Calculus Connections
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| Author | : Asma Harcharras |
| Publisher | : Prentice Hall |
| Total Pages | : 500 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : |
With challenging new standards-based middle school mathematics curricula now in place, future teachers need college-level mathematics instruction that better prepares them for their professional careers. Addresses the importance of learning calculus in preparation for the teaching of middle school mathematics, focusing on concepts and applications to illuminate the connections that exist between college-level calculus and the mathematics taught in today's middle schools. Examines the unique needs of future teachers in comparison to general calculus books. Initiates new topics with engaging discussion rather than the standard formula-proof-example approach. Stresses the interplay between geometry and calculus, and demonstrates the essential power of calculus for computing areas, lengths, surface areas, and volumes. For current or future mathematics teachers, or anyone interested in learning more about calculus.
| Author | : Nicholas H. Wasserman |
| Publisher | : Springer Nature |
| Total Pages | : 226 |
| Release | : 2022-01-03 |
| Genre | : Education |
| ISBN | : 3030891984 |
Getting certified to teach high school mathematics typically requires completing a course in real analysis. Yet most teachers point out real analysis content bears little resemblance to secondary mathematics and report it does not influence their teaching in any significant way. This textbook is our attempt to change the narrative. It is our belief that analysis can be a meaningful part of a teacher's mathematical education and preparation for teaching. This book is a companion text. It is intended to be a supplemental resource, used in conjunction with a more traditional real analysis book. The textbook is based on our efforts to identify ways that studying real analysis can provide future teachers with genuine opportunities to think about teaching secondary mathematics. It focuses on how mathematical ideas are connected to the practice of teaching secondary mathematics–and not just the content of secondary mathematics itself. Discussions around pedagogy are premised on the belief that the way mathematicians do mathematics can be useful for how we think about teaching mathematics. The book uses particular situations in teaching to make explicit ways that the content of real analysis might be important for teaching secondary mathematics, and how mathematical practices prevalent in the study of real analysis can be incorporated as practices for teaching. This textbook will be of particular interest to mathematics instructors–and mathematics teacher educators–thinking about how the mathematics of real analysis might be applicable to secondary teaching, as well as to any prospective (or current) teacher who has wondered about what the purpose of taking such courses could be.
| Author | : Ib H. Madsen |
| Publisher | : Cambridge University Press |
| Total Pages | : 302 |
| Release | : 1997-03-13 |
| Genre | : Mathematics |
| ISBN | : 9780521589567 |
An introductory textbook on cohomology and curvature with emphasis on applications.
| Author | : Mark Ryan |
| Publisher | : John Wiley & Sons |
| Total Pages | : 406 |
| Release | : 2014-06-23 |
| Genre | : Mathematics |
| ISBN | : 1118791339 |
Calculus For Dummies, 2nd Edition (9781118791295) is now being published as Calculus For Dummies, 2nd Edition (9781119293491). While this version features an older Dummies cover and design, the content is the same as the new release and should not be considered a different product. Slay the calculus monster with this user-friendly guide Calculus For Dummies, 2nd Edition makes calculus manageable—even if you're one of the many students who sweat at the thought of it. By breaking down differentiation and integration into digestible concepts, this guide helps you build a stronger foundation with a solid understanding of the big ideas at work. This user-friendly math book leads you step-by-step through each concept, operation, and solution, explaining the "how" and "why" in plain English instead of math-speak. Through relevant instruction and practical examples, you'll soon learn that real-life calculus isn't nearly the monster it's made out to be. Calculus is a required course for many college majors, and for students without a strong math foundation, it can be a real barrier to graduation. Breaking that barrier down means recognizing calculus for what it is—simply a tool for studying the ways in which variables interact. It's the logical extension of the algebra, geometry, and trigonometry you've already taken, and Calculus For Dummies, 2nd Edition proves that if you can master those classes, you can tackle calculus and win. Includes foundations in algebra, trigonometry, and pre-calculus concepts Explores sequences, series, and graphing common functions Instructs you how to approximate area with integration Features things to remember, things to forget, and things you can't get away with Stop fearing calculus, and learn to embrace the challenge. With this comprehensive study guide, you'll gain the skills and confidence that make all the difference. Calculus For Dummies, 2nd Edition provides a roadmap for success, and the backup you need to get there.
