000			02459cam a2200277M 4500
003			OCoLC
005			20251211151628.0
008			200803s2020 xx o 000 0 eng d
020			_a9783030463212
020			_a3030463214
020			_z3030463206
020			_z9783030463205
041			_aEnglish
049			_aMAIN
082			_a515.35 _bMAG
100	1		_aMagnus, Robert
245	1	0	_aFundamental mathematical analysis / _cRobert Magnus
260			_aSwitzerland : _bSpringer, Cham, _c2020.
300			_axx, 433 pages :
505			_a1 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.
520			_aThis 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 pi, Bernoulli numbers, and the Gamma function. Based on decades of teaching experience, this book is written with the undergraduate student in mind. A large number of exercises, many with hints, provide the practice necessary for learning, while the included "nuggets" provide opportunities to deepen understanding and broaden horizons.
856	4	0	_uhttps://ezproxy.lib.gla.ac.uk/login?url=https://link.springer.com/10.1007/978-3-030-46321-2
856	4	0	_zConnect to resource
907			_a.b36417488
942			_2ddc _cBOOKS
999			_c46358 _d46358