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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
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
eBook ISBN:  978-1-4704-5265-0
Product Code:  TEXT/50.E
List Price: $69.00
MAA Member Price: $51.75
AMS Member Price: $51.75
Hardcover ISBN:  978-1-4704-5001-4
eBook: ISBN:  978-1-4704-5265-0
Product Code:  TEXT/50.B
List Price: $144.00 $109.50
MAA Member Price: $108.00 $82.13
AMS Member Price: $108.00 $82.13
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
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
eBook ISBN:  978-1-4704-5265-0
Product Code:  TEXT/50.E
List Price: $69.00
MAA Member Price: $51.75
AMS Member Price: $51.75
Hardcover ISBN:  978-1-4704-5001-4
eBook ISBN:  978-1-4704-5265-0
Product Code:  TEXT/50.B
List Price: $144.00 $109.50
MAA Member Price: $108.00 $82.13
AMS Member Price: $108.00 $82.13
  • Book Details
     
     
    AMS/MAA Textbooks
    Volume: 502019; 509 pp
    MSC: Primary 00; 39

    This is a Revised Edition of: TEXT/2

    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.

    Ancillaries:

    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
  • 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 publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Instructor's Manual – for instructors who have adopted an AMS textbook for a course and need the instructor's manual
    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

This is a Revised Edition of: TEXT/2

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.

Ancillaries:

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 publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Instructor's Manual – for instructors who have adopted an AMS textbook for a course and need the instructor's manual
Examination Copy – for faculty considering an AMS textbook for a course
Accessibility – to request an alternate format of an AMS title
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