Now in Print! The Heart of Calculus

The Heart of Calculus: Explorations and Applications
Philip M. Anselone and John W. Lee
List Price: $60.00 | MAA Member Price: $48.00

This book contains enrichment material for courses in first and second year calculus, differential equations, modeling, and introductory real analysis. It targets talented students who seek a deeper understanding of calculus and its applications. The book can be used in honors courses, undergraduate seminars, independent study, capstone courses taking a fresh look at calculus, and summer enrichment programs. The book develops topics from novel and/or unifying perspectives. Hence, it is also a valuable resource for graduate teaching assistants developing their academic and pedagogical skills and for seasoned veterans who appreciate fresh perspectives.

The explorations, problems, and projects in the book impart a deeper understanding of and facility with the mathematical reasoning that lies at the heart of calculus and conveys something of its beauty and depth. A high level of rigor is maintained. However, with few exceptions, proofs depend only on tools from calculus and earlier. Analytical arguments are carefully structured to avoid epsilons and deltas. Geometric and/or physical reasoning motivates challenging analytical discussions. Consequently, the presentation is friendly and accessible to students at various levels of mathematical maturity. Logical reasoning skills at the level of proof in Euclidean geometry suffice for a productive use of the book.

There are 16 chapters in the book, divided about equally between pure and applied mathematics. The first three chapters are on fundamentals of differential calculus and the last three are on the monumental discoveries of Newton and Kepler on celestial motion and gravitation. The intervening chapters present significant topics in pure and applied mathematics chosen for their intrinsic interest, historical influence, and continuing importance. There is great flexibility in the choice of which chapters to cover and the order of coverage because chapters are essentially independent of each other.

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MAA Books Beat: New Calculus Textbook

by Steve Kennedy, MAA Senior Acquisitions Editor

What do you do at your school with a first–year student who scored a four or five in AP calculus in high school? There is, at least at Carleton, an awkward articulation between the coverage of the AP AB syllabus and our first-year calculus sequence.

For the first several weeks of our Calculus II class we are covering material that is, at least partially, in an AP calculus class: methods of integration; applications of the integral, including arc length and surface area; some elementary differential equations. But students who take Calculus I at Carleton haven’t seen any of this. It makes for a strange dynamic in the classroom: For some students everything is new and confusing; for others (the AP students) large parts are review. The former feel at a disadvantage, the latter a little bored.

We don’t really want to have two strands through our calculus sequence, one for students with AP experience and another for students who take all their calculus at Carleton. Several years ago we took the AP-experienced students and gave them a half-term course in modeling while the non-AP students took our standard Calculus II material. Then the two groups came together for the second half of the term to study sequences and series together. This turned out to be logistically difficult (and confusing to folks in other departments of the college), and we abandoned the experiment after a few years.

New Calculus Textbooks from the MAA

Looking for a new calculus textbook? Check out these two just published by the MAA.

Calculus for the Life Sciences: A Modeling Approach
James L. Cornette and Ralph A. Ackerman

Available only as an ebook. PDF price: $35.00

Freshman and sophomore life sciences students respond well to the modeling approach to calculus, difference equations, and differential equations presented in this book. Examples of population dynamics, pharmacokinetics, and biologically relevant physical processes are introduced in Chapter 1, and these and other life sciences topics are developed throughout the text.

The ultimate goal of calculus for many life sciences students primarily involves modeling living systems with difference and differential equations. Understanding the concepts of derivative and integral is crucial, but the ability to compute a large array of derivatives and integrals is of secondary importance.

Students should have studied algebra, geometry and trigonometry, but may be life sciences students because they have not enjoyed their previous mathematics courses. This text can help them understand the relevance and importance of mathematics to their world. It is not a simplistic approach, however, and indeed is written with the belief that the mathematical depth of a course in calculus for the life sciences should be comparable to that of the traditional course for physics and engineering students.

College Calculus: A One-Term Course for Students with Previous Calculus Experience
Michael E. Boardman and Roger B. Nelsen

List price: $60.00 | MAA Member: $48.00

This textbook is for students who have successfully experienced an introductory calculus course in high school. College Calculus begins with a brief review of some of the content of the high school calculus course, and proceeds to give students a thorough grounding in the remaining topics in single variable calculus, including integration techniques, applications of the definite integral, separable and linear differential equations, hyperbolic functions, parametric equations and polar coordinates, L’Hôpital’s rule and improper integrals, continuous probability models, and infinite series. Each chapter concludes with several “Explorations,” extended discovery investigations to supplement that chapter’s material.

