Advanced Calculus of a Single Variable - Hardcover

Geveci, Tunc

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

Inhaltsangabe

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.

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Über die Autorin bzw. den Autor

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.

Von der hinteren Coverseite

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.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Springer
Erscheinungsdatum
2016
Sprache
Englisch
ISBN 10 
3319278061
ISBN 13 
9783319278063
Einband
Gebundene Ausgabe
Auflage
1
Anzahl der Seiten
394
Kontakt zum Hersteller
ProductSafety@springernature.com
ProductSafety@springernature.com

Poststr. 9
Darmstadt
64293
Deutschland

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