes.
7. Modeling Periodic Behavior.
Introduction to the sine and cosine functions.
Modeling periodic behavior with sine and cosine.
Solving equations with sine and cosine: The inverse functions.
The tangent function.
8. More About the Trigonometric Functions.
Relationships among trigonometric functions.
Approximating sine and cosine with polynomials.
Properties of complex numbers.
The road to chaos.
9. Geometric Models.
Introduction to coordinate systems.
Analytic geometry.
Conic sections: The Ellipse.
Conic sections: The Hyperbola and the Parabola.
Parametric curves.
The polar coordinate system.
Families of curves in polar coordinates.
10. Matrix Algebra and Its Applications.
Geometric vectors.
Linear models.
Scalar products.
Matrix multiplication.
Gaussian elimination.
11. Probability Models (online only).
Introduction to probability models.
Binomial probability and the binomial formula.
Using probability to investigate polynomials.
Geometric probability.
Estimating areas of plane regions.
The normal distribution function.
Waiting time at a red light.
Random patterns in chaos.
12. More About Difference Equations (online only).
Solutions of difference equations.
Constructing solutions of first order difference equations.
Modeling with first order, non-homogeneous difference equations.
Financing a car or a home.
Solving the Fibonacci and other second order difference equations.
The predator-prey model.
Competing species.
Iteration and chaos.
Appendices.
Appendix A: Some Mathematical Moments to Remember.
Absolute Value.
Factorial Notation n!
Summation or Sigma Notation.
Similar Triangles.
Distance Between Points in the Plane.
The Equation of a Circle.
The Equation of an Ellipse.
Completing the Square.
Appendix B: Solving Systems of Linear Equations Algebraically.
Appendix C: Solving Systems of Linear Equations Using Matrices.
Appendix D: Symmetry.
Appendix E: Arithmetic of Complex Numbers.
Appendix F: Introduction to Data Analysis.
Appendix G: 2001 World Population Data.
1. Functions in the Real World.
Functions are all around us.
Describing the behavior of functions.
Representing functions symbolically.
Connecting geometric and symbolic representations.
Mathematical models.
2. Families of Functions.
Introduction.
Linear functions.
Linear functions and Data.
Exponential growth functions.
Exponential decay functions.
Logarithmic functions.
Power functions.
Comparing Rates of Growth and Decay.
Inverse functions.
3. Fitting Functions to Data.
Introduction to Data Analysis.
Linear regression analysis.
Fitting nonlinear functions to data.
How to fit exponential and logarithmic functions to data.
How to fit power functions to data.
How good is the fit?
Linear models with several variables.
4. Extended Families of Functions.
Introduction to polynomial functions.
The behavior of polynomial functions.
Modeling with polynomial functions.
The roots of polynomial equations: Real or complex?
Finding polynomial patterns.
Building new functions from old: Operations on Functions.
Building new functions from old: Shifting, stretching, and shrinking.
Using shifting and stretching to analyze data.
The logistic and surge functions.
5. Modeling with Difference Equations.
Eliminating drugs from the body.
Modeling with difference equations.
The logistic or inhibited growth model.
Newton's Laws of Cooling and Heating.
Geometric sequences and their sums.
6. Introduction to Trigonometry.
The tangent of an angle.
The sine and cosine of an angle.
The sine, cosine and tangent in general.
Relationships among trigonometric functions.
The law of sines and the law of cosnes.
7. Modeling Periodic Behavior.
Introduction to the sine and cosine functions.
Modeling periodic behavior with sine and cosine.
Solving equations with sine and cosine: The inverse functions.
The tangent function.
8. More About the Trigonometric Functions.
Relationships among trigonometric functions.
Approximating sine and cosine with polynomials.
Properties of complex numbers.
The road to chaos.
9. Geometric Models.
Introduction to coordinate systems.
Analytic geometry.
Conic sections: The Ellipse.
Conic sections: The Hyperbola and the Parabola.
Parametric curves.
The polar coordinate system.
Families of curves in polar coordinates.
10. Matrix Algebra and Its Applications.
Geometric vectors.
Linear models.
Scalar products.
Matrix multiplication.
Gaussian elimination.
11. Probability Models (online only).
Introduction to probability models.
Binomial probability and the binomial formula.
Using probability to investigate polynomials.
Geometric probability.
Estimating areas of plane regions.
The normal distribution function.
Waiting time at a red light.
Random patterns in chaos.
12. More About Difference Equations (online only).
Solutions of difference equations.
Constructing solutions of first order difference equations.
Modeling with first order, non-homogeneous difference equations.
Financing a car or a home.
Solving the Fibonacci and other second order difference equations.
The predator-prey model.
Competing species.
Iteration and chaos.
Appendices.
Appendix A: Some Mathematical Moments to Remember.
Absolute Value.
Factorial Notation n!
Summation or Sigma Notation.
Similar Triangles.
Distance Between Points in the Plane.
The Equation of a Circle.
The Equation of an Ellipse.
Completing the Square.
Appendix B: Solving Systems of Linear Equations Algebraically.
Appendix C: Solving Systems of Linear Equations Using Matrices.
Appendix D: Symmetry.
Appendix E: Arithmetic of Complex Numbers.
Appendix F: Introduction to Data Analysis.
Appendix G: 2001 World Population Data.