The book contains a rigorous exposition of calculus of a single real variable. It covers the standard topics of an introductory analysis course, namely, functions, continuity, differentiability, sequences and series of numbers, sequences and series of functions, and integration. A direct treatment of the Lebesgue integral, based solely on the concept of absolutely convergent series, is presented, which is a unique feature of a textbook at this level. The standard material is complemented by topics usually not found in
comparable textbooks, for example, elementary functions are rigorously defined and their properties are carefully derived and an introduction to Fourier series is presented as an example of application of the Lebesgue integral.
The text is for a post-calculus course for students majoring in mathematics or mathematics education. It will provide students with a solid background for further studies in analysis, deepen their understanding of calculus, and provide sound training in rigorous mathematical proof.
By:
Piotr Mikusinski (Univ Of Central Florida Usa), Jan Mikusinski (.) Imprint: World Scientific Publishing Co Pte Ltd Country of Publication: Singapore ISBN:9789813202610 ISBN 10: 9813202610 Pages: 320 Publication Date:17 February 2017 Audience:
College/higher education
,
Professional and scholarly
,
Primary
,
Undergraduate
Format:Hardback Publisher's Status: Active