Fundamental Mathematical Analysis. 1st ed. 2020

種類:

電子ブック

責任表示:

by Robert Magnus

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2020

著者名:

• Magnus, Robert.
• SpringerLink (Online service)

シリーズ名:

Springer Undergraduate Mathematics Series ;

ISBN:

9783030463212 [3030463214]    

注記:

1 Introduction -- 2 Real Numbers -- 3 Sequences and Series -- 4 Functions and Continuity -- 5 Derivatives and Differentiation -- 6 Integrals and Integration -- 7 The Elementary Transcendental Functions -- 8 The Techniques of Integration -- 9 Complex Numbers -- 10 Complex Sequences and Series -- 11 Function Sequences and Function Series -- 12 Improper Integrals -- Index.
This textbook offers a comprehensive undergraduate course in real analysis in one variable. Taking the view that analysis can only be properly appreciated as a rigorous theory, the book recognises the difficulties that students experience when encountering this theory for the first time, carefully addressing them throughout. Historically, it was the precise description of real numbers and the correct definition of limit that placed analysis on a solid foundation. The book therefore begins with these crucial ideas and the fundamental notion of sequence. Infinite series are then introduced, followed by the key concept of continuity. These lay the groundwork for differential and integral calculus, which are carefully covered in the following chapters. Pointers for further study are included throughout the book, and for the more adventurous there is a selection of "nuggets", exciting topics not commonly discussed at this level. Examples of nuggets include Newton's method, the irrationality of π, Bernoulli numbers

ローカル注記:

学内専用E-BOOKS (local access only)