5513:
2690:
198:
239:
5525:
341:
5549:
5537:
2470:, and even images, Fourier analysis can isolate individual components of a compound waveform, concentrating them for easier detection or removal. A large family of signal processing techniques consist of Fourier-transforming a signal, manipulating the Fourier-transformed data in a simple way, and reversing the transformation.
2193:
Scalar analysis is a branch of mathematical analysis dealing with values related to scale as opposed to direction. Values such as temperature are scalar because they describe the magnitude of a value without regard to direction, force, or displacement that value may or may not have.
1848:
allow one (given the position, velocity, acceleration and various forces acting on the body) to express these variables dynamically as a differential equation for the unknown position of the body as a function of time. In some cases, this differential equation (called an
2119:
Modern numerical analysis does not seek exact answers, because exact answers are often impossible to obtain in practice. Instead, much of numerical analysis is concerned with obtaining approximate solutions while maintaining reasonable bounds on errors.
6351:
2081:
in a
Euclidean space, on which the Lebesgue measure cannot be defined consistently, are necessarily complicated in the sense of being badly mixed up with their complement. Indeed, their existence is a non-trivial consequence of the
2026:) additive: the measure of a 'large' subset that can be decomposed into a finite (or countable) number of 'smaller' disjoint subsets, is the sum of the measures of the "smaller" subsets. In general, if one wants to associate a
2123:
Numerical analysis naturally finds applications in all fields of engineering and the physical sciences, but in the 21st century, the life sciences and even the arts have adopted elements of scientific computations.
2879:
Infinite series were present in Greek mathematics, There is no question that Zeno's paradox of the dichotomy (Section 4.1), for example, concerns the decomposition of the number 1 into the infinite series
1002:
1840:
relation involving some continuously varying quantities (modeled by functions) and their rates of change in space or time (expressed as derivatives) is known or postulated. This is illustrated in
6296:
1503:
1263:
424:
used the method of exhaustion in the 3rd century CE to find the area of a circle. From Jain literature, it appears that Hindus were in possession of the formulae for the sum of the
3322:
Real analysis began its growth as an independent subject with the introduction of the modern definition of continuity in 1816 by the Czech mathematician
Bernard Bolzano (1781â1848)
1875:
of that set, intuitively interpreted as its size. In this sense, a measure is a generalization of the concepts of length, area, and volume. A particularly important example is the
6341:
1946:
1382:). Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Most precisely, a sequence can be defined as a
4646:
A Course Of Modern
Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; with an Account of the Principal Transcendental Functions
3295:
1180:
505:, he also estimated the magnitude of the error terms resulting of truncating these series, and gave a rational approximation of some infinite series. His followers at the
6346:
5587:
1340:
1087:
4676:
1043:
2061:
1985:
892:
1299:
1116:
2016:
1917:
956:
932:
912:
2263:, the study of Clifford valued functions that are annihilated by Dirac or Dirac-like operators, termed in general as monogenic or Clifford analytic functions.
5965:
6334:
5970:
3927:
4536:
3250:
5580:
1585:
Complex analysis (traditionally known as the "theory of functions of a complex variable") is the branch of mathematical analysis that investigates
5694:
3913:
6329:
4973:
3941:
2738:
1690:
acting upon these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of
376:, but many of its ideas can be traced back to earlier mathematicians. Early results in analysis were implicitly present in the early days of
225:
6147:
5573:
3031:
3137:
6192:
2977:
2835:
506:
3955:
4740:
5699:
3813:
2782:
1535:
Real analysis (traditionally, the "theory of functions of a real variable") is a branch of mathematical analysis dealing with the
6108:
4693:
604:
introduced the modern definition of continuity in 1816, but
Bolzano's work did not become widely known until the 1870s. In 1821,
2896:+ ... and that Archimedes found the area of the parabolic segment (Section 4.4) essentially by summing the infinite series 1 + â
683:, in which irrational numbers are formally defined, which serve to fill the "gaps" between rational numbers, thereby creating a
967:
560:, which grew, with the stimulus of applied work that continued through the 18th century, into analysis topics such as the
4669:
5709:
4251:
4229:
4207:
4185:
4139:
4117:
4095:
4073:
4051:
3987:
3899:
3867:
3845:
3795:
3773:
3009:
2864:
17:
3885:
3616:
3485:
3015:
6275:
5336:
161:
250:. Differential equations are an important area of mathematical analysis with many applications in science and engineering.
5729:
5724:
3792:
The
Fundamentals of Mathematical Analysis: International Series of Monographs in Pure and Applied Mathematics, Vol. 73-II
612:
widely used in earlier work, particularly by Euler. Instead, Cauchy formulated calculus in terms of geometric ideas and
5481:
4966:
4626:
4600:
4574:
4551:
4514:
4442:
4378:
4353:
4328:
4303:
4278:
4165:
3697:
3649:
3610:
3572:
3517:
3479:
3445:
3409:
3375:
3350:
3315:
3131:
2971:
2944:
2872:
2829:
1837:
2339:, where the lack of an additive inverse is compensated somewhat by the idempotent rule A + A = A.
5553:
2613:
704:
413:
218:
4070:
Problems and
Theorems in Analysis II: Theory of Functions. Zeros. Polynomials. Determinants. Number Theory. Geometry
6142:
5826:
5017:
4792:
4398:
3827:
2578:
2137:
538:
allowed him to determine the maxima and minima of functions and the tangents of curves. Descartes's publication of
4033:
1706:
etc. operators between function spaces. This point of view turned out to be particularly useful for the study of
1456:
5889:
5649:
5431:
4872:
4799:
3004:. Chinese studies in the history and philosophy of science and technology. Vol. 130. Springer. p. 279.
653:
498:
667:
Towards the end of the 19th century, mathematicians started worrying that they were assuming the existence of a
6400:
5816:
5529:
4782:
4658:
4406:
3544:
2528:
2125:
2034:
subset of a given set while satisfying the other axioms of a measure, one only finds trivial examples like the
565:
3095:
1191:
5821:
5714:
4959:
4787:
4733:
4418:
4402:
3564:
2813:
2733:
2392:
2254:
569:
6375:
5719:
5541:
4501:
4488:
3210:
Rajagopal, C. T.; Rangachari, M. S. (June 1978). "On an untapped source of medieval
Keralese Mathematics".
2718:
2159:
1539:
and real-valued functions of a real variable. In particular, it deals with the analytic properties of real
388:
211:
3713:
3246:
2540:
Foundation of
Analysis: The Arithmetic of Whole Rational, Irrational and Complex Numbers, by Edmund Landau
5761:
5456:
5012:
3969:
3770:
The
Fundamentals of Mathematical Analysis: International Series in Pure and Applied Mathematics, Volume 1
715:
545:
522:
The modern foundations of mathematical analysis were established in 17th century Europe. This began when
54:
312:, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from
6379:
5843:
5027:
4464:
4006:"Theory of functions of a real variable (Teoria functsiy veshchestvennoy peremennoy, chapters I to IX)"
2038:. This problem was resolved by defining measure only on a sub-collection of all subsets; the so-called
1845:
1120:
711:
548:, is considered to be the establishment of mathematical analysis. It would be a few decades later that
1922:
1670:
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of
6239:
6172:
6167:
6130:
5661:
5634:
5604:
5441:
5413:
5050:
2070:
1995:
176:
166:
156:
1675:
6096:
6091:
6000:
5960:
5676:
5486:
4726:
2912:. Both these examples are special cases of the result we express as summation of a geometric series
2518:
2437:
2218:
2133:
1129:
853:
452:
403:
made more explicit, but informal, use of the concepts of limits and convergence when they used the
2644:
Complex
Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable, by
1679:
1304:
1051:
6285:
5371:
5361:
5331:
5265:
5000:
4650:
4636:
2382:
2372:
2240:
2074:
1844:, where the motion of a body is described by its position and velocity as the time value varies.
1683:
502:
494:
490:
486:
474:
5921:
3307:
3299:
2433:
1010:
633:
391:. (Strictly speaking, the point of the paradox is to deny that the infinite sum exists.) Later,
6290:
6280:
6254:
6076:
6071:
6066:
6061:
6019:
5982:
5928:
5654:
5644:
5622:
5469:
5366:
5346:
5341:
5270:
4995:
4904:
4804:
4713:
4452:
3280:
2723:
2492:
2487:
2482:
2429:
2279:, which differs in some interesting and surprising ways from its real and complex counterparts.
