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Elementary Mathematical Models offers instructors an alternative to standard college algebra, quantitative literacy, and liberal arts mathematics courses.
Presuming only a background of exposure to high school algebra, the text introduces students to the methodology of mathematical modeling, which plays a role in nearly all real applications of mathematics. A course based on this text would have as its primary goal preparing students to be competent consumers of mathematical modeling in their future studies. Such a course would also provide students with an understanding of the modeling process and a facility with much of the standard, non-trigonometric, content of college algebra and precalculus.
This book builds, successively, a series of growth models defi ned in terms of simple recursive patterns of change corresponding to arithmetic, quadratic, geometric, and logistic growth. Students discover and come to understand linear, polynomial, exponential, and logarithmic functions in the context of analyzing these models of intrinsically — and scientifically — interesting phenomena including polar ice extent, antibiotic resistance, and viral internet videos. Students gain a deep appreciation for the power and limitations of mathematical modeling in the physical, life, and social sciences as questions of modeling methodology are carefully and constantly addressed. Realistic examples are used consistently throughout the text, and every topic is illustrated with models that are constructed from and compared to real data. The text is extremely attractive and the exposition is extraordinarily clear. The lead author of this text is the recipient of nine MAA awards for expository writing including the Ford, Evans, Pólya, and Allendoerfer awards and the Beckenbach Book prize. Great care has been taken by accomplished expositors to make the book readable by students. Those students will also benefi t from more than 1,000 carefully crafted exercises.
Preface to Second Edition
Note for Students
Sequences and Number Patterns
Number Patterns
Exercises
Position Numbers, Graphs, and Subscript Notation
Exercises
Difference and Functional Equations
Exercises
Arithmetic Growth Models
Properties of Arithmetic Growth
Exercises
Applications of Arithmetic Growth
Exercises
Linear Functions and Equations
Exercises
Applying Linear Functions and Equations
Exercises
Quadratic Growth
Properties of Quadratic Growth
Exercises
Applications of Quadratic Growth
Exercises
Quadratic Functions and Equations
Exercises
Quadratic Models for Revenue and Profit
Exercises
Geometric Growth
Properties of Geometric Growth Sequences
Exercises
Applications of Geometric Growth Sequences
Exercises
Exponential Functions
Exercises
Applications of Exponential Functions
Exercises
More About e
Exercises
Mixed Growth Models
Properties of Mixed Growth Sequences
Exercises
Applications of Mixed Growth Sequences
Exercises
Logistic Growth
Properties of Logistic Growth Sequences
Exercises
Chaos in Logistic Growth Sequences
Exercises
Refined Logistic Growth
Exercises
Selected Answers to Exercises
Bibliography
Index