The text is ideal as the basis of a course focused on the needs of prospective majors in the STEM disciplines (science, technology, engineering, and mathematics). A one-term course based on this text provides students with a solid foundation in single variable calculus and prepares them for the next course in college level mathematics, be it multivariable calculus, linear algebra, a course in discrete mathematics, statistics, etc.

JMM 2015: Teaching Calculus with a Tablet

Attending the Joint Mathematics Meetings in San Antonio, TX, this year? Join us for this MAA Special Session!

Teaching Calculus with a Tablet

Gwyneth Whieldon, Hood College

Integrating technology into the classroom has been a hot topic over the past decade but best practices in the use of tablets, phones, and laptops for mathematics education are still being developed. In this workshop, participants will have a chance to demo the MAA electronic textbook Calculus: Modeling and Application and see how a textbook designed specifically to be read and interacted with on a tablet can be integrated into their own classrooms. We will introduce several apps to supplement an electronic textbook (and, more generally, for use in a technology-based calculus course) and suggest techniques for introducing students to a calculus sequence very different from any math classes they have taken before.

Monday, January 12

3:00-4:15pm

Room 213B

Convention Center

Stop by the MAA Pavilion in the exhibit hall for more information.

New in the MAA Store: Ordinary Differential Equations

Ordinary Differential Equations: From Calculus to Dynamical Systems
By Virginia W. Noonburg
List Price: $60.00
MAA Member: $48.00

This book presents a modern treatment of material traditionally covered in the sophomore-level course in ordinary differential equations. While this course is usually required for engineering students the material is attractive to students in any field of applied science, including those in the biological sciences.

The standard analytic methods for solving first and second-order differential equations are covered in the first three chapters. Numerical and graphical methods are considered, side-by-side with the analytic methods, and are then used throughout the text. An early emphasis on the graphical treatment of autonomous first-order equations leads easily into a discussion of bifurcation of solutions with respect to parameters.

The fourth chapter begins the study of linear systems of first-order equations and includes a section containing all of the material on matrix algebra needed in the remainder of the text. Building on the linear analysis, the fifth chapter brings the student to a level where two-dimensional nonlinear systems can be analyzed graphically via the phase plane. The study of bifurcations is extended to systems of equations, using several compelling examples, many of which are drawn from population biology. In this chapter the student is gently introduced to some of the more important results in the theory of dynamical systems. A student project, involving a problem recently appearing in the mathematical literature on dynamical systems, is included at the end of Chapter 5.

A full treatment of the Laplace transform is given in Chapter 6, with several of the examples taken from the biological sciences. An appendix contains completely worked-out solutions to all of the odd-numbered exercises.

The book is aimed at students with a good calculus background that want to learn more about how calculus is used to solve real problems in today's world. It can be used as a text for the introductory differential equations course, and is readable enough to be used even if the class is being "flipped." The book is also accessible as a self-study text for anyone who has completed two terms of calculus, including highly motivated high school students. Graduate students preparing to take courses in dynamical systems theory will also find this text useful.

Order your copy today in the MAA Store.

New Textbook Coming Soon

Ordinary Differential Equations: From Calculus to Dynamical Systems

by V. W. Noonburg

Catalog Code: FCDS

This book presents a modern treatment of material traditionally covered in the sophomore-level course in ordinary differential equations. While this course is usually required for engineering students, the material is attractive to students in any field of applied science, including those in the biological sciences.

The standard analytic methods for solving first and second-order differential equations are covered in the first three chapters. Numerical and graphical methods are considered side-by-side with the analytic methods and are then used throughout the text. An early emphasis on the graphical treatment of autonomous first-order equations leads easily onto a discussion of bifurcation of solutions with respect to parameters.

The fourth chapter begins the study of linear systems of first-order equations and includes a section containing all of the material on matrix algebra needed in the remainder of the text. Building on the linear analysis, the fifth chapter brings the student to a level where two-dimensional nonlinear systems can be analyzed graphically via the phase plane. The study of bifurcations is extended to systems of equations using several compelling examples, many of which are drawn from population biology. In this chapter, the student is gently introduced to some of the more important results in the theory of dynamical systems. A student project involving a problem recently appearing in the mathematical literature on dynamical systems is included at the end of chapter 5.

