A First Course in Analysis

This concise text clearly presents the material needed for year-long analysis courses for advanced undergraduates or beginning graduates.

John B. Conway (Author)

9781107173149, Cambridge University Press

Hardback, published 25 July 2017

375 pages
26 x 18.4 x 2 cm, 0.92 kg

'This book is an excellent textbook on analysis from a well-known author. It is addressed to undergraduate students and will be useful for lecturers as well. The presentation is reader-friendly and a student reading it can feel as if the material is presented by the favorite teacher. The book is well-marked with accents: immediately it is clear if this is an important definition or theorem, or if it is a technical phrase. Most proofs of statements are completely clear and concise. The parts of proofs left as exercises to the reader require a careful study of the material.' Ivan Podvigin, zbMATH

This rigorous textbook is intended for a year-long analysis or advanced calculus course for advanced undergraduate or beginning graduate students. Starting with detailed, slow-paced proofs that allow students to acquire facility in reading and writing proofs, it clearly and concisely explains the basics of differentiation and integration of functions of one and several variables, and covers the theorems of Green, Gauss, and Stokes. Minimal prerequisites are assumed, and relevant linear algebra topics are reviewed right before they are needed, making the material accessible to students from diverse backgrounds. Abstract topics are preceded by concrete examples to facilitate understanding, for example, before introducing differential forms, the text examines low-dimensional examples. The meaning and importance of results are thoroughly discussed, and numerous exercises of varying difficulty give students ample opportunity to test and improve their knowledge of this difficult yet vital subject.

1. The real numbers
2. Differentiation
3. Integration
4. Sequences of functions
5. Metric and Euclidean spaces
6. Differentiation in higher dimensions
7. Integration in higher dimensions
8. Curves and surfaces
9. Differential forms.

Subject Areas: Complex analysis, complex variables [PBKD], Real analysis, real variables [PBKB]