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＜電子ブック＞
From Calculus to Analysis / by Steen Pedersen

版	1st ed. 2015.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2015
大きさ	XIX, 342 p. 48 illus., 14 illus. in color : online resource
著者標目	*Pedersen, Steen author SpringerLink (Online service)
件　名	LCSH:Integral equations LCSH:Algebra LCSH:Mathematical analysis FREE:Integral Equations FREE:Algebra FREE:Analysis
一般注記	Part I -- Limits -- Introduction to Continuity -- Sets of Real Numbers -- Counting -- Continuity -- Derivatives and their Applications -- The Riemann Integral -- The Logarithm and the Exponential Function -- Part II -- Convergence of Sequences -- Series -- Trigonometric Functions and Applications -- Fourier Series -- Topology -- Appendices This textbook features applications including a proof of the Fundamental Theorem of Algebra, space filling curves, and the theory of irrational numbers.  In addition to the standard results of advanced calculus, the book  contains several interesting applications of these results. The text is intended to form a bridge between calculus and analysis. It is based on the authors lecture notes used and revised nearly every year over the last decade. The book contains numerous illustrations and cross references throughout, as well as exercises with solutions at the end of each section HTTP:URL=https://doi.org/10.1007/978-3-319-13641-7

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