A full treatment of the Laplace transform is given in Chapter 6, with several of the examples taken from the biological sciences. An appendix contains completely worked-out solutions to all of the odd-numbered exercises.

The book is aimed at students with a good calculus background who want to learn more about how calculus is used to solve real problems in today's world. It can be used as a text for the introductory differential equations course, and is readable enough to be used even if the class is being “flipped.” The book is also accessible as a self-study text for anyone who has completed two terms of calculus, including highly motivated high school students. Graduate students preparing to take courses in dynamical systems theory will also find this text useful.

To see all of our textbooks visit the MAA website.

JMM 2014: Online Calculus Textbook Session

Heading to Baltimore, MD for the Joint Mathematics Meetings? Be sure to join authors Lawrence C. Moore and David A. Smith for a demonstration of their online interactive textbook, Calculus: Modeling and Application. For only $35, students can receive one-year's access to two semesters of single-variable calculus. Bring a laptop or tablet and stay after the demonstration for the authors' guidance as you explore further. Session attendees will receive free access to the book for 60 days.

Online Calculus Textbook Session

Friday, January 17
3:30 pm
Baltimore Convention Center
Room 340

 

 

 To learn more about the book, click here. 

To learn more about the session, contact Carol Baxter at cbaxter@maa.org.

MAA Books Beat: Calculus Online and Geometric Excursions

Written by Steve Kennedy, MAA Books Beat is a new column that will appear in MAA Focus. The first article, Calculus Online and Geometric Excursions, appears in the December 2013/January 2014 issue. 

Calculus Online and Geometric Excursions

by Steve Kennedy

My department used the same calculus text for well over a decade. We’re a traditional place, and we used a traditional text. It is a splendid book–terrific exposition with great problems. A year or so ago, yet another edition came out, and we, collectively, gulped when we saw the price tag. More than $200. We decided to stop fiddling around and look seriously at alternatives. After a long and careful comparison period during which we read and discussed a big pile of calculus books, we chose an alternate text. This text features good exposition and good problems and, more to my present point, a price tag $100 lower than the original book.

The publisher’s representative of our original text learned of our decision and the reason for it, and offered various discount prices for various lengths of time. After considering the options, we moved on to the new text. This bargaining session left me feeling annoyed and manipulated. I’m a teacher. I’m not interested in playing negotiating games. I want to help my students learn and grow, and I would like publishers to help me by providing good books at fair prices–not marketing manipulations and games.

Now I work for a publisher. A publisher that, I believe, shares my view that our role is to provide quality books, especially textbooks, at reasonable prices. This publisher also puts out the newsmagazine you are reading. My new job (just part time; I’m still a math teacher) is to acquire those quality books from you, the MAA members who are writing them.

Your probably don’t think of the MAA as a publisher, and that’s natural. We are, primarily, a collective of professionals working together to advance and promote mathematics. But producing books of enduring value is a part of that collective effort. We’re a funny kind of publisher because the people writing the books and the people buying the books are, essentially, the same: MAA members.

One part of my new job is to market those books. I’m not really sure how best to do that, although I’m dead-set against backroom bargaining and rapid edition switching designed to kill the used-book market. I prefer to calmly point out to you the virtues of some of our books. I intend to use this space on a regular basis to highlight some of the terrific books we are publishing. I intend also to, frequently and loudly, point out the following: We publish really good books at very reasonable prices. You ought to buy them.

Let me tell you about two of them.

Beckenbach Book Prize 2014

The Beckenbach Book Prize, established in 1986, is the successor to the MAA Book Prize established in 1982. It is named for the late Edwin Beckenbach, a long-time leader in the publications program of the Association and a well-known professor of mathematics at the University of California at Los Angeles. The Prize of $2,500 is intended to recognize the author(s) of a distinguished, innovative book published by the MAA and to encourage the writing of such books. The award is not given on a regularly scheduled basis. To be considered for the Beckenbach Prize a book must have been published during the five years preceding the Award.

