Elementary mathematical models : order aplenty and a glimpse of chaos / Dan Kalman.

Format:

Book

Author/Creator:

Kalman, Dan.

Series:

Classroom resource materials (Unnumbered)

Classroom resource materials

Language:

English

Subjects (All):

Mathematical models.

Mathematical analysis.

Physical Description:

1 online resource (362 p.)

Edition:

1st ed.

Place of Publication:

[Washington, D.C.] : Mathematical Association of America, c1997.

Language Note:

English

Summary:

The language of mathematics has proven over centuries of application to be an indispensable tool for the expression and analysis of real problems. With numerical, graphical, and theoretical methods, this book examines the relevance of mathematical models to phenomena ranging from population growth and economics to medicine and the physical sciences. In a book written for the intelligent and literate non-mathematician, Kalman aims at an understanding of the power and utility of quantitative methods rather than at technical mastery of mathematical operations. He shows first that mathematical models can serve a critical function in understanding the world, and he concludes with a discussion of the problems encountered by traditional algebraic assumptions in chaos theory. Though models can often approximate future events based on existing data and quantitative relationships, Kalman shows that the appearance of regularity and order can often be misleading. By beginning with quantitative models and ending with an introduction to chaos, Kalman offers a broad treatment of both the power and limitations of quantitatively-based predictions.

Contents:

""cover ""; ""copyright page""; ""title page""; ""Preface""; ""Teaching EMM""; ""Classroom Experience""; ""Acknowledgments""; ""Contents""; ""1 Overview""; ""An Example""; ""Three Methods: Numerical, Graphical, Theoretical""; ""Mathematical Models""; ""Chaos""; ""Summary""; ""Exercises""; ""Solutions to Selected Exercises""; ""2 Sequences and Difference Equations""; ""Sequences""; ""Difference Equations""; ""The Numerical Approach""; ""The Graphical Approach""; ""The Theoretical Approach""; ""Back to Reality""; ""Sample Difference Equations""; ""Summary""; ""Exercises""

""Solutions to Selected Exercises""""3 Arithmetic Growth""; ""The Arithmetic Growth Difference Equation""; ""Examples""; ""Numerical, Graphical, and Theoretical Properties""; ""Proportional Reasoning and Continuous Models""; ""Beyond Arithmetic Growth: Oil Reserves""; ""Summary""; ""Exercises""; ""Solutions to Selected Exercises""; ""4 Linear Graphs, Functions, and Equations""; ""Linear Functions and Equations""; ""Continuous Models""; ""Algebra and Solving Linear Equations""; ""Graphs of Linear Equations""; ""Fitting a Line to Data""; ""Formulating Linear Models""; ""Summary""

""Exercises""""Solutions to Selected Exercises""; ""5 Quadratic Growth Models""; ""A New School Population Example""; ""Quadratic Growth Models""; ""Quadratic Growth Difference Equations""; ""Applications of Quadratic Growth""; ""Properties of Quadratic Growth Models""; ""Whole Number Sums and sum Notation""; ""Summary""; ""Exercises""; ""Solutions to Selected Exercises""; ""6 Quadratic Graphs, Functions, andEquations""; ""Quadratic Functions and Equations""; ""Algebraic Considerations""; ""Graphs""; ""Solving Equations""; ""An Example""; ""Summary""; ""Exercises""

""Solutions to Selected Exercises""""7 Polynomial and Rational Functions""; ""Algebraic Aspects of Polynomials""; ""Graphing Polynomials""; ""Solving Polynomial Equations""; ""Applications of Polynomials""; ""Graphs of Rational Functions""; ""Summary""; ""Exercises""; ""Solutions to Selected Exercises""; ""8 Fitting a Line to Data""; ""Defining ``Best""""; ""An Error Function""; ""Finding the Best Slope""; ""Three-Dimensional Parabolas""; ""Summary""; ""Exercises""; ""Solutions to Selected Exercises""; ""9 Geometric Growth""; ""The Geometric Growth Assumption""

""The Geometric Growth Difference Equation""""Functional Equation""; ""Exponential Functions""; ""Additional Applications""; ""Summary""; ""Exercises""; ""Solutions to Selected Exercises""; ""10 Exponential Functions""; ""Graphs""; ""Algebraic Properties""; ""Solving Equations""; ""The number e""; ""Summary""; ""Exercises""; ""Solutions to Selected Exercises""; ""11 More On Logarithms""; ""Rules for Logarithms""; ""Logarithmic Scales""; ""The pH Scale""; ""Transforming Data""; ""Summary""; ""Exercises""; ""Solutions to Selected Exercises""; ""12 Geometric Sums and Mixed Models""

""Geometric Sums""

Notes:

Includes index.

Description based on print version record.

ISBN:

1-61444-601-6

OCLC:

929120312