Elementary Mathematical Models

✍ Scribed by Dan Kalman, Sacha Forgoston, Albert Goetz

• Publisher: American Mathematical Society
• Year: 2019
• Tongue: English
• Leaves: 528
• Edition: 2
• Category: Library

✦ Synopsis

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 scientifi cally—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.

✦ Table of Contents

Cover
Title page
Copyright
Contents
Preface to Second Edition
Note for Students
Chapter 1. Sequences and Number Patterns
1.1. Number Patterns
1.1. Exercises
1.2. Position Numbers, Graphs, and Subscript Notation
1.2. Exercises
1.3. Difference and Functional Equations
1.3. Exercises
Chapter 2. Arithmetic Growth Models
2.1. Properties of Arithmetic Growth
2.1. Exercises
2.2. Applications of Arithmetic Growth
2.2. Exercises
2.3. Linear Functions and Equations
2.3. Exercises
2.4. Applying Linear Functions and Equations
2.4. Exercises
Chapter 3. Quadratic Growth
3.1. Properties of Quadratic Growth
3.1. Exercises
3.2. Applications of Quadratic Growth
3.2. Exercises
3.3. Quadratic Functions and Equations
3.3. Exercises
3.4. Quadratic Models for Revenue and Profit
3.4. Exercises
Chapter 4. Geometric Growth
4.1. Properties of Geometric Growth Sequences
4.1. Exercises
4.2. Applications of Geometric Growth Sequences
4.2. Exercises
4.3. Exponential Functions
4.3. Exercises
4.4. Applications of Exponential Functions
4.4. Exercises
4.5. More About oldmath 𝑒
4.5. Exercises
Chapter 5. Mixed Growth Models
5.1. Properties of Mixed Growth Sequences
5.1. Exercises
5.2. Applications of Mixed Growth Sequences
5.2. Exercises
Chapter 6. Logistic Growth
6.1. Properties of Logistic Growth Sequences
6.1. Exercises
6.2. Chaos in Logistic Growth Sequences
6.2. Exercises
6.3. Refined Logistic Growth
6.3. Exercises
Selected Answers to Exercises
1.1. Exercises
1.2. Exercises
1.3. Exercises
2.1. Exercises
2.2. Exercises
2.3. Exercises
2.4. Exercises
3.1. Exercises
3.2. Exercises
3.3. Exercises
3.4. Exercises
4.1. Exercises
4.2. Exercises
4.3. Exercises
4.4. Exercises
4.5. Exercises
5.1. Exercises
5.2. Exercises
6.1. Exercises
6.2. Exercises
6.3. Exercises
Bibliography
Index
Back Cover