2236:
2226:
2214:
2176:
1949:
1806:
1802:
1729:
1707:
1622:
1618:
1586:
1540:
1383:
959:
747:
668:
597:
561:
557:
305:
171:
146:
49:
3028:
2375:, which is developed from constructive logic like constructive analysis but also incorporates
1836:
Differential equations arise in many areas of science and technology, specifically whenever a
6207:
6187:
6125:
6054:
5833:
5811:
5686:
5496:
5426:
5303:
5227:
5166:
5151:
5146:
5005:
4897:
4892:
4856:
4852:
4777:
4640:
4158:
Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable
3637:
3391:
3121:
2713:
2703:
2523:
2508:
2425:
2362:
2282:
2046:
1862:
1789:
1761:
1687:
1649:
1371:
684:
609:
605:
373:
278:
247:
181:
2961:
2807:
1728:
Harmonic analysis is a branch of mathematical analysis concerned with the representation of
758:
greatly improved measure theory, and introduced his own theory of integration, now known as
6365:
6259:
6244:
6159:
6086:
6049:
6044:
6034:
5794:
5748:
5476:
5356:
5351:
5275:
5176:
4924:
4829:
4644:
4472:
3556:
3167:
2856:
2770:
2728:
2560:
2554:
2497:
2417:
2386:
2314:
2304:
2188:
2113:
2109:
1954:
1752:), and of their generalizations. Harmonic analysis has applications in areas as diverse as
1637:
1626:
935:
865:
818:
759:
719:
581:
478:
404:
348:
286:
141:
100:
69:
1814:
8:
6234:
6103:
6014:
5901:
5872:
5596:
5491:
5401:
5323:
5222:
5156:
5113:
5103:
5083:
4919:
4909:
4862:
3437:
2708:
2443:
2413:
2336:
2332:
2320:
2310:
2300:
2129:
1850:
1841:
1699:
1665:
1602:
1564:
1552:
1548:
1361:
1278:
1267:
1095:
849:
783:
775:
723:
656:
approach, thus founding the modern field of mathematical analysis. Around the same time,
577:
418:
360:
321:
317:
266:
262:
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4708:
3171:
2774:
743:
6371:
6024:
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5992:
5975:
5955:
5938:
5848:
5671:
5517:
5436:
5376:
5308:
5298:
5237:
5212:
5088:
5045:
5040:
4941:
4824:
4541:
4496:
4492:
4457:
4434:
4019:
3430:
3273:
3227:
3193:
3076:
3068:
2936:
2929:
2924:
2695:
2590:
2572:
2366:
2250:
2095:
2078:
2066:
2001:
1902:
1896:
1711:
1594:
941:
917:
897:
467:
460:
201:
105:
4413:. Vol. 1â3. Translated by Gould, S. H. (2nd ed.). Cambridge, Massachusetts:
6197:
5933:
5911:
5838:
5799:
5776:
5565:
5512:
5232:
5217:
5161:
5108:
4914:
4877:
4654:
4622:
4596:
4570:
4547:
4510:
4438:
4374:
4349:
4324:
4299:
4274:
4161:
4005:
3727:
3693:
3682:
3645:
3606:
3568:
3540:
3513:
3475:
3461:
3441:
3405:
3371:
3346:
3339:
3311:
3127:
3080:
3005:
2967:
2940:
2868:
2825:
2689:
2544:
2503:
2447:
2421:
2346:
2342:
2260:
2232:
1868:
1769:
1765:
1745:
1723:
1695:
1633:
1367:
810:
771:
692:
645:
608:
began to put calculus on a firm logical foundation by rejecting the principle of the
553:
540:
531:
425:
396:
392:
377:
325:
290:
282:
243:
197:
4020:"Theory of functions of a real variable =Teoria functsiy veshchestvennoy peremennoy"
3231:
2515:
that possess a complicated internal structure but behave in a simple manner locally.
238:
6115:
5906:
5894:
5877:
5855:
5804:
5756:
5617:
5446:
5421:
5293:
5141:
5078:
4867:
4847:
4702:
4528:
4414:
4048:
Problems and Theorems in Analysis I: Series. Integral Calculus. Theory of Functions
3598:
3345:. Walter Rudin Student Series in Advanced Mathematics (3rd ed.). McGrawâHill.
3219:
3197:
3188:
3183:
3175:
3060:
2817:
2621:
2608:
2584:
2354:
2350:
2290:
2286:
2035:
1876:
1749:
1703:
1645:
1580:
739:
700:
676:
657:
649:
637:
629:
573:
429:
381:
3928:"A Course of Higher Mathematics Vol 4 Integral and Partial Differential Equations"
6221:
6177:
6004:
5948:
5943:
5882:
5704:
5629:
5386:
5313:
5242:
5035:
4882:
4819:
4814:
4809:
4506:
3592:
3532:
3507:
3471:
3465:
3395:
3035:
2999:
2602:
2566:
2376:
2326:
2266:
2163:
2153:
2083:
1880:
1590:
1568:
1394:
1390:
833:
625:
601:
356:
123:
4694:
Earliest Known Uses of Some of the Words of Mathematics: Calculus & Analysis
4665:(vi+608 pages) (reprinted: 1935, 1940, 1946, 1950, 1952, 1958, 1962, 1963, 1992)
3096:"Summation of Convergent Geometric Series and the concept of approachable Sunya"
2617:
2257:
and the application of the theory of partial differential equations to geometry.
1994:
Technically, a measure is a function that assigns a non-negative real number or
5865:
5464:
5391:
5098:
4426:
3158:
Seal, Sir Brajendranath (1915), "The positive sciences of the ancient Hindus",
2657:
2651:
2639:
2627:
2596:
1773:
1741:
1691:
1614:
1090:
845:
755:
731:
727:
641:
593:
408:
301:
151:
1694:
and the formulation of properties of transformations of functions such as the
824:
Much of analysis happens in some metric space; the most commonly used are the
463:
6394:
6182:
6137:
6120:
5766:
5639:
5252:
5184:
5136:
4886:
4842:
4563:ĂlĂ©ments d'analyse rĂ©elle : CAPES et agrĂ©gation interne de mathĂ©matiques
3689:
2467:
2294:
2273:
2105:
2043:
1757:
1610:
1598:
1530:
829:
779:
767:
763:
613:
482:
76:
3914:"A Course of Higher Mathematics Vol 3-2 Complex Variables Special Functions"
3755:
3741:
726:), commonly known as "monsters", began to be investigated. In this context,
6202:
6081:
5860:
5771:
5666:
5194:
5189:
5093:
4610:
4584:
4566:
4524:
3425:
3334:
2757:
2645:
2633:
2548:
2478:
Techniques from analysis are used in many areas of mathematics, including:
2203:
2141:
1777:
1753:
1671:
860:
837:
800:
735:
688:
680:
549:
385:
329:
4951:
4092:
Mathematical Analysis: A Modern Approach to Advanced Calculus, 2nd Edition
3942:"A Course of Higher Mathematics Vol 5 Integration and Functional Analysis"
616:. Thus, his definition of continuity required an infinitesimal change in
407:
to compute the area and volume of regions and solids. The explicit use of
6313:
6229:
5396:
5060:
4983:
4618:
4592:
3667:
Vector and Tensor Analysis with Applications (Dover Books on Mathematics)
3588:
3401:
2663:
1818:
1795:
1641:
1536:
806:
672:
448:
297:
258:
114:
40:
2821:
750:. In the early 20th century, calculus was formalized using an axiomatic
687:
set: the continuum of real numbers, which had already been developed by
372:
Mathematical analysis formally developed in the 17th century during the
6249:
5381:
5260:
5055:
4772:
3223:
2760:
and Karl Stromberg, "Real and Abstract Analysis", Springer-Verlag, 1965
2675:
2511:, the application of calculus to specific mathematical spaces known as
2463:
1810:
1652:, complex analysis is widely applicable to two-dimensional problems in
751:
535:
433:
400:
344:
270:
119:
109:
4255:
4233:
4211:
4189:
4143:
4121:
4099:
4077:
4055:
3991:
3871:
3849:
3799:
3777:
3602:
3072:
3048:
580:. During this period, calculus techniques were applied to approximate
359:
with more and more sides. This was an early but informal example of a
6297:
The Unreasonable Effectiveness of Mathematics in the Natural Sciences
5612:
4480:
3179:
2101:
2023:
2019:
1988:
1826:
1387:
825:
527:
4487:
2656:
Functional Analysis: Introduction to Further Topics in Analysis, by
2428:
in particular. Examples of important differential equations include
5285:
5204:
5131:
4929:
4767:
4762:
4397:
3064:
2638:
Real Analysis: Measure Theory, Integration, and Hilbert Spaces, by
2512:
2323:â applies ideas from analysis and topology to set-valued functions.
2222:
2144:
are essential in simulating living cells for medicine and biology.
2112:) for the problems of mathematical analysis (as distinguished from
1991:
is its length in the everyday sense of the wordâââspecifically, 1.
1798:
1560:
1556:
1544:
1519:
1355:
814:
661:
313:
309:
274:
91:
81:
2671:
Real and Functional Analysis, by Vladimir Bogachev, Oleg Smolyanov
2626:
Mathematical Analysis: A Modern Approach to Advanced Calculus, by
5070:
3370:. Undergraduate Texts in Mathematics. New York: Springer-Verlag.
1830:
1822:
1653:
1606:
841:
696:
648:. The contributions of these mathematicians and others, such as
436:
uses the sum of a geometric series in his Kalpasƫtra in 433
421:
86:
2404:
Techniques from analysis are also found in other areas such as:
534:, which is the precursor to modern calculus. Fermat's method of
340:
6352:
European Community on Computational Methods in Applied Sciences
5916:
5734:
4204:
Functional Analysis: Introduction to Further Topics in Analysis
2303:, the study of which parts of analysis can be carried out in a
1892:
1884:
1872:
1733:
600:. Real analysis began to emerge as an independent subject when
523:
456:
4136:
Real Analysis: Measure Theory, Integration, and Hilbert Spaces
3093:
2459:
6347:
International Council for Industrial and Applied Mathematics
3756:"ĐŃŃŃ ĐŽĐžŃŃĐ”ŃĐ”ĐœŃОалŃĐœĐŸĐłĐŸ Đž ĐžĐœŃДгŃĐ°Đ»ŃĐœĐŸĐłĐŸ ĐžŃŃĐžŃĐ»Đ”ĐœĐžŃ. ĐąĐŸĐŒ III"
3126:(3 ed.). Jones & Bartlett Learning. p. xxvii.
3001:
A comparison of Archimedes' and Liu Hui's studies of circles
1433:
running from 1 to infinity understood) the distance between
4698:
4459:
The foundations of analysis: a straightforward introduction
2244:
1888:
1737:
352:
3728:"ĐŃŃŃ ĐŽĐžŃŃĐ”ŃĐ”ĐœŃОалŃĐœĐŸĐłĐŸ Đž ĐžĐœŃДгŃĐ°Đ»ŃĐœĐŸĐłĐŸ ĐžŃŃĐžŃĐ»Đ”ĐœĐžŃ. ĐąĐŸĐŒ I"
3120:
Zill, Dennis G.; Wright, Scott; Wright, Warren S. (2009).
2559:
The Fundamentals of Mathematical Analysis (2 volumes), by
1593:. It is useful in many branches of mathematics, including
363:, one of the most basic concepts in mathematical analysis.
4748:
4471:
997:{\displaystyle d\colon M\times M\rightarrow \mathbb {R} }
3900:"A Course of Higher Mathematics Vol 2 Advanced Calculus"
2577:
A Course of Higher Mathematics (5 volumes, 6 parts), by
2253:
involves the use of geometrical methods in the study of
1871:
is a systematic way to assign a number to each suitable
1674:
endowed with some kind of limit-related structure (e.g.
