000			03228nam a2200445 i 4500
001			OTLid0000243
003			MnU
005			20241120064010.0
006			m o d s
007			cr
008			180907s2016 mnu o 0 0 eng d
020			_a9781365605529
040			_aMnU _beng _cMnU
050		4	_aQA1
050		4	_aQA37.3
050		4	_aQA299.6-433
100	1		_aLafferriere, Beatriz _eauthor
245	0	0	_aIntroduction to Mathematical Analysis I _cBeatriz Lafferriere
250			_aSecond Edition
264		2	_aMinneapolis, MN _bOpen Textbook Library
264		1	_a[Place of publication not identified] _bPortland State University Library _c[2016]
264		4	_c©2016.
300			_a1 online resource
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	0		_aOpen textbook library.
505	0		_a1 Tools for Analysis -- 2 Sequences -- 3 Limits and Continuity -- 4 Differentiation -- 5 Solutions and Hints for Selected Exercises
520	0		_aOur goal with this textbook is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs. The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. The lecture notes also contain many well-selected exercises of various levels. Although these topics are written in a more abstract way compared with those available in some textbooks, teachers can choose to simplify them depending on the background of the students. For instance, rather than introducing the topology of the real line to students, related topological concepts can be replaced by more familiar concepts such as open and closed intervals. Some other topics such as lower and upper semicontinuity, differentiation of convex functions, and generalized differentiation of non-differentiable convex functions can be used as optional mathematical projects. In this way, the lecture notes are suitable for teaching students of different backgrounds. The second edition includes a number of improvements based on recommendations from students and colleagues and on our own experience teaching the course over the last several years. In this edition we streamlined the narrative in several sections, added more proofs, many examples worked out in detail, and numerous new exercises. In all we added over 50 examples in the main text and 100 exercises (counting parts).
542	1		_fAttribution-NonCommercial
546			_aIn English.
588	0		_aDescription based on online resource
650		0	_aMathematics _vTextbooks
650		0	_aApplied mathematics _vTextbooks
650		0	_aAnalysis _vTextbooks
700	1		_aLafferriere, Gerardo _eauthor
700	1		_aNguyen, Mau Nam _eauthor
710	2		_aOpen Textbook Library _edistributor
856	4	0	_uhttps://open.umn.edu/opentextbooks/textbooks/243 _zAccess online version
999			_c38507 _d38507