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In this textbook there are fourteen chapters that are mostly indpendent of each other. For a typical semester course the instructor can choose several of the sections but would not be able to cover all of them. The text is full of exercises and activities to keep the students actively engaged. Each chapter has a number of short videos to emphasize the key ideas or show how to solve examples.

This book does a very good job conveying what it is like to “do” mathematics as a creative activity. Each of the four chapters presents a topic as a sequence of problems, conjectures, explorations, heuristic approaches, and rigorous justification. Because the number of topics is small there is time for students to explore without being rushed to “learn” the material. Courses that would use this book are not pre-requisite courses and so there is not the pressure to cover the content. Although written for students with minimal background, this book could profitably be used in an upper level course for advanced students or for independent study courses or for senior project/thesis ideas.

In addition to the goal of students gaining computational fluency this text aims to develop mathematical thinking with a greater emphasis on analysis and interpretation of results. The book pays attention to problem solving strategies and the use of estimation to support the development of critical thinking in students.

The Mathematics Department of the University of Washington designed its precalculus to concentrate on two goals: a review of the essential mathematics needed to succeed in calculus, and an emphasis on problem solving, the idea being to gain both experience and confidence in working with a particular set of mathematical toolsThis text was written with those goals in mind. It does not look like the widely used precalculus texts on the market. The actual text is short and there are not a lot of routine drill exercises. Instead the book emphasizes multi-part story problems in a conscious attempt to engage students at a deeper level in order to prepare them for the calculus, science, and engineering courses they will soon be taking. There are 20 problem sets, one set at the end of each chapter. The web site also has twenty years of exams (midterms and finals) and their solutions.

The authors are instructors at large community colleges in Ohio, and the book has now been adopted at several other locations. Those who have used the book expect to continue using it. One community college instructor now using it for the fourth time says he highly recommends the book to other colleagues and that his students often make positive comments about the book. He has found the authors “very approachable and helpful when I had questions or concerns.” Send email to the authors for more information about course adoptions of their books.

From the MAA review of this book: 'The discussions and explanations are succinct and to the point, in a way that pleases mathematicians who don’t like calculus books to go on and on.' The book covers the standard material in a calculus course for science and engineering. The size of the book is such that an instructor does not have to skip sections in order to fit the material into the typical course schedule. The single variable material is contained in eleven chapters beginning with analytic geometry and ending with sequences and series. The multivariable material consists of five chapters and includes with the vector calculus of in two and three dimensions through the divergence theorem. The book ends with a final chapter on differential equations. There are sufficiently many exercises at the end of each sections, but not as many as the much bigger commercial texts. Also available are WeBWorK problem sets keyed to the sections of the text. Some students and instructors may want to use something like a Schaum’s outline for additional problems.

Rather than detailed explanations and worked out examples, this book uses activities intended to be done by the students in order to present the standard concepts and computational techniques of calculus. The student activities provide most of the material to be assigned as homework, but since the book does not contain the usual routine exercises, instructors wanting such exercises will need to supply their own or use a homework system such as WebWork. With this approach Active Calculus makes it possible to teach an inquiry based learning course without severely restricting the material covered. The book has now been used for several years at Grand Valley State (the authors’ institution) and other colleges and universities.

This is a text for the standard three-semester course in single and multivariable calculus for science and engineering students. The authors are part of the APEX (Affordable Print and Electronic Textbooks) consortium based at VMI, which is developing other open textbooks as well. This text has been adopted for all sections of calculus at VMI and at Southern Virginia University. The visual presentation is clear and pleasing, and the organization and style are reminiscent of the best known commercial textbooks and is now in version 3.0.