417:, a work rediscovered in the 20th century. In Asia, the
4523:
3886:"A Course of Higher Mathematics Vol 3 1 Linear Algebra"
2601:
Theory of Functions of a Real Variable (2 volumes), by
1809:
that relates the values of the function itself and its
1420:
becomes very large. That is, for an abstract sequence (
762:, which proved to be a big improvement over Riemann's.
5595:
2668:
Analysis (3 volumes), by Herbert Amann, Joachim Escher
1400:
One of the most important properties of a sequence is
644:
and others studied partial differential equations and
5966:
Numerical methods for ordinary differential equations
2049:
2004:
1957:
1925:
1905:
1459:
1307:
1281:
1194:
1132:
1098:
1054:
1013:
970:
944:
920:
900:
868:
664:, and made significant advances in complex analysis.
296:
These theories are usually studied in the context of
6342:
Société de Mathématiques Appliquées et Industrielles
6335:
Japan Society for Industrial and Applied Mathematics
5971:
Numerical methods for partial differential equations
5685:
2998:
Dun, Liu; Fan, Dainian; Cohen, Robert Sonné (1966).
2685:
2175:, is a branch of mathematical analysis dealing with
1632:
Complex analysis is particularly concerned with the
509:
further expanded his works, up to the 16th century.
6158:
3684:
Theory and Application of Digital Signal Processing
3279:. The Mathematical Association of America. p.
3209:
2553:Differential and Integral Calculus (3 volumes), by
1412:) sequence has a limit if it approaches some point
4456:
4344:Bogachev, Vladimir I.; Smolyanov, Oleg G. (2021).
3681:
3429:
3338:
3272:
2928:
2565:A Course Of Mathematical Analysis (2 volumes), by
2055:
2010:
1979:
1940:
1911:
1817:. Differential equations play a prominent role in
1497:
1334:
1293:
1257:
1174:
1110:
1081:
1037:
996:
950:
926:
906:
886:
4343:
2763:
2345:â analysis of the idempotent semiring called the
1571:and related properties of real-valued functions.
466:used infinitesimal and used what is now known as
6392:
3664:
3119:
1461:
848:(which describes size rather than distance) and
844:. Examples of analysis without a metric include
501:. Alongside his development of Taylor series of
451:established a method that would later be called
4709:Mathematical Analysis â EncyclopĂŠdia Britannica
4635:
1404:. Informally, a sequence converges if it has a
695:. Around that time, the attempts to refine the
6330:Society for Industrial and Applied Mathematics
4411:Mathematics: Its Content, Methods, and Meaning
4294:Amann, Herbert; Escher, Joachim (2008-05-16).
2963:Infinitesimal Methods of Mathematical Analysis
2739:Timeline of calculus and mathematical analysis
2389:, rather than classical, logic and set theory.
2369:, rather than classical, logic and set theory.
2272:, the study of analysis within the context of
5581:
4967:
4734:
4699:Basic Analysis: Introduction to Real Analysis
2849:
2473:
703:led to the study of the "size" of the set of
459:in the 5th century. In the 12th century, the
219:
6148:Supersymmetric theory of stochastic dynamics
3384:
3046:
2595:Mathematical Analysis: A Special Course, by
1948:. For instance, the Lebesgue measure of the
1740:. This includes the study of the notions of
1648:parts of any analytic function must satisfy
1498:{\displaystyle \lim _{n\to \infty }a_{n}=x.}
620:to correspond to an infinitesimal change in
328:) or specific distances between objects (a
4981:
4318:
4293:
4268:
3878:
3679:
3537:Lectures on Ordinary Differential Equations
3454:
3049:"On the Use of Series in Hindu Mathematics"
2997:
2065:. This means that the empty set, countable
856:that need not have any sense of distance).
5588:
5574:
4974:
4960:
4741:
4727:
3636:
3549:
3418:
3304:The History of Mathematics: A Brief Course
3238:
2801:
2799:
1636:of complex variables (or, more generally,
821:) between elements of the set is defined.
507:Kerala School of Astronomy and Mathematics
226:
212:
3828:"A Course of Mathematical Analysis Vol 2"
3814:"A Course of Mathematical Analysis Vol 1"
3665:Borisenko, A. I.; Tarapov, I. E. (1979).
3187:
2917:
2855:
2329:, the study of convex sets and functions.
1928:
1783:
1275:By taking the third property and letting
990:
624:. He also introduced the concept of the
437:
4560:
4319:Amann, Herbert; Escher, Joachim (2009).
4269:Amann, Herbert; Escher, Joachim (2004).
3742:"ĐŃĐœĐŸĐČŃ ĐŒĐ°ŃĐ”ĐŒĐ°ŃĐžŃĐ”ŃĐșĐŸĐłĐŸ Đ°ĐœĐ°Đ»ĐžĐ·Đ°. ĐąĐŸĐŒ II"
3264:
2632:Principles of Mathematical Analysis, by
1409:
1258:{\displaystyle d(x,z)\leq d(x,y)+d(y,z)}
432:series as early as the 4th century BCE.
339:
237:
4475:; Pfaffenberger, William Elmer (1981).
4451:
4425:
3984:Mathematical Analysis: A Special Course
3390:
3203:
3094:K. B. Basant, Satyananda Panda (2013).
2796:
2583:Differential And Integral Calculus, by
2395:, which is developed in a smooth topos.
1349:
355:inside a circle by finding the area of
14:
6393:
3460:
3365:
3270:
3244:
2805:
2607:Problems in Mathematical Analysis, by
2589:A Course of Mathematical Analysis, by
2571:Mathematical Analysis (2 volumes), by
2385:, which is built upon a foundation of
2365:, which is built upon a foundation of
2077:of measurable subsets are measurable.
2042:subsets, which are required to form a
1659:
1366:A sequence is an ordered list. Like a
5569:
4955:
4722:
4609:
4583:
3555:
3424:
3333:
3294:
3212:Archive for History of Exact Sciences
2959:
2923:
2769:
2089:
789:
679:then constructed the real numbers by
324:that has a definition of nearness (a
5536:
4477:Foundations of mathematical analysis
4368:
3956:"Differential and Integral Calculus"
3505:
3157:
3103:Indian Journal of History of Science
2865:Springer Science+Business Media Inc.
2453:
2407:
1717:
316:; however, it can be applied to any
5548:
4589:Principles of Mathematical Analysis
4114:Principles of Mathematical Analysis
4034:"Problems in Mathematical Analysis"
3970:"A Course of Mathematical Analysis"
3587:
3341:Principles of Mathematical Analysis
2534:
2313:â analytical notions developed for
2100:Numerical analysis is the study of
1574:
628:, and started the formal theory of
24:
5597:Industrial and applied mathematics
4391:
3642:Introduction to Numerical Analysis
2424:is based on applied analysis, and
2197:
2182:
2147:
1471:
25:
6412:
5827:Stochastic differential equations
4687:
4489:Nikol'skiÄ , Sergey Mikhailovich
3680:Rabiner, L. R.; Gold, B. (1975).
3597:. American Mathematical Society.
3594:An Introduction to Measure Theory
2966:. Horwood Publishing. p. 8.
2674:Real and Functional Analysis, by
2614:Problems and Theorems in Analysis
2458:When processing signals, such as
2235:deals with the representation of
2138:stochastic differential equations
1883:, which assigns the conventional
1856:
778:was in the air, and in the 1920s
414:The Method of Mechanical Theorems
6143:Supersymmetric quantum mechanics
5547:
5535:
5524:
5523:
5511:
4682:from the original on 2007-04-19.
3688:. Englewood Cliffs, New Jersey:
2688:
2335:â analysis in the context of an
2289:and their functions and gives a
2136:is important for data analysis;
1941:{\displaystyle \mathbb {R} ^{n}}
1524:
1508:
794:
720:nowhere differentiable functions
587:
269:, and related theories, such as
196:
6025:Stochastic variational calculus
5817:Ordinary differential equations
5432:Computational complexity theory
4873:Least-squares spectral analysis
4800:Fundamental theorem of calculus
4561:Rombaldi, Jean-Ătienne (2004).
4362:
4337:
4312:
4287:
4262:
4240:
4218:
4196:
4174:
4150:
4128:
4106:
4084:
4062:
4040:
4026:
4012:
3998:
3976:
3962:
3948:
3934:
3920:
3906:
3892:
3856:
3834:
3820:
3806:
3784:
3762:
3748:
3734:
3720:
3706:
3673:
3658:
3630:
3619:from the original on 2019-12-27
3581:
3526:
3509:Ordinary Differential Equations
3499:
3488:from the original on 2020-09-09
3467:A Course in Functional Analysis
3359:
3327:
3287:
3253:from the original on 2008-10-12
3151:
3140:from the original on 2019-04-21
3123:Calculus: Early Transcendentals
3113:
3018:from the original on 2016-06-17
2980:from the original on 2016-06-11
2838:from the original on 2016-05-17
2785:from the original on 2015-07-26
2543:Introductory Real Analysis, by
2399:
2208:
2132:(planets, stars and galaxies);
2126:Ordinary differential equations
859:Formally, a metric space is an
5822:Partial differential equations
5695:Arbitrary-precision arithmetic
4670:"Real Analysis â Course Notes"
3561:Partial Differential Equations
3306:. Wiley-Interscience. p.
3087:
3040:
2991:
2953:
2751:
2529:Partial differential equations
2255:partial differential equations
1998:to (certain) subsets of a set
1736:as the superposition of basic
1468:
1323:
1311:
1252:
1240:
1231:
1219:
1210:
1198:
1169:
1157:
1148:
1136:
1070:
1058:
986:
881:
869:
570:partial differential equations
544:in 1637, which introduced the
517:
13:
1:
5710:Interactive geometry software
4419:American Mathematical Society
3669:. Dover Books on Mathematics.
3644:(2nd ed.). McGraw-Hill.
3565:American Mathematical Society
2814:American Mathematical Society
2744:
2734:Smooth infinitesimal analysis
2393:Smooth infinitesimal analysis
2297:and infinitely large numbers.
