A First Course in Analysis

Inbunden, Engelska, 2017

Del i serien Cambridge Mathematical Textbooks

541 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2017-07-25
Mått:184 x 260 x 20 mm
Vikt:920 g
Format:Inbunden
Språk:Engelska
Serie:Cambridge Mathematical Textbooks
Antal sidor:358
Förlag:Cambridge University Press
ISBN:9781107173149

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Mer om författaren

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).

Recensioner i media

'This is an excellent text for a first course in analysis in one and several variables for students who know some linear algebra. The book starts with the real numbers, does differentiation and integration first in one variable, then in several, and finally covers differential forms and Stokes' theorem. The style is friendly and conversational, and hews to the principal of going from the specific to the general, making it a pleasure to read.' John McCarthy, Washington University, St. Louis

Innehållsförteckning

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.