A First Course in Analysis

Erscheinungsjahr 2017
ISBN: 978-1-107-17314-9
Verlag: Cambridge University Press

Buch, Englisch, 375 Seiten, Format (B × H): 183 mm x 260 mm, Gewicht: 868 g

Reihe: Cambridge Mathematical Textbooks

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.

Autoren/Hrsg.

Conway, John B.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis

Inhaltsverzeichnis

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.

Über Autor(innen)

Conway, John B.
John B. Conway is Professor Emeritus of Mathematics at George Washington University, Washington DC. He is the author of eleven books, including Mathematical Connections: A Capstone Course (2010), A Course in Functional Analysis (2010), and the two-volume Functions of One Complex Variable (1995).