1919:-dimensional Euclidean space
1794:A differential equation is a
1175:{\displaystyle d(x,y)=d(y,x)}
738:developed what is now called
4502:Encyclopaedia of Mathematics
4371:Real and Functional Analysis
4346:Real and Functional Analysis
3714:"Introductory Real Analysis"
2719:Multiple rule-based problems
2160:A History of Vector Analysis
1853:) may be solved explicitly.
1698:as transformations defining
1408:. Continuing informally, a (
1335:{\displaystyle d(x,y)\geq 0}
1082:{\displaystyle d(x,y)\geq 0}
716:nowhere continuous functions
7:
5762:Computational number theory
5725:Numerical-analysis software
4649:(4th ed.). Cambridge:
3275:Euler: The Master of Us All
2861:Mathematics and its History
2859:(2004). "Infinite Series".
2806:Jahnke, Hans Niels (2003).
2681:
1899:to suitable subsets of the
1513:
596:introduced the notion of a
546:Cartesian coordinate system
443:
10:
6417:
5482:Films about mathematicians
4617:(3rd ed.). New York:
4591:(3rd ed.). New York:
4531:; Sbordone, Carlo (1996).
4465:Cambridge University Press
4248:Analysis II: Third Edition
3400:(3rd ed.). New York:
2474:Other areas of mathematics
2446:is also a major factor in
2201:
2186:
2157:
2151:
2093:
2018:. It must assign 0 to the
1860:
1787:
1721:
1663:
1578:
1528:
1517:
1359:
1353:
1121:identity of indiscernibles
1038:{\displaystyle x,y,z\in M}
798:
654:(Δ, Ύ)-definition of limit
367:
335:
136:Relationship with sciences
6360:
6322:
6306:
6268:
6220:
6168:Algebra of physical space
6033:
5991:
5785:
5747:
5635:Automated theorem proving
5603:
5505:
5455:
5412:
5322:
5284:
5251:
5203:
5175:
5122:
5069:
5051:Philosophy of mathematics
5026:
4991:
4938:
4838:
4757:
4703:Creative Commons BY-NC-SA
4615:Real and Complex Analysis
4226:Analysis I: Third Edition
2662:Analysis (2 volumes), by
2285:, which investigates the
2221:, as opposed to ordinary
1833:, and other disciplines.
1563:of the real numbers, and
854:topological vector spaces
660:introduced his theory of
512:
378:ancient Greek mathematics
5961:Numerical linear algebra
5487:Recreational mathematics
4637:Whittaker, Edmund Taylor
3864:Mathematical Analysis II
3506:Ince, Edward L. (1956).
3366:Abbott, Stephen (2001).
3271:Dunham, William (1999).
2960:Pinto, J. Sousa (2004).
2775:"analysis | mathematics"
2519:Differentiable manifolds
2438:Einstein field equations
2134:numerical linear algebra
1640:). Because the separate
730:developed his theory of
556:independently developed
455:to find the volume of a
389:paradox of the dichotomy
308:. Analysis evolved from
5700:Finite element analysis
5650:Constraint satisfaction
5372:Mathematical statistics
5362:Mathematical psychology
5332:Engineering mathematics
5266:Algebraic number theory
4651:at the University Press
4493:"Mathematical analysis"
4453:Binmore, Kenneth George
3842:Mathematical Analysis I
3189:2027/mdp.39015004845684
2779:EncyclopĂŠdia Britannica
2383:Paraconsistent analysis
2373:Intuitionistic analysis
2217:deals with extremizing
2177:vector-valued functions
2108:(as opposed to general
2056:{\displaystyle \sigma }
1416:, called the limit, as
1301:, it can be shown that
1045:, the following holds:
503:trigonometric functions
485:, of functions such as
481:expansions, now called
475:Madhava of Sangamagrama
411:appears in Archimedes'
6255:Mathematical economics
5929:Multivariable calculus
5812:Differential equations
5655:Constraint programming
5645:Computational geometry
5518:Mathematics portal
5367:Mathematical sociology
5347:Mathematical economics
5342:Mathematical chemistry
5271:Analytic number theory
5152:Differential equations
4805:Calculus of variations
4778:Differential equations
4641:Watson, George Neville
4533:Analisi Matematica Due
3638:Hildebrand, Francis B.
3539:, Dover Publications,
3512:. Dover Publications.
3392:Ahlfors, Lars Valerian
3368:Understanding Analysis
2931:History of Mathematics
2724:Multivariable calculus
2493:Continuous probability
2488:Analytic combinatorics
2483:Analytic number theory
2426:differential equations
2215:Calculus of variations
2110:symbolic manipulations
2057:
2012:
1981:
1942:
1913:
1784:Differential equations
1623:electrical engineering
1619:mechanical engineering
1499:
1336:
1295:
1259:
1176:
1112:
1083:
1039:
998:
952:
928:
908:
888:
809:, a metric space is a
748:Baire category theorem
562:calculus of variations
558:infinitesimal calculus
382:infinite geometric sum
364:
251:
6401:Mathematical analysis
6208:Supersymmetry algebra
6193:Representation theory
6188:Renormalization group
5834:Differential geometry
5715:Optimization software
5687:Mathematical software
5497:Mathematics education
5427:Theory of computation
5147:Hypercomplex analysis
4898:Representation theory
4857:quaternionic analysis
4853:Hypercomplex analysis
4751:mathematical analysis
4714:Calculus and Analysis
4473:Johnsonbaugh, Richard
4431:Mathematical Analysis
4409:, eds. (March 1969).
3557:Evans, Lawrence Craig
3300:"Beyond the Calculus"
3047:Singh, A. N. (1936).
2857:Stillwell, John Colin
2809:A History of Analysis
2771:Stillwell, John Colin
2714:Hypercomplex analysis
2704:Constructive analysis
2650:Complex Analysis, by
2524:Differential topology
2509:Differential geometry
2500:in information theory
2412:The vast majority of
2363:Constructive analysis
2283:Non-standard analysis
2058:
2013:
1982:
1980:{\displaystyle \left}
1943:
1914:
1863:Measure (mathematics)
1790:Differential equation
1762:representation theory
1638:meromorphic functions
1559:of real numbers, the
1500:
1337:
1296:
1260:
1177:
1113:
1084:
1040:
999:
953:
929:
909:
889:
887:{\displaystyle (M,d)}
610:generality of algebra
598:mathematical function
592:In the 18th century,
473:In the 14th century,
453:Cavalieri's principle
419:Chinese mathematician
374:Scientific Revolution
343:
248:differential equation
241:
27:Branch of mathematics
18:Mathematical Analysis
6260:Mathematical finance
6245:Social choice theory
6160:Algebraic structures
6109:in quantum mechanics
6045:Analytical mechanics
6011:Stochastic processes
5983:Variational calculus
5795:Approximation theory
5720:Statistical software
5477:Informal mathematics
5357:Mathematical physics
5352:Mathematical finance
5337:Mathematical biology
5276:Diophantine geometry
4830:Table of derivatives
4369:Lang, Serge (2012).
2729:Paraconsistent logic
2561:Grigorii Fichtenholz
2555:Grigorii Fichtenholz
2498:Differential entropy
2434:Schrödinger equation
2315:stochastic processes
2189:Scalar (mathematics)
2114:discrete mathematics
2047:
2002:
1955:
1923:
1903:
1627:quantum field theory
1625:, and particularly,
1457:
1350:Sequences and limits
1342: (
1305:
1279:
1192:
1130:
1096:
1052:
1011:
968:
942:
918:
898:
866:
760:Lebesgue integration
724:space-filling curves
712:pathological objects
584:by continuous ones.
578:generating functions
461:Indian mathematician
405:method of exhaustion
393:Greek mathematicians
349:method of exhaustion
322:mathematical objects
263:continuous functions
101:Discrete mathematics
6235:Operations research
6104:Perturbation theory
5902:Multilinear algebra
5873:Functional analysis
5730:Numerical libraries
5662:Computational logic
5492:Mathematics and art
5402:Operations research
5157:Functional analysis
4910:Continuous function
4863:Functional analysis
4497:Hazewinkel, Michiel
3438:McGraw-Hill Science
3432:Functional Analysis
3172:1916Natur..97..177.
2925:Smith, David Eugene
2709:History of calculus
2444:Functional analysis
2430:Newton's second law
2414:classical mechanics
2337:idempotent semiring
2333:Idempotent analysis
2321:Set-valued analysis
2311:Stochastic calculus
2301:Computable analysis
2130:celestial mechanics
2104:that use numerical
2079:Non-measurable sets
1842:classical mechanics
1692:spaces of functions
1666:Functional analysis
1660:Functional analysis
1603:applied mathematics
1362:Limit of a sequence
1294:{\displaystyle z=x}
1268:triangle inequality
1111:{\displaystyle x=y}
850:functional analysis
784:functional analysis
776:normed vector space
707:of real functions.
701:Riemann integration
380:. For instance, an
35:Part of a series on
6372:Mathematics portal
6269:Other applications
5993:Probability theory
5976:Validated numerics
5956:Numerical analysis
5849:Geometric analysis
5839:Differential forms
5672:Information theory
5437:Numerical analysis
5046:Mathematical logic
5041:Information theory
4942:Mathematics portal
4825:Lists of integrals
4399:Aleksandrov, A. D.
3462:Conway, John Bligh
3247:"Pierre de Fermat"
3245:Pellegrino, Dana.
3224:10.1007/BF00348142
3034:2016-05-26 at the
2937:Dover Publications
2696:Mathematics portal
2591:Aleksandr Khinchin
2504:Differential games
2251:Geometric analysis
2239:or signals as the
2096:Numerical analysis
2090:Numerical analysis
2053:
2008:
1977:
1938:
1909:
1897:Euclidean geometry
1851:equation of motion
1805:of one or several
1746:Fourier transforms
1712:integral equations
1650:Laplace's equation
1634:analytic functions
1595:algebraic geometry
1495:
1475:
1386:whose domain is a
1332:
1291:
1255:
1172:
1108:
1079:
1035:
1007:such that for any
994:
948:
924:
904:
884:
813:where a notion of
790:Important concepts
772:integral equations
693:decimal expansions
365:
291:analytic functions
283:infinite sequences
252:
202:Mathematics Portal
6388:
6387:
6222:Decision sciences
6216:
6215:
6198:Spacetime algebra
5890:Harmonic analysis
5856:Dynamical systems
5800:Clifford analysis
5777:Discrete geometry
5743:
5742:
5563:
5562:
5162:Harmonic analysis
4949:
4948:
4915:Special functions
4878:Harmonic analysis
4529:Marcellini, Paolo
4407:Lavrent'ev, M. A.
