Multivariable Calculus from Graphical, Numerical, and Symbolic Points of View


Book Description

The text addresses a general mathematical audience: mathematics majors, science and engineering majors, and non-science majors. [The authors] assume little more mathematical maturity than for single-variable calculus, but the presentation is not rigorous in the sense of mathematical analysis. [They] want students to encounter, understand, and use the main concepts and methods of multivariable calculus and to see how they extend the simpler objects and ideas of elementary calculus ... [They] assume that students have the "usual" one-year, single-variable calculus preparation, but little or nothing more than that.-About this preliminary ed













MAA Notes


Book Description




Advanced Calculus (Revised Edition)


Book Description

An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.




Student Assessment in Calculus


Book Description

It doesn't matter whether you teach a reform or traditional course, whether you have large or small sections, or whether you use lectures or laboratories. The bottom line is the same: When all is said and done, what counts is what our students understand. And that's what Student Assessment in Calculus is about. - Back cover.




UMAP Modules


Book Description




Research in Collegiate Mathematics Education IV


Book Description

This fourth volume of Research in Collegiate Mathematics Education (RCME IV) reflects the themes of student learning and calculus. Included are overviews of calculus reform in France and in the U.S. and large-scale and small-scale longitudinal comparisons of students enrolled in first-year reform courses and in traditional courses. The work continues with detailed studies relating students' understanding of calculus and associated topics. Direct focus is then placed on instruction and student comprehension of courses other than calculus, namely abstract algebra and number theory. The volume concludes with a study of a concept that overlaps the areas of focus, quantifiers. The book clearly reflects the trend towards a growing community of researchers who systematically gather and distill data regarding collegiate mathematics' teaching and learning. This series is published in cooperation with the Mathematical Association of America.




Enhancing Undergraduate Learning with Information Technology


Book Description

Enhancing Undergraduate Learning with Information Technology reports on a meeting of scientists, policy makers, and researchers convened to discuss new approaches to undergraduate science, mathematics, and technology education. The goal of the workshop was to inform workshop participants and the public about issues surrounding the use of information technology in education. To reach this goal, the workshop participants paid particular attention to the following issues: What educational technologies currently exist and how they are being used to transform undergraduate science, engineering, mathematics, and technology education; What is known about the potential future impact of information technology on teaching and learning at the undergraduate level; How to evaluate the impact of information technology on teaching and learning; and What the future might hold.




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