An Introduction to Analysis 1st Edition by Robert C Gunning ISBN 0691178798 9780691178790

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ISBN 10: 0691178798
ISBN 13: 9780691178790
Author: Robert C Gunning

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

An Introduction to Analysis 1st Edition Table of contents:

1 Algebraic Fundamentals
1.1 Sets and Numbers
1.2 Groups, Rings, and Fields
1.3 Vector Spaces
2 Topological Fundamentals
2.1 Normed Spaces
2.2 Metric Spaces
2.3 Topological Spaces
2.4 Compact Sets
3 Mappings
3.1 Continuous Mappings
3.2 Differentiable Mappings
3.3 Analytic Mappings
4 Linear Mappings
4.1 Endomorphisms
4.2 Inner Product Spaces
5 Geometry of Mappings
5.1 Inverse Mapping Theorem
5.2 Implicit Function Theorem
5.3 Rank Theorem
6 Integration
6.1 Riemann Integral
6.2 Calculation of Integrals
7 Differential Forms
7.1 Line Integrals
7.2 Differential Forms
7.3 Integrals of Differential Forms
Index

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Tags: Robert C Gunning, Introduction, Analysis