4403:Kolmogorov, A. N.
3011:978-0-7923-3463-7
2822:10.1090/hmath/024
2545:Andrey Kolmogorov
2454:Signal processing
2448:quantum mechanics
2422:quantum mechanics
2408:Physical sciences
2347:tropical semiring
2343:Tropical analysis
2287:hyperreal numbers
2261:Clifford analysis
2233:Harmonic analysis
2225:which deals with
2011:{\displaystyle X}
1912:{\displaystyle n}
1770:quantum mechanics
1766:signal processing
1724:Harmonic analysis
1718:Harmonic analysis
1696:Fourier transform
1460:
1393:set, such as the
951:{\displaystyle M}
927:{\displaystyle d}
907:{\displaystyle M}
718:, continuous but
646:harmonic analysis
582:discrete problems
532:analytic geometry
434:ÄcÄrya BhadrabÄhu
326:topological space
257:is the branch of
244:strange attractor
236:
235:
191:
190:
16:(Redirected from
6408:
6173:Feynman integral
6156:
6155:
6116:Potential theory
6005:random variables
5895:Fourier analysis
5878:Operator algebra
5805:Clifford algebra
5757:Computer algebra
5683:
5682:
5590:
5583:
5576:
5567:
5566:
5551:
5550:
5539:
5538:
5527:
5526:
5516:
5515:
5447:Computer algebra
5422:Computer science
5142:Complex analysis
4976:
4969:
4962:
4953:
4952:
4868:Fourier analysis
4848:Complex analysis
4749:Major topics in
4743:
4736:
4729:
4720:
4719:
4683:
4681:
4674:
4664:
4632:
4606:
4580:
4557:
4545:
4520:
4484:
4468:
4462:
4448:
4433:(2nd ed.).
4422:
4415:The M.I.T. Press
4385:
4384:
4366:
4360:
4359:
4341:
4335:
4334:
4316:
4310:
4309:
4291:
4285:
4284:
4266:
4260:
4259:
4244:
4238:
4237:
4222:
4216:
4215:
4200:
4194:
4193:
4182:Complex Analysis
4178:
4172:
4171:
4154:
4148:
4147:
4132:
4126:
4125:
4110:
4104:
4103:
4088:
4082:
4081:
4066:
4060:
4059:
4044:
4038:
4037:
4030:
4024:
4023:
4016:
4010:
4009:
4002:
3996:
3995:
3980:
3974:
3973:
3966:
3960:
3959:
3952:
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3945:
3938:
3932:
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3918:
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3910:
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3860:
3854:
3853:
3838:
3832:
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3824:
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3788:
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3781:
3766:
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3752:
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3738:
3732:
3731:
3724:
3718:
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3704:
3703:
3687:
3677:
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3655:
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3579:
3578:
3553:
3547:
3530:
3524:
3523:
3503:
3497:
3496:
3494:
3493:
3470:(2nd ed.).
3458:
3452:
3451:
3435:
3422:
3416:
3415:
3397:Complex Analysis
3388:
3382:
3381:
3363:
3357:
3356:
3344:
3331:
3325:
3324:
3291:
3285:
3284:
3278:
3268:
3262:
3261:
3259:
3258:
3242:
3236:
3235:
3207:
3201:
3200:
3191:
3180:10.1038/097177a0
3155:
3149:
3148:
3146:
3145:
3117:
3111:
3110:
3100:
3091:
3085:
3084:
3044:
3038:
3026:
3024:
3023:
2995:
2989:
2988:
2986:
2985:
2957:
2951:
2950:
2934:
2921:
2915:
2914:
2863:(2nd ed.).
2853:
2847:
2846:
2844:
2843:
2803:
2794:
2793:
2791:
2790:
2767:
2761:
2755:
2698:
2693:
2692:
2616:(2 volumes), by
2609:Boris Demidovich
2585:Nikolai Piskunov
2579:Vladimir Smirnov
2535:Famous Textbooks
2377:choice sequences
2355:min-plus algebra
2351:max-plus algebra
2062:
2060:
2059:
2054:
2036:counting measure
2017:
2015:
2014:
2009:
1986:
1984:
1983:
1978:
1976:
1972:
1947:
1945:
1944:
1939:
1937:
1936:
1931:
1918:
1916:
1915:
1910:
1877:Lebesgue measure
1750:Fourier analysis
1688:linear operators
1686:, etc.) and the
1605:; as well as in
1581:Complex analysis
1575:Complex analysis
1504:
1502:
1501:
1496:
1485:
1484:
1474:
1446:approaches 0 as
1341:
1339:
1338:
1333:
1300:
1298:
1297:
1292:
1264:
1262:
1261:
1256:
1181:
1179:
1178:
1173:
1117:
1115:
1114:
1109:
1089:, with equality
1088:
1086:
1085:
1080:
1044:
1042:
1041:
1036:
1003:
1001:
1000:
995:
993:
957:
955:
954:
949:
933:
931:
930:
925:
913:
911:
910:
905:
893:
891:
890:
885:
740:naive set theory
652:, developed the
630:complex analysis
574:Fourier analysis
439:
357:regular polygons
228:
221:
214:
200:
64:
63:
32:
31:
21:
6416:
6415:
6411:
6410:
6409:
6407:
6406:
6405:
6391:
6390:
6389:
6384:
6356:
6318:
6302:
6264:
6212:
6178:Poisson algebra
6154:
6036:
6029:
5987:
5883:Operator theory
5781:
5739:
5705:Tensor software
5681:
5630:Automata theory
5599:
5594:
5564:
5559:
5510:
5501:
5451:
5408:
5387:Systems science
5318:
5314:Homotopy theory
5280:
5247:
5199:
5171:
5118:
5065:
5036:Category theory
5022:
4987:
4980:
4950:
4945:
4934:
4883:P-adic analysis
4834:
4820:Matrix calculus
4815:Tensor calculus
4810:Vector calculus
4773:Differentiation
4753:
4747:
4690:
4679:
4672:
4668:
4661:
4629:
4603:
4577:
4554:
4539:
4537:Liguori Editore
4517:
4507:Springer-Verlag
4445:
4427:Apostol, Tom M.
4394:
4392:Further reading
4389:
4388:
4381:
4367:
4363:
4356:
4342:
4338:
4331:
4317:
4313:
4306:
4292:
4288:
4281:
4267:
4263:
4246:
4245:
4241:
4224:
4223:
4219:
4202:
4201:
4197:
4180:
4179:
4175:
4168:
4156:
4155:
4151:
4134:
4133:
4129:
4112:
4111:
4107:
4090:
4089:
4085:
4068:
4067:
4063:
4046:
4045:
4041:
4032:
4031:
4027:
4018:
4017:
4013:
4004:
4003:
3999:
3982:
3981:
3977:
3968:
3967:
3963:
3954:
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3949:
3940:
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3935:
3926:
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3826:
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3821:
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3807:
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3785:
3768:
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3763:
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3700:
3678:
3674:
3663:
3659:
3652:
3635:
3631:
3622:
3620:
3613:
3603:10.1090/gsm/126
3586:
3582:
3575:
3554:
3550:
3533:Witold Hurewicz
3531:
3527:
3520:
3504:
3500:
3491:
3489:
3482:
3472:Springer-Verlag
3459:
3455:
3448:
3423:
3419:
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3389:
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3353:
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3288:
3269:
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3256:
3254:
3243:
3239:
3208:
3204:
3156:
3152:
3143:
3141:
3134:
3118:
3114:
3098:
3092:
3088:
3045:
3041:
3036:Wayback Machine
3029:Chapter, p. 279
3021:
3019:
3012:
2996:
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2983:
2981:
2974:
2958:
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2947:
2922:
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2911:
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2899:
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2891:
2887:
2883:
2875:
2854:
2850:
2841:
2839:
2832:
2804:
2797:
2788:
2786:
2768:
2764:
2756:
2752:
2747:
2694:
2687:
2684:
2603:Isidor Natanson
2573:Vladimir Zorich
2567:Sergey Nikolsky
2537:
2476:
2466:, light waves,
2456:
2410:
2402:
2327:Convex analysis
2211:
2206:
2200:
2198:Tensor analysis
2191:
2185:
2183:Scalar analysis
2173:vector calculus
2169:Vector analysis
2166:
2164:Vector Analysis
2156:
2154:Vector calculus
2150:
2148:Vector analysis
2098:
2092:
2084:axiom of choice
2048:
2045:
2044:
2003:
2000:
1999:
1962:
1958:
1956:
1953:
1952:
1932:
1927:
1926:
1924:
1921:
1920:
1904:
1901:
1900:
1881:Euclidean space
1867:A measure on a
1865:
1859:
1801:for an unknown
1792:
1786:
1726:
1720:
1668:
1662:
1591:complex numbers
1583:
1577:
1533:
1527:
1522:
1516:
1511:
1480:
1476:
1464:
1458:
1455:
1454:
1441:
1428:
1410:singly-infinite
1395:natural numbers
1391:totally ordered
1364:
1358:
1352:
1306:
1303:
1302:
1280:
1277:
1276:
1193:
1190:
1189:
1131:
1128:
1127:
1097:
1094:
1093:
1053:
1050:
1049:
1012:
1009:
1008:
989:
969:
966:
965:
943:
940:
939:
919:
916:
915:
899:
896:
895:
867:
864:
863:
852:(which studies
834:Euclidean space
803:
797:
792:
705:discontinuities
675:without proof.
