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Elementary Mathematical Models: An Accessible Development without Calculus, Second Edition

Dan Kalman American University, Washington, DC
MAA Press: An Imprint of the American Mathematical Society
Available Formats:
Hardcover ISBN: 978-1-4704-5001-4
Product Code: TEXT/50
List Price: $75.00 MAA Member Price:$56.25
AMS Member Price: $56.25 Electronic ISBN: 978-1-4704-5265-0 Product Code: TEXT/50.E List Price:$75.00
MAA Member Price: $56.25 AMS Member Price:$56.25
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $112.50 MAA Member Price:$84.38
AMS Member Price: $84.38 Click above image for expanded view Elementary Mathematical Models: An Accessible Development without Calculus, Second Edition Dan Kalman American University, Washington, DC MAA Press: An Imprint of the American Mathematical Society Available Formats:  Hardcover ISBN: 978-1-4704-5001-4 Product Code: TEXT/50  List Price:$75.00 MAA Member Price: $56.25 AMS Member Price:$56.25
 Electronic ISBN: 978-1-4704-5265-0 Product Code: TEXT/50.E
 List Price: $75.00 MAA Member Price:$56.25 AMS Member Price: $56.25 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$112.50 MAA Member Price: $84.38 AMS Member Price:$84.38
• Book Details

AMS/MAA Textbooks
Volume: 502019; 509 pp
MSC: Primary 00; 39;

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 defined 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 benefit from more than 1,000 carefully crafted exercises.

The following additional resources are available for instructors who have adopted Elementary Mathematical Models for a course: (1) An instructor's guide; (2) A collection of 'clicker questions,' and (3) A solutions manual for exercises in the text.

To access these resources, please send email to textbooks@ams.org for more information.

Readership

Undergraduate students interested in modeling with precalculus mathematics.

• 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
• Additional Material

• Reviews

• With a focus on real-world applications and an emphasis on using algebra as a means to an end, the book offers a very accessible course for students wishing to improve their quantitative literacy. Those students wishing to start making connections between algebraic concepts and the real world will surely find them in this textbook.

Andrew Lee, US Military Academy
• 'Elementary Mathematical Models' offers instructors an alternative to standard college algebra, quantitative literacy, and liberal arts mathematics courses. This book builds, successively, a series of growth models defined in terms of simple recursive patterns of change corresponding to arithmetic, quadratic, geometric, and logistic growth.

Tom G. Schulte, MAA Reviews
• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Accessibility – to request an alternate format of an AMS title
Volume: 502019; 509 pp
MSC: Primary 00; 39;

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 defined 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 benefit from more than 1,000 carefully crafted exercises.

The following additional resources are available for instructors who have adopted Elementary Mathematical Models for a course: (1) An instructor's guide; (2) A collection of 'clicker questions,' and (3) A solutions manual for exercises in the text.

To access these resources, please send email to textbooks@ams.org for more information.

Readership

Undergraduate students interested in modeling with precalculus mathematics.

• 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
• With a focus on real-world applications and an emphasis on using algebra as a means to an end, the book offers a very accessible course for students wishing to improve their quantitative literacy. Those students wishing to start making connections between algebraic concepts and the real world will surely find them in this textbook.

Andrew Lee, US Military Academy
• 'Elementary Mathematical Models' offers instructors an alternative to standard college algebra, quantitative literacy, and liberal arts mathematics courses. This book builds, successively, a series of growth models defined in terms of simple recursive patterns of change corresponding to arithmetic, quadratic, geometric, and logistic growth.

Tom G. Schulte, MAA Reviews
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.