Volume: 50; 2019; 509 pp; Hardcover
MSC: Primary 00; 39;
Print ISBN: 978-1-4704-5001-4
Product Code: TEXT/50
List Price: $75.00
AMS Member Price: $56.25
MAA Member Price: $56.25
Electronic ISBN: 978-1-4704-5265-0
Product Code: TEXT/50.E
List Price: $75.00
AMS Member Price: $56.25
MAA Member Price: $56.25
Supplemental Materials
Elementary Mathematical Models: An Accessible Development without Calculus, Second Edition
Share this pageDan Kalman; Sacha Forgoston; Albert Goetz
MAA Press: An Imprint of the American Mathematical Society
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.
Reviews & Endorsements
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
Table of Contents
Table of Contents
Elementary Mathematical Models: An Accessible Development without Calculus, Second Edition
- Cover Cover11
- Title page iii5
- Copyright iv6
- Contents v7
- Preface to Second Edition vii9
- Note for Students xv17
- Chapter 1. Sequences and Number Patterns 119
- Chapter 2. Arithmetic Growth Models 3957
- Chapter 3. Quadratic Growth 121139
- Chapter 4. Geometric Growth 201219
- 4.1. Properties of Geometric Growth Sequences 201219
- 4.1. Exercises 214232
- 4.2. Applications of Geometric Growth Sequences 219237
- 4.2. Exercises 236254
- 4.3. Exponential Functions 247265
- 4.3. Exercises 264282
- 4.4. Applications of Exponential Functions 270288
- 4.4. Exercises 283301
- 4.5. More About �oldmath 𝑒 290308
- 4.5. Exercises 294312
- Chapter 5. Mixed Growth Models 297315
- Chapter 6. Logistic Growth 359377
- Selected Answers to Exercises 441459
- 1.1. Exercises 441459
- 1.2. Exercises 444462
- 1.3. Exercises 447465
- 2.1. Exercises 449467
- 2.2. Exercises 451469
- 2.3. Exercises 453471
- 2.4. Exercises 457475
- 3.1. Exercises 459477
- 3.2. Exercises 462480
- 3.3. Exercises 464482
- 3.4. Exercises 465483
- 4.1. Exercises 467485
- 4.2. Exercises 469487
- 4.3. Exercises 474492
- 4.4. Exercises 476494
- 4.5. Exercises 479497
- 5.1. Exercises 481499
- 5.2. Exercises 484502
- 6.1. Exercises 488506
- 6.2. Exercises 493511
- 6.3. Exercises 495513
- Bibliography 501519
- Index 505523
- Back Cover Back Cover1528