626:Cauchy sequence
602:Bernard Bolzano
590:
520:
515:
479:infinite series
468:Rolle's theorem
446:
384:is implicit in
370:
351:to compute the
338:
271:differentiation
246:arising from a
232:
187:
186:
137:
129:
128:
124:Decision theory
72:
28:
23:
22:
15:
12:
11:
5:
6414:
6404:
6403:
6386:
6385:
6383:
6382:
6369:
6361:
6358:
6357:
6355:
6354:
6349:
6344:
6339:
6338:
6337:
6326:
6324:
6320:
6319:
6317:
6316:
6310:
6308:
6304:
6303:
6301:
6300:
6293:
6288:
6283:
6278:
6272:
6270:
6266:
6265:
6263:
6262:
6257:
6252:
6247:
6242:
6237:
6232:
6226:
6224:
6218:
6217:
6214:
6213:
6211:
6210:
6205:
6200:
6195:
6190:
6185:
6180:
6175:
6170:
6164:
6162:
6153:
6152:
6151:
6150:
6145:
6135:
6134:
6133:
6128:
6118:
6113:
6112:
6111:
6101:
6100:
6099:
6094:
6089:
6084:
6079:
6074:
6069:
6059:
6058:
6057:
6052:
6041:
6039:
6031:
6030:
6028:
6027:
6022:
6017:
6008:
5997:
5995:
5989:
5988:
5986:
5985:
5980:
5979:
5978:
5973:
5968:
5963:
5953:
5952:
5951:
5946:
5941:
5936:
5926:
5925:
5924:
5919:
5914:
5909:
5899:
5898:
5897:
5887:
5886:
5885:
5880:
5870:
5869:
5868:
5866:Control theory
5863:
5853:
5852:
5851:
5846:
5841:
5831:
5830:
5829:
5824:
5819:
5809:
5808:
5807:
5797:
5791:
5789:
5783:
5782:
5780:
5779:
5774:
5769:
5764:
5759:
5753:
5751:
5745:
5744:
5741:
5740:
5738:
5737:
5732:
5727:
5722:
5717:
5712:
5707:
5702:
5697:
5691:
5689:
5680:
5679:
5674:
5669:
5664:
5659:
5658:
5657:
5647:
5642:
5637:
5632:
5627:
5626:
5625:
5620:
5609:
5607:
5601:
5600:
5593:
5592:
5585:
5578:
5570:
5561:
5560:
5558:
5557:
5545:
5533:
5521:
5506:
5503:
5502:
5500:
5499:
5494:
5489:
5484:
5479:
5474:
5473:
5472:
5465:Mathematicians
5461:
5459:
5457:Related topics
5453:
5452:
5450:
5449:
5444:
5439:
5434:
5429:
5424:
5418:
5416:
5410:
5409:
5407:
5406:
5405:
5404:
5399:
5394:
5392:Control theory
5384:
5379:
5374:
5369:
5364:
5359:
5354:
5349:
5344:
5339:
5334:
5328:
5326:
5320:
5319:
5317:
5316:
5311:
5306:
5301:
5296:
5290:
5288:
5282:
5281:
5279:
5278:
5273:
5268:
5263:
5257:
5255:
5249:
5248:
5246:
5245:
5240:
5235:
5230:
5225:
5220:
5215:
5209:
5207:
5201:
5200:
5198:
5197:
5192:
5187:
5181:
5179:
5173:
5172:
5170:
5169:
5167:Measure theory
5164:
5159:
5154:
5149:
5144:
5139:
5134:
5128:
5126:
5120:
5119:
5117:
5116:
5111:
5106:
5101:
5096:
5091:
5086:
5081:
5075:
5073:
5067:
5066:
5064:
5063:
5058:
5053:
5048:
5043:
5038:
5032:
5030:
5024:
5023:
5021:
5020:
5015:
5010:
5009:
5008:
5003:
4992:
4989:
4988:
4979:
4978:
4971:
4964:
4956:
4947:
4946:
4939:
4936:
4935:
4933:
4932:
4927:
4922:
4917:
4912:
4907:
4901:
4900:
4895:
4893:Measure theory
4890:
4887:P-adic numbers
4880:
4875:
4870:
4865:
4860:
4850:
4845:
4839:
4836:
4835:
4833:
4832:
4827:
4822:
4817:
4812:
4807:
4802:
4797:
4796:
4795:
4790:
4785:
4775:
4770:
4758:
4755:
4754:
4746:
4745:
4738:
4731:
4723:
4717:
4716:
4711:
4706:
4701:by Jiri Lebl (
4696:
4689:
4688:External links
4686:
4685:
4684:
4666:
4659:
4643:(1927-01-02).
4633:
4628:978-0070542341
4627:
4607:
4602:978-0070542358
4601:
4581:
4576:978-2868836816
4575:
4558:
4553:978-8820726751
4552:
4535:(in Italian).
4521:
4516:978-1402006098
4515:
4485:
4469:
4449:
4444:978-0201002881
4443:
4435:AddisonâWesley
4423:
4393:
4390:
4387:
4386:
4380:978-1461269380
4379:
4361:
4355:978-3030382216
4354:
4336:
4330:978-3764374792
4329:
4311:
4305:978-3764374723
4304:
4286:
4280:978-3764371531
4279:
4261:
4239:
4217:
4195:
4173:
4167:978-0070006577
4166:
4160:. 1979-01-01.
4149:
4127:
4105:
4083:
4061:
4039:
4025:
4011:
3997:
3975:
3961:
3947:
3933:
3919:
3905:
3891:
3877:
3855:
3833:
3819:
3805:
3783:
3761:
3747:
3733:
3719:
3705:
3699:978-0139141010
3698:
3672:
3657:
3651:978-0070287617
3650:
3629:
3612:978-0821869192
3611:
3580:
3574:978-0821807729
3573:
3563:. Providence:
3548:
3525:
3519:978-0486603490
3518:
3498:
3481:978-0387972459
3480:
3453:
3447:978-0070542365
3446:
3417:
3411:978-0070006577
3410:
3383:
3377:978-0387950600
3376:
3358:
3352:978-0070542358
3351:
3326:
3317:978-0471180821
3316:
3286:
3263:
3237:
3202:
3150:
3133:978-0763759957
3132:
3112:
3086:
3065:10.1086/368443
3039:
3010:
2990:
2973:978-1898563990
2972:
2952:
2946:978-0486204307
2945:
2916:
2909:
2905:
2901:
2897:
2893:
2889:
2885:
2881:
2874:978-0387953366
2873:
2848:
2831:978-0821826232
2830:
2795:
2762:
2749:
2748:
2746:
2743:
2742:
2741:
2736:
2731:
2726:
2721:
2716:
2711:
2706:
2700:
2699:
2683:
2680:
2679:
2678:
2672:
2669:
2666:
2660:
2654:
2648:
2642:
2636:
2630:
2624:
2611:
2605:
2599:
2597:Georgiy Shilov
2593:
2587:
2581:
2575:
2569:
2563:
2557:
2551:
2541:
2536:
2533:
2532:
2531:
2526:
2521:
2516:
2506:
2501:
2495:
2490:
2485:
2475:
2472:
2455:
2452:
2409:
2406:
2401:
2398:
2397:
2396:
2390:
2387:paraconsistent
2380:
2370:
2360:
2359:
2358:
2330:
2324:
2318:
2308:
2298:
2295:infinitesimals
2280:
2270:-adic analysis
2264:
2258:
2248:
2230:
2210:
2207:
2202:Main article:
2199:
2196:
2187:Main article:
2184:
2181:
2171:, also called
2152:Main article:
2149:
2146:
2094:Main article:
2091:
2088:
2052:
2007:
1975:
1971:
1968:
1965:
1961:
1935:
1930:
1908:
1861:Main article:
1858:
1857:Measure theory
1855:
1788:Main article:
1785:
1782:
1774:tidal analysis
1742:Fourier series
1722:Main article:
1719:
1716:
1664:Main article:
1661:
1658:
1615:thermodynamics
1579:Main article:
1576:
1573:
1529:Main article:
1526:
1523:
1518:Main article:
1515:
1512:
1510:
1507:
1506:
1505:
1494:
1491:
1488:
1483:
1479:
1473:
1470:
1467:
1463:
1437:
1424:
1370:, it contains
1354:Main article:
1351:
1348:
1331:
1328:
1325:
1322:
1319:
1316:
1313:
1310:
1290:
1287:
1284:
1273:
1272:
1265: (
1254:
1251:
1248:
1245:
1242:
1239:
1236:
1233:
1230:
1227:
1224:
1221:
1218:
1215:
1212:
1209:
1206:
1203:
1200:
1197:
1187:
1182: (
1171:
1168:
1165:
1162:
1159:
1156:
1153:
1150:
1147:
1144:
1141:
1138:
1135:
1125:
1118: (
1107:
1104:
1101:
1091:if and only if
1078:
1075:
1072:
1069:
1066:
1063:
1060:
1057:
1034:
1031:
1028:
1025:
1022:
1019:
1016:
1005:
1004:
992:
988:
985:
982:
979:
976:
973:
947:
923:
903:
883:
880:
877:
874:
871:
846:measure theory
799:Main article:
796:
793:
791:
788:
774:. The idea of
768:Hilbert spaces
710:Also, various
614:infinitesimals
589:
586:
519:
516:
514:
511:
445:
442:
409:infinitesimals
369:
366:
337:
334:
234:
233:
231:
230:
223:
216:
208:
205:
204:
193:
192:
189:
188:
185:
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179:
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154:
