Ebook Info
- Published: 2016
- Number of pages: 180 pages
- Format: PDF
- File Size: 9.13 MB
- Authors: Roger B. Nelsen
Description
To the benefit of both teachers and students, Cameos for Calculus presents fifty short visual and geometric enhancements to the first-year calculus course. These range from mainstream topics, such as the derivative and combinatorial formulas used to compute Riemann sums, to equally accessible material less often encountered in the course, such as the Cauchy–Schwarz inequality and the Euler–Mascheroni constant. The fifty cameos are grouped into five sections: Limits and Differentiation; Integration; Infinite Series; Additional Topics; and an appendix on precalculus topics. Many of these also include exercises with solutions to enhance learning. By gathering various cameos, including many adapted from journal articles and some created for this book, Nelsen presents a collection accessible to teachers of calculus, both for use in the classroom and as supplementary explorations for students.
User’s Reviews
Editorial Reviews: Review Visualizing mathematical ideas usually reduces the complexity of topics and therefore have educational value. This plays an essential role in courses such as calculus, which are both fundamental and scheduled for first year students. Sometimes, a suitable graph or graphic contains the whole idea of a proof. These are known as “proofs without words.” After his several books gathering Proofs Without Words, the author has now written a book on calculus, combining similar ideas with some exact arguments. The book under review is an interesting and pretty collection of proofs of material from the first-year course, all based on visualizing ideas. They include several theorems about limits and differentiation (Part I), integration (Part II), infinite series (Part III), and several additional topics (Part IV). The final part of the book is an appendix (Part V) covering some precalculus topics. Finally, the author gives solutions to the exercises, which are at the end of many of the chapters. This is not a standard textbook, but it is a very useful complement for both students and instructors in a first-year calculus course. –Mehdi Hassani, MAA ReviewsVisualization is one of the most important tools in teaching undergraduate mathematics courses. We all use diagrams and graphs in our calculus classes, from quick improvised doodles to elaborate figures that support arguments in a proof. They are most effective when the connection between an identity or inequality and the corresponding diagram is clearly visible. In the preface of this book, the author begins with the two different meanings of the word cameo as a “brief appearance of a known figure” (in film and theater) or a “precious or semiprecious stone” (for gemologists). The 50 cameos in this aim at combining these two definitions. Many of these visualizations are quite standard and can be found in most calculus textbooks. Others, however, are more unusual, are particularly clever and/or especially enlightening. Many cameos are reminiscent of the well-known “Proofs without words” books or columns, and indeed, the College Mathematics Journal, where they typically first appeared, is a standard source for much of this book. My person favorite is Cameo 40 (“Approximating pi with Maclaurin series”), where visual proofs of two arctan identities for pi/4 are presented. Inequalities are particularly well represented in this book, which is one of its strengths. Tehre are also two cameos each on hyperbolic functions and conic sections, two other topics that are all to often neglected in calculus courses. Most cameos come with exercises (with solutions in the back of the book), and all have a list of sources. Portraits of famous mathematicians can also be found throughout the book. The five parts of this book (with the numbers of cameos) are Limits and Differentiation(15), Free Download Cameos for Calculus: Visualization in the First-Year Course (Classroom Resource Materials) in PDF formatKeywords
Cameos for Calculus: Visualization in the First-Year Course (Classroom Resource Materials) PDF Free Download
Download Cameos for Calculus: Visualization in the First-Year Course (Classroom Resource Materials) 2016 PDF Free
Cameos for Calculus: Visualization in the First-Year Course (Classroom Resource Materials) 2016 PDF Free Download
Download Cameos for Calculus: Visualization in the First-Year Course (Classroom Resource Materials) PDF
Free Download Ebook Cameos for Calculus: Visualization in the First-Year Course (Classroom Resource Materials)
