Vector and Geometric Calculus (Geometric Algebra & Calculus) - Softcover

Alan Macdonald

Softcover

ISBN 10: 1480132454 ISBN 13: 9781480132450

Publisher: CreateSpace Independent Publishing Platform, 2012

Synopsis

This textbook for the undergraduate vector calculus course presents a unified treatment of vector and geometric calculus.

This is the printing of July 2026.The discussion of parameter requirements on p. 49 has been improved. The new one page Section 4.2, Tangent Spaces, is a significant improvement. It defines and proves quickly the basic properties of tangent
spaces of all dimensions. I’ve added a discussion of continuity of functions on manifolds (p. 49). All errors known to me have been corrected

The book is a sequel to the text Linear and Geometric Algebra by the same author. That text is a prerequisite for this one. Its web page is at faculty.luther.edu/~macdonal/laga.

Linear algebra and vector calculus have provided the basic vocabulary of mathematics in dimensions greater than one for the past one hundred years. Just as geometric algebra generalizes linear algebra in powerful ways, geometric calculus generalizes vector calculus in powerful ways.

Traditional vector calculus topics are covered, as they must be, since readers will encounter them in other texts and out in the world.

Differential geometry is used today in many disciplines. A final chapter is devoted to it.

Download the book's table of contents, preface, and index at the book's web site: faculty.luther.edu/~macdonal/vagc.

From a review of Linear and Geometric Algebra:
Alan Macdonald's text is an excellent resource if you are just beginning the study of geometric algebra and would like to learn or review traditional linear algebra in the process. The clarity and evenness of the writing, as well as the originality of presentation that is evident throughout this text, suggest that the author has been successful as a mathematics teacher in the undergraduate classroom. This carefully crafted text is ideal for anyone learning geometric algebra in relative isolation, which I suspect will be the case for many readers.
-- Jeffrey Dunham, William R. Kenan Jr. Professor of Natural Sciences, Middlebury College

About this title

About the Author

Alan Macdonald is Professor Emeritus of Mathematics at Luther College in Decorah Iowa. He received a PhD in mathematics from The University of Michigan in 1970. His research interests include geometric algebra and the foundations of physics. His web page is at faculty.luther.edu/~macdonal.

Edition details

• Publisher: CreateSpace Independent Publishing Platform
• Publication date: 2012
• Language: English
• ISBN 10: 1480132454
• ISBN 13: 9781480132450
• Binding: Paperback
• Number of pages: 211