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144:
138:
135:
134:
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126:
117:
112:
103:
98:
89:
84:
79:
73:
68:
67:
60:
59:
58:
57:
52:
44:
43:
37:
36:
26:
9:
6:
4:
3:
2:
6413:
6402:
6399:
6398:
6396:
6381:
6377:
6373:
6370:
6368:
6367:
6363:
6362:
6359:
6353:
6350:
6348:
6345:
6343:
6340:
6336:
6333:
6332:
6331:
6328:
6327:
6325:
6323:Organizations
6321:
6315:
6312:
6311:
6309:
6305:
6298:
6294:
6292:
6289:
6287:
6284:
6282:
6279:
6277:
6274:
6273:
6271:
6267:
6261:
6258:
6256:
6253:
6251:
6248:
6246:
6243:
6241:
6238:
6236:
6233:
6231:
6228:
6227:
6225:
6223:
6219:
6209:
6206:
6204:
6201:
6199:
6196:
6194:
6191:
6189:
6186:
6184:
6183:Quantum group
6181:
6179:
6176:
6174:
6171:
6169:
6166:
6165:
6163:
6161:
6157:
6149:
6146:
6144:
6141:
6140:
6139:
6138:Supersymmetry
6136:
6132:
6129:
6127:
6124:
6123:
6122:
6121:String theory
6119:
6117:
6114:
6110:
6107:
6106:
6105:
6102:
6098:
6095:
6093:
6090:
6088:
6085:
6083:
6080:
6078:
6075:
6073:
6070:
6068:
6065:
6064:
6063:
6060:
6056:
6053:
6051:
6048:
6047:
6046:
6043:
6042:
6040:
6038:
6032:
6026:
6023:
6021:
6020:Path integral
6018:
6016:
6012:
6009:
6006:
6002:
6001:Distributions
5999:
5998:
5996:
5994:
5990:
5984:
5981:
5977:
5974:
5972:
5969:
5967:
5964:
5962:
5959:
5958:
5957:
5954:
5950:
5947:
5945:
5942:
5940:
5937:
5935:
5932:
5931:
5930:
5927:
5923:
5920:
5918:
5915:
5913:
5910:
5908:
5905:
5904:
5903:
5900:
5896:
5893:
5892:
5891:
5888:
5884:
5881:
5879:
5876:
5875:
5874:
5871:
5867:
5864:
5862:
5859:
5858:
5857:
5854:
5850:
5847:
5845:
5842:
5840:
5837:
5836:
5835:
5832:
5828:
5825:
5823:
5820:
5818:
5815:
5814:
5813:
5810:
5806:
5803:
5802:
5801:
5798:
5796:
5793:
5792:
5790:
5788:
5784:
5778:
5775:
5773:
5770:
5768:
5767:Combinatorics
5765:
5763:
5760:
5758:
5755:
5754:
5752:
5750:
5746:
5736:
5733:
5731:
5728:
5726:
5723:
5721:
5718:
5716:
5713:
5711:
5708:
5706:
5703:
5701:
5698:
5696:
5693:
5692:
5690:
5688:
5684:
5678:
5675:
5673:
5670:
5668:
5665:
5663:
5660:
5656:
5653:
5652:
5651:
5648:
5646:
5643:
5641:
5640:Coding theory
5638:
5636:
5633:
5631:
5628:
5624:
5621:
5619:
5616:
5615:
5614:
5611:
5610:
5608:
5606:
5605:Computational
5602:
5598:
5591:
5586:
5584:
5579:
5577:
5572:
5571:
5568:
5556:
5555:
5546:
5544:
5543:
5534:
5532:
5531:
5522:
5520:
5519:
5514:
5508:
5507:
5504:
5498:
5495:
5493:
5490:
5488:
5485:
5483:
5480:
5478:
5475:
5471:
5468:
5467:
5466:
5463:
5462:
5460:
5458:
5454:
5448:
5445:
5443:
5440:
5438:
5435:
5433:
5430:
5428:
5425:
5423:
5420:
5419:
5417:
5415:
5414:Computational
5411:
5403:
5400:
5398:
5395:
5393:
5390:
5389:
5388:
5385:
5383:
5380:
5378:
5375:
5373:
5370:
5368:
5365:
5363:
5360:
5358:
5355:
5353:
5350:
5348:
5345:
5343:
5340:
5338:
5335:
5333:
5330:
5329:
5327:
5325:
5321:
5315:
5312:
5310:
5307:
5305:
5302:
5300:
5297:
5295:
5292:
5291:
5289:
5287:
5283:
5277:
5274:
5272:
5269:
5267:
5264:
5262:
5259:
5258:
5256:
5254:
5253:Number theory
5250:
5244:
5241:
5239:
5236:
5234:
5231:
5229:
5226:
5224:
5221:
5219:
5216:
5214:
5211:
5210:
5208:
5206:
5202:
5196:
5193:
5191:
5188:
5186:
5185:Combinatorics
5183:
5182:
5180:
5178:
5174:
5168:
5165:
5163:
5160:
5158:
5155:
5153:
5150:
5148:
5145:
5143:
5140:
5138:
5137:Real analysis
5135:
5133:
5130:
5129:
5127:
5125:
5121:
5115:
5112:
5110:
5107:
5105:
5102:
5100:
5097:
5095:
5092:
5090:
5087:
5085:
5082:
5080:
5077:
5076:
5074:
5072:
5068:
5062:
5059:
5057:
5054:
5052:
5049:
5047:
5044:
5042:
5039:
5037:
5034:
5033:
5031:
5029:
5025:
5019:
5016:
5014:
5011:
5007:
5004:
5002:
4999:
4998:
4997:
4994:
4993:
4990:
4985:
4977:
4972:
4970:
4965:
4963:
4958:
4957:
4954:
4944:
4943:
4937:
4931:
4928:
4926:
4923:
4921:
4918:
4916:
4913:
4911:
4908:
4906:
4903:
4902:
4899:
4896:
4894:
4891:
4888:
4884:
4881:
4879:
4876:
4874:
4871:
4869:
4866:
4864:
4861:
4858:
4854:
4851:
4849:
4846:
4844:
4843:Real analysis
4841:
4840:
4837:
4831:
4828:
4826:
4823:
4821:
4818:
4816:
4813:
4811:
4808:
4806:
4803:
4801:
4798:
4794:
4791:
4789:
4786:
4784:
4781:
4780:
4779:
4776:
4774:
4771:
4769:
4765:
4764:
4760:
4759:
4756:
4752:
4744:
4739:
4737:
4732:
4730:
4725:
4724:
4721:
4715:
4712:
4710:
4707:
4704:
4700:
4697:
4695:
4692:
4691:
4678:
4671:
4667:
4662:
4656:
4652:
4648:
4647:
4642:
4638:
4634:
4630:
4624:
4620:
4616:
4612:
4611:Rudin, Walter
4608:
4604:
4598:
4594:
4590:
4586:
4585:Rudin, Walter
4582:
4578:
4572:
4568:
4565:(in French).
4564:
4559:
4555:
4549:
4543:
4538:
4534:
4530:
4526:
4525:Fusco, Nicola
4522:
4518:
4512:
4508:
4504:
4503:
4498:
4494:
4490:
4486:
4482:
4478:
4474:
4470:
4466:
4461:
4460:
4454:
4450:
4446:
4440:
4436:
4432:
4428:
4424:
4420:
4416:
4412:
4408:
4404:
4400:
4396:
4395:
4382:
4376:
4372:
4365:
4357:
4351:
4347:
4340:
4332:
4326:
4322:
4315:
4307:
4301:
4297:
4290:
4282:
4276:
4272:
4265:
4257:
4253:
4249:
4243:
4235:
4231:
4227:
4221:
4213:
4209:
4205:
4199:
4191:
4187:
4183:
4177:
4169:
4163:
4159:
4153:
4145:
4141:
4137:
4131:
4123:
4119:
4115:
4109:
4101:
4097:
4093:
4087:
4079:
4075:
4071:
4065:
4057:
4053:
4049:
4043:
4035:
4029:
4021:
4015:
4007:
4001:
3993:
3989:
3985:
3979:
3971:
3965:
3957:
3951:
3943:
3937:
3929:
3923:
3915:
3909:
3901:
3895:
3887:
3881:
3873:
3869:
3865:
3859:
3851:
3847:
3843:
3837:
3829:
3823:
3815:
3809:
3801:
3797:
3793:
3787:
3779:
3775:
3771:
3765:
3757:
3751:
3743:
3737:
3729:
3723:
3715:
3709:
3701:
3695:
3691:
3690:Prentice-Hall
3686:
3685:
3676:
3668:
3661:
3653:
3647:
3643:
3639:
3633:
3618:
3614:
3608:
3604:
3600:
3596:
3595:
3590:
3584:
3576:
3570:
3566:
3562:
3558:
3552:
3546:
3542:
3538:
3534:
3529:
3521:
3515:
3511:
3510:
3502:
3487:
3483:
3477:
3473:
3469:
3468:
3463:
3457:
3449:
3443:
3439:
3434:
3433:
3427:
3426:Rudin, Walter
3421:
3413:
3407:
3403:
3399:
3398:
3393:
3387:
3379:
3373:
3369:
3362:
3354:
3348:
3343:
3342:
3336:
3335:Rudin, Walter
3330:
3323:
3319:
3313:
3309:
3305:
3301:
3297:
3290:
3282:
3277:
3276:
3267:
3252:
3248:
3241:
3233:
3229:
3225:
3221:
3218:(2): 89â102.
3217:
3213:
3206:
3199:
3195:
3190:
3185:
3181:
3177:
3173:
3169:
3166:(2426): 177,
3165:
3161:
3154:
3139:
3135:
3129:
3125:
3124:
3116:
3108:
3104:
3097:
3090:
3082:
3078:
3074:
3070:
3066:
3062:
3058:
3054:
3050:
3043:
3037:
3033:
3030:
3017:
3013:
3007:
3003:
3002:
2994:
2979:
2975:
2969:
2965:
2964:
2956:
2948:
2942:
2938:
2933:
2932:
2926:
2920:
2913:
2876:
2870:
2867:p. 170.
2866:
2862:
2858:
2852:
2837:
2833:
2827:
2823:
2819:
2816:. p. 7.
