Advanced Calculus of a Single Variable - Hardcover

Geveci, Tunc

 
9783319278063: Advanced Calculus of a Single Variable
Hardcover
ISBN 10: 3319278061 ISBN 13: 9783319278063
Publisher: Springer, 2016

Synopsis

This advanced undergraduate textbook is based on a one-semester course on single variable calculus that the author has been teaching at San Diego State University for many years. The aim of this classroom-tested book is to deliver a rigorous discussion of the concepts and theorems that are dealt with informally in the first two semesters of a beginning calculus course. As such, students are expected to gain a deeper understanding of the fundamental concepts of calculus, such as limits (with an emphasis on ε-δ definitions), continuity (including an appreciation of the difference between mere pointwise and uniform continuity), the derivative (with rigorous proofs of various versions of L’Hôpital’s rule) and the Riemann integral (discussing improper integrals in-depth, including the comparison and Dirichlet tests). 

Success in this course is expected to prepare students for more advanced courses in real and complex analysis and this book willhelp to accomplish this. The first semester of advanced calculus can be followed by a rigorous course in multivariable calculus and an introductory real analysis course that treats the Lebesgue integral and metric spaces, with special emphasis on Banach and Hilbert spaces.

"synopsis" may belong to another edition of this title.

About the Author

Tunc Geveci is Professor Emeritus in the Department of Mathematics & Statistics at San Diego State University. His main publications have been in the fields of partial differential equations, numerical analysis, and the calculus of variations and optimal control.

From the Back Cover

This advanced undergraduate textbook is based on a one-semester course on single variable calculus that the author has been teaching at San Diego State University for many years. The aim of this classroom-tested book is to deliver a rigorous discussion of the concepts and theorems that are dealt with informally in the first two semesters of a beginning calculus course. As such, students are expected to gain a deeper understanding of the fundamental concepts of calculus, such as limits (with an emphasis on ε-δ definitions), continuity (including an appreciation of the difference between mere pointwise and uniform continuity), the derivative (with rigorous proofs of various versions of L’Hôpital’s rule) and the Riemann integral (discussing improper integrals in-depth, including the comparison and Dirichlet tests). 

Success in this course is expected to prepare students for more advanced courses in real and complex analysis and this book willhelp to accomplish this. The first semester of advanced calculus can be followed by a rigorous course in multivariable calculus and an introductory real analysis course that treats the Lebesgue integral and metric spaces, with special emphasis on Banach and Hilbert spaces.

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
2016
Language
English
ISBN 10 
3319278061
ISBN 13 
9783319278063
Binding
Hardcover
Edition number
1
Number of pages
394

Other Popular Editions of the Same Title

9783319802206: Advanced Calculus of a Single Variable

Featured Edition

ISBN 10:  3319802208 ISBN 13:  9783319802206
Publisher: Springer, 2018
Softcover