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001			on1091029414
003			OCoLC
005			20220908100155.0
006			m o d
007			cr cnu---unuuu
008			190401s2019 njua ob 001 0 eng d
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020			_a9780691189161 _q(electronic bk.)
020			_a0691189161 _q(electronic bk.)
020			_z0691181314
020			_z9780691181318
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029	1		_aAU@ _b000068214775
035			_a(OCoLC)1091029414
037			_a22573/ctvc5q6hj _bJSTOR
037			_a9453319 _bIEEE
050		4	_aQA21
072		7	_aMAT _x039000 _2bisacsh
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082	0	4	_a510.9 _223
049			_aMAIN
100	1		_aBressoud, David M., _d1950- _eauthor. _965306
245	1	0	_aCalculus reordered : _ba history of the big ideas / _cDavid M. Bressoud.
264		1	_aPrinceton, New Jersey : _bPrinceton University Press, _c[2019]
300			_a1 online resource (xvi, 224 pages) : _billustrations
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
520	8		_aCalculus Reordered takes readers on a remarkable journey through hundreds of years to tell the story of how calculus grew to what we know today. David Bressoud explains why calculus is credited to Isaac Newton and Gottfried Leibniz in the seventeenth century, and how its current structure is based on developments that arose in the nineteenth century. Bressoud argues that a pedagogy informed by the historical development of calculus presents a sounder way for students to learn this fascinating area of mathematics. Delving into calculus's birth in the Hellenistic Eastern Mediterranean--especially Syracuse in Sicily and Alexandria in Egypt--as well as India and the Islamic Middle East, Bressoud considers how calculus developed in response to essential questions emerging from engineering and astronomy. He looks at how Newton and Leibniz built their work on a flurry of activity that occurred throughout Europe, and how Italian philosophers such as Galileo Galilei played a particularly important role. In describing calculus's evolution, Bressoud reveals problems with the standard ordering of its curriculum: limits, differentiation, integration, and series. He contends instead that the historical order--which follows first integration as accumulation, then differentiation as ratios of change, series as sequences of partial sums, and finally limits as they arise from the algebra of inequalities--makes more sense in the classroom environment. Exploring the motivations behind calculus's discovery, Calculus Reordered highlights how this essential tool of mathematics came to be.
504			_aIncludes bibliographical references and index.
588	0		_aOnline resource; title from PDF title page (EBSCO, April 2, 2019).
588	0		_aPrint version record.
505	0		_aCover; Contents; Preface; Chapter 1. Accumulation; 1.1. Archimedes and the Volume of the Sphere; 1.2. The Area of the Circle and the Archimedean Principle; 1.3. Islamic Contributions; 1.4. The Binomial Theorem; 1.5. Western Europe; 1.6. Cavalieri and the Integral Formula; 1.7. Fermat's Integral and Torricelli's Impossible Solid; 1.8. Velocity and Distance; 1.9. Isaac Beeckman; 1.10. Galileo Galilei and the Problem of Celestial Motion; 1.11. Solving the Problem of Celestial Motion; 1.12. Kepler's Second Law; 1.13. Newton's Principia; Chapter 2. Ratios of Change; 2.1. Interpolation
505	8		_a2.2. Napier and the Natural Logarithm; 2.3. The Emergence of Algebra; 2.4. Cartesian Geometry; 2.5. Pierre de Fermat; 2.6. Wallis's Arithmetic of Infinitesimals; 2.7. Newton and the Fundamental Theorem; 2.8. Leibniz and the Bernoullis; 2.9. Functions and Differential Equations; 2.10. The Vibrating String; 2.11. The Power of Potentials; 2.12. The Mathematics of Electricity and Magnetism; Chapter 3. Sequences of Partial Sums; 3.1. Series in the Seventeenth Century; 3.2. Taylor Series; 3.3. Euler's Influence; 3.4. D'Alembert and the Problem of Convergence; 3.5. Lagrange Remainder Theorem
505	8		_aTeaching Series as Sequences of Partial Sums; Teaching Limits as the Algebra of Inequalities; The Last Word; Notes; Bibliography; Index; Image Credits
590			_aIEEE _bIEEE Xplore Princeton University Press eBooks Library
650		0	_aCalculus. _965307
650		0	_aMathematics _xHistory. _963890
650		6	_aCalcul infinit�esimal. _965308
650		6	_aMath�ematiques _xHistoire. _963893
650		7	_acalculus. _2aat _965309
650		7	_aMATHEMATICS _xEssays. _2bisacsh _964120
650		7	_aMATHEMATICS _xPre-Calculus. _2bisacsh _964121
650		7	_aMATHEMATICS _xReference. _2bisacsh _964122
650		7	_aMATHEMATICS _xCalculus. _2bisacsh _916300
650		7	_aCalculus. _2fast _0(OCoLC)fst00844119 _965307
650		7	_aMathematics. _2fast _0(OCoLC)fst01012163 _911584
655		0	_aElectronic books. _93294
655		4	_aElectronic books. _93294
655		7	_aHistory. _2fast _0(OCoLC)fst01411628 _95289
776	0	8	_iPrint version: _aBRESSOUD, DAVID M. _tCALCULUS REORDERED. _d[Place of publication not identified], PRINCETON University PRES, 2019 _z0691181314 _w(OCoLC)1059262130
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