This textbook, originally published by W. H. Freeman in 1995, is the result of the Five College Calculus Project, a multi-year project funded by the NSF beginning in 1986. The unifying concept of a dynamical system is used throughout to develop calculus in the broader context of scientific questions. “Therefore, differential equations belong at the center of calculus, and technology makes this possible at the introductory level.” The text is aimed at a broad audience as the authors believe “that calculus is one of the great bonds that unifies science. All students should have an opportunity to see how the language and tools of calculus help forge that bond.” (Quotes are from the overview on the book’s home page, which gives an excellent picture of the nature of this unusual book.)

Originally published in 1980 by Benjamin/Cummings, the current edition was published by Springer-Verlag in 1985 and is still in print. The publisher makes the PDF versions freely available and allows individuals to print single copies for their own use.

The book covers all the material of single and multivariable calculus that is normally in a three semester course for science, mathematics, and engineering students. The style is less formal and more personal than the typical text, and it has a definite point of view that helps keep the book to a reasonable length. Still, there are some non-traditional topics such as a bit of linear algebra in two and three dimensions in the chapter on vectors and a section on complex numbers in the chapter on polar coordinates.

This is a textbook for mainstream calculus typically taught over three semesters. The production qualities are high and the books look like commercially published books. There are overlapping chapters in each volume to provide some flexibility in scheduling and to minimize the chance that more than one volume will be required for each semester. The student guide consists of a separate Word document for each section. Each section has “Checkpoint Problems” within the text and answers to these at the end of each volume.

The book has the material typically covered in the third semester of a mainstream calculus course for science, mathematics, and engineering students. There are 420 exercises grouped into easy, moderate, and challenging categories. There are answers and some hints for the odd-numbered problems and for some of the even-numbered problems. Some exercises require the student to write programs for numerical approximations with code samples given in Java, but any programming language could be used.

The book is subtitled “Differential Equations for Engineers” and is suitable for the typical one term course for science and engineering students that follows calculus. The book lends itself to a variety of course designs. Beyond the first two chapters there is not a strict linear dependency for the remaining chapters. The book stands on its own but can also be used with IODE, a free software package developed at the University of Illinois for experimenting with differential equations.

These texts are appropriate for a first course in differential equations for one or two semesters. There are more than 2000 exercises, and the student manual has solutions for most of the even numbered ones.

This book is a well-organized text with carefully constructed examples, a full quota of exercises with solutions, and an emphasis that is algebraic rather than geometric. The book is Sage-enabled with approximately 90 examples of Sage code spread throughout. The book sections can be loaded into Sage as worksheets so that the code can be evaluated immediately; however, it is not necessary to use Sage in order to make use of this textbook.

This book has the standard content of a course for science, math, and engineering students that follows calculus. A semester of calculus is the explicit prerequisite, but most students would have three semesters of calculus and for them some of the beginning sections of the book can be skipped. Each chapter ends with three or four applications of that chapter’s subject.

Brown University has two introductory linear algebra courses. This text is used in the honors course that emphasizes proofs. The book’s title suggests that it is not the typical approach to linear algebra even among those books that are more theoretical.

From the author’s preface: 'This text is an expansion and refinement of lecture notes I developed while teaching proofs courses over the past ten years. It is written for an audience of mathematics majors at Virginia Commonwealth University, a large state university….However, I am mindful of a larger audience. I believe this book is suitable for almost any undergraduate mathematics program.' Designed for the typical bridge course that follows calculus and introduces the students to the language and style of more theoretical mathematics, Book of Proof has 13 chapters grouped into four sections: (I) Fundamentals, (II) How to Prove Conditional Statements, (III) More on Proof, (IV) Relations, Functions, and Cardinality. One math professor who has used the book writes: 'Hammack’s book is great. I’ve used the book twice now, will use it again, and have recommended it to other instructors. I have used it in a discrete math course which serves as a “transition” course for our majors.'

This book is designed for the transition course between calculus and differential equations and the upper division mathematics courses with an emphasis on proof and abstraction. The book has been used by the author and several other faculty at Southern Connecticut State University. There are nine chapters and more than enough material for a semester course. Student reviews are favorable.