An Introduction to Analysis

Robert C. Gunning

ISBN 10: 0691178798 / ISBN 13: 9780691178790

Verlag: Princeton University Press, US, 2018

Beschreibung

An essential undergraduate textbook on algebra, topology, and calculusAn Introduction to Analysis is an essential primer on basic results in algebra, topology, and calculus for undergraduate students considering advanced degrees in mathematics. Ideal for use in a one-year course, this unique textbook also introduces students to rigorous proofs and formal mathematical writing--skills they need to excel.With a range of problems throughout, An Introduction to Analysis treats n-dimensional calculus from the beginning-differentiation, the Riemann integral, series, and differential forms and Stokes's theorem-enabling students who are serious about mathematics to progress quickly to more challenging topics. The book discusses basic material on point set topology, such as normed and metric spaces, topological spaces, compact sets, and the Baire category theorem. It covers linear algebra as well, including vector spaces, linear mappings, Jordan normal form, bilinear mappings, and normal mappings.Proven in the classroom, An Introduction to Analysis is the first textbook to bring these topics together in one easy-to-use and comprehensive volume.Provides a rigorous introduction to calculus in one and several variablesIntroduces students to basic topologyCovers topics in linear algebra, including matrices, determinants, Jordan normal form, and bilinear and normal mappingsDiscusses differential forms and Stokes's theorem in n dimensionsAlso covers the Riemann integral, integrability, improper integrals, and series expansions.

Bestandsnummer des Verkäufers LU-9780691178790

Bibliografische Details

• Titel: An Introduction to Analysis
• Verlag: Princeton University Press, US
• Erscheinungsjahr: 2018
• Sprache: Englisch
• ISBN-10: 0691178798
• ISBN-13: 9780691178790
• Einband: Hardback
• Zustand: New
• Gewicht: 907 Gramm

Über diesen Titel

Inhaltsangabe

An essential undergraduate textbook on algebra, topology, and calculus

An Introduction to Analysis is an essential primer on basic results in algebra, topology, and calculus for undergraduate students considering advanced degrees in mathematics. Ideal for use in a one-year course, this unique textbook also introduces students to rigorous proofs and formal mathematical writing--skills they need to excel.

With a range of problems throughout, An Introduction to Analysis treats n-dimensional calculus from the beginning―differentiation, the Riemann integral, series, and differential forms and Stokes's theorem―enabling students who are serious about mathematics to progress quickly to more challenging topics. The book discusses basic material on point set topology, such as normed and metric spaces, topological spaces, compact sets, and the Baire category theorem. It covers linear algebra as well, including vector spaces, linear mappings, Jordan normal form, bilinear mappings, and normal mappings.

Proven in the classroom, An Introduction to Analysis is the first textbook to bring these topics together in one easy-to-use and comprehensive volume.

• Provides a rigorous introduction to calculus in one and several variables
• Introduces students to basic topology
• Covers topics in linear algebra, including matrices, determinants, Jordan normal form, and bilinear and normal mappings
• Discusses differential forms and Stokes's theorem in n dimensions
• Also covers the Riemann integral, integrability, improper integrals, and series expansions

Über die Autorin bzw. den Autor

Robert C. Gunning is professor of mathematics at Princeton University. His books include Lectures on Riemann Surfaces and Lectures on Complex Analytic Varieties (both Princeton).