Basic Insights in Vector Calculus: With a Supplement on Mathematical Understanding - Hardcover

Terrance J Quinn; Zine Boudhraa; Sanjay Rai

Hardcover

ISBN 10: 9811222568 ISBN 13: 9789811222566

Publisher: World Scientific Publishing Co, 2020

Synopsis

Basic Insights in Vector Calculus provides an introduction to three famous theorems of vector calculus, Green's theorem, Stokes' theorem and the divergence theorem (also known as Gauss's theorem). Material is presented so that results emerge in a natural way. As in classical physics, we begin with descriptions of flows. The book will be helpful for undergraduates in Science, Technology, Engineering and Mathematics, in programs that require vector calculus. At the same time, it also provides some of the mathematical background essential for more advanced contexts which include, for instance, the physics and engineering of continuous media and fields, axiomatically rigorous vector analysis, and the mathematical theory of differential forms. There is a Supplement on mathematical understanding. The approach invites one to advert to one's own experience in mathematics and, that way, identify elements of understanding that emerge in all levels of learning and teaching. Prerequisites are competence in single-variable calculus. Some familiarity with partial derivatives and the multi-variable chain rule would be helpful. But for the convenience of the reader we review essentials of single- and multi-variable calculus needed for the three main theorems of vector calculus. Carefully developed Problems and Exercises are included, for many of which guidance or hints are provided.

About this title

About the Author

Terrance J Quinn got his PhD in 1992 (mathematics). His post-doctoral positions were in Ireland (Trinity College (1992 1993), and University College Cork (1993 1995). He went on to faculty positions at Texas A&M International (1995 2001), Ohio University Southern (2001 2006), and Middle Tennessee State University (MTSU) (2006 2018)). While at Ohio University Southern, Quinn won the Outstanding Professor of the Year Award for Ohio University Regional Higher Education, as well as Faculty of the Year Award at Ohio University Southern Campus.

Zine Boudhraa joined the Department of Mathematics at the Rockville Campus in August 1998. He received his M.A. from the University of Maryland at College Park and his PhD from Kent State University in Ohio. Dr Boudhraa served seven years as Math Science Center Faculty Coordinator, three years as Math Program Coordinator, and two years as Developmental Mathematics Coordinator.

Sanjay Rai currently serves as the Senior Vice President for Academic Affairs at Montgomery College in Maryland. He has had a distinguished academic career as faculty, chair, dean, and vice president/provost, amassing student and institutional successes along the way. He was the principal investigator (PI) on the Project Portal to Success in Engineering, a federal FIPSE grant, as well as co-PI for the ACCESS Engineering grant for from the National Science Foundation, for S-STEM (Scholarships in Science, Technology, Engineering and Mathematics).

Edition details

• Publisher: World Scientific Publishing Co
• Publication date: 2020
• Language: English
• ISBN 10: 9811222568
• ISBN 13: 9789811222566
• Binding: Hardcover
• Number of pages: 252