| Author | : Marilyn Paula Carlson |
| Publisher | : MAA |
| Total Pages | : 340 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 9780883851838 |
The chapters in this volume convey insights from mathematics education research that have direct implications for anyone interested in improving teaching and learning in undergraduate mathematics. This synthesis of research on learning and teaching mathematics provides relevant information for any math department or individual faculty member who is working to improve introductory proof courses, the longitudinal coherence of precalculus through differential equations, students' mathematical thinking and problem-solving abilities, and students' understanding of fundamental ideas such as variable and rate of change. Other chapters include information about programs that have been successful in supporting students' continued study of mathematics. The authors provide many examples and ideas to help the reader infuse the knowledge from mathematics education research into mathematics teaching practice. University mathematicians and community college faculty spend much of their time engaged in work to improve their teaching. Frequently, they are left to their own experiences and informal conversations with colleagues to develop new approaches to support student learning and their continuation in mathematics. Over the past 30 years, research in undergraduate mathematics education has produced knowledge about the development of mathematical understandings and models for supporting students' mathematical learning. Currently, very little of this knowledge is affecting teaching practice. We hope that this volume will open a meaningful dialogue between researchers and practitioners toward the goal of realizing improvements in undergraduate mathematics curriculum and instruction.
| Author | : Aleksandr Mikha?lovich Vinogradov |
| Publisher | : World Scientific |
| Total Pages | : 310 |
| Release | : 2009 |
| Genre | : Mathematics |
| ISBN | : 9812819053 |
In this unique book, written in a reasonably self-contained manner, the theory of linear connections is systematically presented as a natural part of differential calculus over commutative algebras. This not only makes easy and natural numerous generalizations of the classical theory and reveals various new aspects of it, but also shows in a clear and transparent manner the intrinsic structure of the associated differential calculus. The notion of a OC fat manifoldOCO introduced here then allows the reader to build a well-working analogy of this OC connection calculusOCO with the usual one."
| Author | : Michael Spivak |
| Publisher | : Westview Press |
| Total Pages | : 164 |
| Release | : 1965 |
| Genre | : Science |
| ISBN | : 9780805390216 |
This book uses elementary versions of modern methods found in sophisticated mathematics to discuss portions of "advanced calculus" in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level.
| Author | : Deborah Hughes-Hallett |
| Publisher | : John Wiley & Sons |
| Total Pages | : 488 |
| Release | : 2017-12-11 |
| Genre | : Mathematics |
| ISBN | : 1119275563 |
A text for interactive Calculus courses, featuring innovative problems This sixth edition of Applied Calculus engages students with well-constructed problems and content to deepen understanding. The Rule of Four approach is supported in the text, where concepts are presented graphically, numerically, symbolically, and verbally. Students with a range of learning styles will be able to progress in the subject as they are exposed to a range of exercises. This is a loose-leaf edition.
| Author | : Roland Backhouse |
| Publisher | : Springer |
| Total Pages | : 401 |
| Release | : 2003-07-31 |
| Genre | : Computers |
| ISBN | : 3540477977 |
Program construction is about turning specifications of computer software into implementations. Recent research aimed at improving the process of program construction exploits insights from abstract algebraic tools such as lattice theory, fixpoint calculus, universal algebra, category theory, and allegory theory. This textbook-like tutorial presents, besides an introduction, eight coherently written chapters by leading authorities on ordered sets and complete lattices, algebras and coalgebras, Galois connections and fixed point calculus, calculating functional programs, algebra of program termination, exercises in coalgebraic specification, algebraic methods for optimization problems, and temporal algebra.
| Author | : R. W. R. Darling |
| Publisher | : Cambridge University Press |
| Total Pages | : 288 |
| Release | : 1994-09-22 |
| Genre | : Mathematics |
| ISBN | : 9780521468008 |
Introducing the tools of modern differential geometry--exterior calculus, manifolds, vector bundles, connections--this textbook covers both classical surface theory, the modern theory of connections, and curvature. With no knowledge of topology assumed, the only prerequisites are multivariate calculus and linear algebra.