The 2014 Beckenbach Book Prize winner is:

A Historian Looks Back: The Calculus as Algebra  and Selected Writings by Judith Grabiner Judith Grabiner has written extensively on the history of mathematics. This collection, representing some of Grabiner's finest work, highlights the benefits of studying the development of mathematical ideas and the relationship between culture and mathematics. A large part of the book (Part I) is a welcome reprinting of Grabiner's The Calculus as Algebra: J.-L. Lagrange, 1736-1813 (1990), which focuses on Lagrange's pioneering effort to reduce the calculus to algebra. Ten articles (Part II) span a range of other mathematical topics, including widely held myths about the history of mathematics and the work of such mathematicians as Descartes, Newton, and Maclaurin. Six of these articles won awards from the MAA for expository excellence. This collection is an inspiring resource for courses on the history of mathematics. It reveals the creativity that has produced the mathematics we see as the finished product in textbooks.

The MAA will be honoring Judith Grabiner and her book at the 2014 Joint Mathematics Meetings in Baltimore. Learn more here.

Betty Mayfield Reviews Calculus: Modeling and Application

Betty Mayfield reviews Calculus: Modeling and Application by David Smith and Lang Moore in the November issue of The American Mathematical Monthly.

Sit back. Relax. Close your eyes. Now imagine that you are picking up a calculus textbook. Feel its mighty heft. Open it to see the formulas inside the front cover, the table of integrals at the back of the book, the solutions to odd-numbered exercises. Scan the table of contents for the familiar topics, in the familiar order. Flip open to a page at random and admire the colorful graphics, the theorems helpfully boxed and shaded, the examples carefully worked out. Note the many exercises you may assign to your students. Resist the urge to call the university bookstore and ask how much they are charging this semester for this impressive tome.

Now imagine a completely different kind of text—different both in content and delivery. In fact, you are reading it on your iPad. That book might be David Smith and Lang Moore’s Calculus: Modeling and Application (CMA), available through the MAA Bookstore as an electronic text. It is a direct descendent of The Calculus Reader [2], one of the more popular texts to grow out of the calculus reform movement of the 1990s [1], and it retains much of the flavor of that earlier book. Its emphasis is on the use of authentic real-world problems to motivate learning new mathematics; on the use of technology for graphing, computation and exploration; and on collaboration among students as they discover patterns and construct their own mathematical knowledge.

Read the full review here.

Teaching with MAA's Online Calculus Textbook

Dr. Gwyn Whieldon, Assistant Professor of Mathematics at Hood College, talks about using MAA's online interactive textbook Calculus: Modeling and Application in her classes. 

Interested in using Calculus: Modeling and Application? Learn more here.

Online Calculus Textbook for Only $35

Calculus: Modeling and Application by Lawrence C. Moore and David A. Smith is an online interactive calculus textbook. For only $35, this textbook covers two semesters of single variable calculus. Features Use of real-world contexts for motivation  Guided discovery learning Hands-on activities (including built-in applets) A problem-solving orientation Encouragement of teamwork  Written responses to questions  Tools for self-checking of results  Free access to the text for adopters  Access to the Calculus: Modeling and Application library as well as the national WeBWorK library All exercises potentially machine-gradable

 Sample Chapters can be viewed at calculuscourse.maa.org/sample.

 To learn more, click here.

Debbie Gochenaur Reviews Uncommon Mathematical Excursions

Debbie Gochenaur reviews Uncommon Mathematical Excursions: Polynomia and Related Realms by Dan Kalman as part of MAA Reviews. Offering an assortment of topics in the algebra, geometry, and calculus curricula, this book is intended as an enrichment for those familiar with these topics at the upper-secondary or introductory college math level. While the book may be geared especially for teachers who have taught their courses enough times to be thoroughly comfortable with the content, advanced students, as well as scientists and mathematicians in general, may find topics within this book intriguing. It has the potential to appeal to a broad audience. The book is meant to guide the readers in exploring ideas that are related to his/her core mathematical knowledge. The book is divided into three parts — The Province of Polynomia, Maxiministan, and The Calculusian Republic. Kalman ensures that the reader can make connections to known undergraduate mathematics and advanced secondary topics in the algebra, geometry, and calculus domains; he works to help the reader make extensions and perhaps understand more clearly the depth of mathematics in these seemingly elementary topics. Overall, the reader may be surprised by aspects of a particular topic that will lead to a greater understanding and appreciation for the mathematics. Read the full review here. Purchase your copy in the MAA Store.

