Calculus: The Analysis of Functions - Softcover

Taylor, Peter D.

9780921332374: Calculus: The Analysis of Functions

Softcover

ISBN 10: 0921332378 ISBN 13: 9780921332374

Publisher: Wall & Emerson, Inc., 1992

This is a Calculus text with a difference. The focus is on concepts and on problems and approaches to solving them, rather than on the techniques and methods of Calculus. The subject matter is that of introductory, single-variable Calculus, but with a heavy emphasis on intuitive inferences from graphing, and includes a chapter on probability. This is a groundbreaking text in the Calculus Reform movement.

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About the Author:

Peter D. Taylor is Professor of Mathematics and Biology at Queen's University in Canada. He earned his Ph.D. in mathematics at Harvard University in 1969. He research interests center around genetic models of animal behavior. He has been Governor for Canada of the Mathematical Association of America, and received the first Distinguished Teaching Award of the Mathematical Association of America, Seaway Section in 1992.

Review:

Peter Taylor ... has designed a calculus course that emphasizes the concepts of calculus far more than the symbolic manipulations.... Instructors who want to adopt an interactive teaching style will find this book with its marvelous collection of problems extremely helpful, and their students will learn to think more about the concepts of calculus. -- Andrew M. Gleason, Hollis Professor of Mathematics and Natural Philosophy, Harvard University

This book is the result of a rethink about the teaching of calculus to college and high school students, a fresh approach that focuses on the concepts and the problems. It is an interesting book and one that will be appreciated by teachers. The author, who is Professor of Mathematics and Biology at Queens University, is a senior figure in mathematics education in Canada. A new approach to calculus from such a source must obviously be of interest to teachers.

The approach is relaxed and leisurely, aimed at building up students' understanding of concepts before hitting them with techniques. Thus, the first chapter is devoted to a variety of pre-calculus problems in preparation for the more formal work which follows. Throughout the book there is a wealth of lovely examples.

This book is a statement about how calculus might better be taught and it contains any amount of good material. If ever you were seeking inspiration for an exciting lesson, this would be a good place to look. I also think it will be very valuable in teaching training. Its careful approach to concept building and to the process of doing mathematics will be particularly helpful to those who might otherwise unwittingly gloss over their future students' problems. -- Mathematics in Education and Industry

This book sets out an introductory course in the analysis of functions. On the whole, the course is intended to fit the first two semesters of college calculus. The approach differs from traditional calculus courses in perhaps three ways: It emphasizes applications to the physical and behavioral sciences, particularly the basic ideas of mathematical modeling. The author tried to choose examples that relate to the students' experience. It emphasizes qualitative analysis of functions, especially how to draw the right picture and use it to guide the analysis, or how to solve an optimization problem given only the function graph. It attempts to be a process-based curriculum; that is, the material and the problems are primarily chosen with any eye to engaging the student in the process of doing mathematics through such things as classroom activity, small group work, project work, problem solving, reading and writing. -- Fachinformationszentrum Karlsruhe

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