New Material in Calculus and Its Origins

Calculus and Its Origins now includes material on the origins of differential equations! The author, Dave Perkins, explains how he gathered the information with the help of his colleagues below. "In the months after Calculus & Its Origins was initially printed, I gradually grew sorry that I had not included any material concerning the origins of differential equations. It's my understanding that calculus was born not only out of pure curiosity but also, more importantly, out of the desire to quantify scientific observations. Differential equations are the calculus-based expression of such observations. When I learned that the book would be reprinted, I eagerly asked for permission to include a few pages on the subject. The MAA folks graciously agreed. On the very day I asked, I opened the March 2013 College Mathematics Journal to the article "Who solved the Bernoulli differential equation and how did they do it?" by Adam Parker. What amazing luck! Even better, Adam agreed to talk to me on the phone, whereupon he helped me to sort out my ideas for the new material I wished to include in the second printing. I eventually chose several of the earliest differential equations to outline as exercises (all exercises in the book are extended outlines of some historically important result, rather than being simply lists of practice questions). The first exercise describes Descartes's solution to a problem posed to him by Florimund de Beaune, a man of many interests whose differential equation related to the behavior of sound. The other problems concern equations posed by two of the Bernoulli brothers. Time was short, so I posted a plea for help to my Project NExT email group, wondering if perhaps a person or two could look at my first draft of these problems over the ensuing 36 hours. Not only did I get immediate offers, but two group members cross-posted my request to other lists. Soon I had a dozen confirmed helpers who committed to my quick time frame. The offers kept coming, and I told each person that I had plenty of help, but would send them my material if they'd like to see it nevertheless. Every one said, "Please do send the problems. I'd like to see them!" To me, this testifies to both a widespread love for the history of mathematics and the collegiality that I have always encountered among mathematicians. This warmth and this curiosity are what prompted me to ask if I could write this blog post, to share my feel-good story and publicly say thank you. My colleagues who reacted so quickly and in such caring detail to my new material are now listed in the preface of the second edition, but I want to thank them again. They are Adam Parker, Jennifer Daniel, William Dunham, Melissa Hoover, Lynne Ipina, Dan Kemp, Will Murray, and Fred Rickey. My thanks as well to Carol Baxter and Beverly Ruedi at the MAA for their efforts in including the new material." Purchase your copy today at the MAA Store or the MAA eBooks Store.

Calculus Demonstration at MAA MathFest #MAAthFest

Where: MAA MathFest 2012 in Madison, Wisconsin

When: 2 PM, August 3 at the MAA Pavillion in the Exhibit Hall 

Tired of your traditional Calculus textbook? Stop by the MAA Pavillion at 2 PM for a conversation and demonstration of Lang Moore and David A. Smith's Calculus: Modeling & Application, the MAA's interactive Calculus textbook. 

More MAA Book Events and Sales at MAA MathFest 2012 

Bressoud Reviews MAA's Calculus: Modeling and Application Interactive Textbook

MAA Past President David Bressoud reviewed Calculus: Modeling and Application, 2nd Edition in his May Launchings Column. Bressoud has been using the MAA online textbook to teach Single Variable Calculus at Macalester College. 


"One of the greatest benefits of online textbooks is the ability to embed links to definitions, animations, and software programs. Smith and Moore’s textbook is liberally sprinkled with links to explorations that are available in Maple, Mathcad, and Mathematica. There also are links to WeBWorK, where a library of problems linked to the sections of their book is available. "


Read the full column "Are Textbooks Better Online?"

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Calculus: Modeling and Application, 2nd Edition, by David A. Smith and Lawrence C. Moore of Duke University, responds to advances in technology that permit the integration of text and student activities into a unified whole. In this approach, students can use mathematics to structure their understanding of and investigate questions in the world around them, to formulate problems and find solutions, then to communicate their results to others.

This interactive textbook covers two semesters of single-variable calculus. Its features include use of real-world contexts for motivation, guided discovery learning, hands-on activities (including built-in applets), a problem-solving orientation, encouragement of teamwork, written responses to questions, tools for self-checking of results, intelligent use of technology, and high expectation of students.