2815:
2811:
2810:
2802:
2800:
2784:
2780:
2776:
2772:
2766:
2759:
2754:
2750:
2740:
2737:
2735:
2732:
2730:
2727:
2725:
2722:
2720:
2717:
2715:
2712:
2710:
2707:
2705:
2702:
2701:
2697:
2691:
2686:
2677:
2673:
2670:
2667:
2665:
2661:
2659:
2655:
2653:
2649:
2647:
2643:
2641:
2637:
2635:
2631:
2629:
2625:
2623:
2619:
2615:
2612:
2610:
2606:
2604:
2600:
2598:
2594:
2592:
2588:
2586:
2582:
2580:
2576:
2574:
2570:
2568:
2564:
2562:
2558:
2556:
2552:
2550:
2546:
2542:
2539:
2538:
2530:
2527:
2525:
2522:
2520:
2517:
2514:
2510:
2507:
2505:
2502:
2499:
2496:
2494:
2491:
2489:
2486:
2484:
2481:
2480:
2479:
2471:
2469:
2468:seismic waves
2465:
2461:
2451:
2449:
2445:
2441:
2439:
2435:
2431:
2427:
2423:
2419:
2415:
2405:
2394:
2391:
2388:
2384:
2381:
2378:
2374:
2371:
2368:
2364:
2361:
2356:
2352:
2348:
2344:
2341:
2340:
2338:
2334:
2331:
2328:
2325:
2322:
2319:
2316:
2312:
2309:
2306:
2302:
2299:
2296:
2293:treatment of
2292:
2288:
2284:
2281:
2278:
2277:-adic numbers
2276:
2271:
2269:
2265:
2262:
2259:
2256:
2252:
2249:
2246:
2242:
2241:superposition
2238:
2234:
2231:
2228:
2224:
2220:
2216:
2213:
2212:
2205:
2195:
2190:
2180:
2178:
2174:
2170:
2165:
2161:
2155:
2145:
2143:
2142:Markov chains
2139:
2135:
2131:
2127:
2121:
2117:
2115:
2111:
2107:
2106:approximation
2103:
2097:
2087:
2085:
2080:
2076:
2072:
2071:intersections
2068:
2064:
2050:
2041:
2037:
2033:
2029:
2025:
2021:
2005:
1997:
1992:
1990:
1973:
1969:
1966:
1963:
1959:
1951:
1933:
1906:
1898:
1894:
1890:
1886:
1882:
1878:
1874:
1870:
1864:
1854:
1852:
1847:
1846:Newton's laws
1843:
1839:
1838:deterministic
1834:
1832:
1828:
1824:
1820:
1816:
1812:
1808:
1804:
1800:
1797:
1791:
1781:
1779:
1775:
1771:
1767:
1763:
1759:
1758:number theory
1755:
1751:
1747:
1743:
1739:
1735:
1731:
1725:
1715:
1713:
1709:
1705:
1701:
1697:
1693:
1689:
1685:
1681:
1677:
1676:inner product
1673:
1672:vector spaces
1667:
1657:
1655:
1651:
1647:
1643:
1639:
1635:
1630:
1628:
1624:
1620:
1616:
1612:
1611:hydrodynamics
1608:
1604:
1600:
1599:number theory
1596:
1592:
1588:
1582:
1572:
1570:
1566:
1562:
1558:
1554:
1550:
1546:
1542:
1538:
1532:
1531:Real analysis
1525:Real analysis
1521:
1509:Main branches
1492:
1489:
1486:
1481:
1477:
1465:
1453:
1452:
1451:
1450:â â, denoted
1449:
1445:
1440:
1436:
1432:
1427:
1423:
1419:
1415:
1411:
1407:
1403:
1398:
1396:
1392:
1389:
1385:
1381:
1377:
1374:(also called
1373:
1369:
1363:
1357:
1347:
1345:
1329:
1326:
1320:
1317:
1314:
1308:
1288:
1285:
1282:
1270:
1269:
1249:
1246:
1243:
1237:
1234:
1228:
1225:
1222:
1216:
1213:
1207:
1204:
1201:
1195:
1188:
1185:
1166:
1163:
1160:
1154:
1151:
1145:
1142:
1139:
1133:
1126:
1123:
1122:
1105:
1102:
1099:
1092:
1076:
1073:
1067:
1064:
1061:
1055:
1048:
1047:
1046:
1032:
1029:
1026:
1023:
1020:
1017:
1014:
983:
980:
977:
974:
971:
964:
963:
962:
961:
945:
937:
921:
914:is a set and
901:
878:
875:
872:
862:
857:
855:
851:
847:
843:
839:
838:vector spaces
835:
831:
830:complex plane
827:
822:
820:
816:
812:
808:
802:
795:Metric spaces
787:
785:
781:
777:
773:
769:
765:
761:
757:
753:
749:
745:
741:
737:
733:
729:
725:
721:
717:
713:
708:
706:
702:
698:
694:
690:
686:
682:
681:Dedekind cuts
678:
674:
670:
665:
663:
659:
655:
651:
647:
643:
639:
635:
631:
627:
623:
619:
615:
611:
607:
603:
599:
595:
588:Modernization
585:
583:
579:
575:
571:
567:
563:
559:
555:
551:
547:
543:
542:
537:
533:
529:
525:
510:
508:
504:
500:
496:
492:
488:
484:
483:Taylor series
480:
476:
471:
469:
465:
462:
458:
454:
450:
441:
435:
431:
427:
423:
420:
416:
415:
410:
406:
402:
398:
394:
390:
387:
383:
379:
375:
362:
358:
354:
350:
346:
342:
333:
331:
327:
323:
319:
315:
311:
307:
303:
299:
294:
292:
288:
284:
280:
276:
272:
268:
264:
261:dealing with
260:
256:
249:
245:
240:
229:
224:
222:
217:
215:
210:
209:
207:
206:
203:
199:
195:
194:
183:
180:
178:
175:
173:
170:
168:
165:
163:
160:
158:
155:
153:
150:
148:
145:
143:
140:
139:
133:
132:
125:
121:
118:
116:
113:
111:
107:
104:
102:
99:
97:
93:
90:
88:
85:
83:
80:
78:
77:Number theory
75:
74:
71:
66:
65:
62:
61:
56:
53:
51:
48:
47:
46:
45:
42:
39:
38:
34:
33:
30:
19:
6378: /
6374: /
6364:
6240:Optimization
6203:Superalgebra
6062:Field theory
6035:Mathematical
6013: /
5861:Chaos theory
5844:Gauge theory
5786:
5772:Graph theory
5667:Cryptography
5552:
5540:
5528:
5509:
5442:Optimization
5304:Differential
5228:Differential
5195:Order theory
5190:Graph theory
5123:
5094:Group theory
4940:
4761:
4750:
4645:
4614:
4588:
4567:EDP Sciences
4562:
4532:
4500:
4479:. New York:
4476:
4458:
4430:
4410:
4370:
4364:
4345:
4339:
4321:Analysis III
4320:
4314:
4295:
4289:
4270:
4264:
4247:
4242:
4225:
4220:
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4198:
4181:
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4091:
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4047:
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4000:
3983:
3978:
3964:
3950:
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3908:
3894:
3880:
3863:
3858:
3841:
3836:
3822:
3808:
3791:
3786:
3769:
3764:
3750:
3736:
3722:
3708:
3683:
3675:
3666:
3660:
3641:
3632:
3621:. Retrieved
3593:
3589:Tao, Terence
3583:
3560:
3551:
3536:
3528:
3508:
3501:
3490:. Retrieved
3466:
3456:
3431:
3420:
3396:
3386:
3367:
3361:
3340:
3329:
3321:
3303:
3296:Cooke, Roger
3289:
3274:
3266:
3255:. Retrieved
3240:
3215:
3211:
3205:
3163:
3159:
3153:
3142:. Retrieved
3122:
3115:
3106:
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3089:
3056:
3052:
3042:
3020:. Retrieved
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2982:. Retrieved
2962:
2955:
2930:
2919:
2878:
2860:
2851:
2840:. Retrieved
2808:
2787:. Retrieved
2778:
2765:
2758:Edwin Hewitt
2753:
2646:Lars Ahlfors
2634:Walter Rudin
2618:George PĂłlya
2549:Sergei Fomin
2477:
2457:
2442:
2411:
2403:
2400:Applications
2367:constructive
2274:
2267:
2209:Other topics
2204:Tensor field
2192:
2172:
2168:
2167:
2122:
2118:
2099:
2069:, countable
2039:
2031:
2027:
1993:
1989:real numbers
1866:
1835:
1796:mathematical
1793:
1778:neuroscience
1754:music theory
1727:
1708:differential
1669:
1631:
1609:, including
1584:
1547:, including
1537:real numbers
1534:
1447:
1443:
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1425:
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1405:
1401:
1399:
1379:
1375:
1365:
1344:non-negative
1343:
1274:
1266:
1183:
1119:
1006:
861:ordered pair
858:
823:
804:
801:Metric space
709:
691:in terms of
689:Simon Stevin
673:real numbers
666:
621:
617:
591:
541:La Géométrie
539:
521:
472:
447:
412:
371:
330:metric space
304:numbers and
295:
254:
253:
95:
29:
6380:topics list
6314:Mathematics
6230:Game theory
6131:Topological
6097:Topological
6092:Statistical
6055:Hamiltonian
5554:WikiProject
5397:Game theory
5377:Probability
5114:Homological
5104:Multilinear
5084:Commutative
5061:Type theory
5028:Foundations
4984:mathematics
4768:Integration
4619:McGraw-Hill
4593:McGraw-Hill
4540: [
4296:Analysis II
3402:McGraw-Hill
3059:: 606â628.
2664:Terence Tao
2658:Elias Stein
2652:Elias Stein
2640:Elias Stein
2628:Tom Apostol
2622:GĂĄbor SzegĆ
2464:radio waves
2219:functionals
2075:complements
1819:engineering
1813:of various
1811:derivatives
1549:convergence
1402:convergence
807:mathematics
766:introduced
746:proved the
714:, (such as
662:integration
650:Weierstrass
518:Foundations
464:BhÄskara II
449:Zu Chongzhi
275:integration
259:mathematics
167:Linguistics
157:Computation
152:Geosciences
115:Probability
41:Mathematics
6286:Psychology
6250:Statistics
6050:Lagrangian
5677:Statistics
5613:Algorithms
5382:Statistics
5261:Arithmetic
5223:Arithmetic
5089:Elementary
5056:Set theory
4793:stochastic
4660:0521067944
4271:Analysis I
4256:9380250657
4234:9380250649
4212:0691113874
4190:0691113858
4144:0691113866
4122:0070856133
4100:0201002884
4078:3540636862
4056:3540636404
3992:1483169561
3872:3662569663
3850:3662569558
3800:1483213153
3778:0080134734
3623:2018-10-26
3545:0486495108
3492:2016-02-11
3257:2008-02-24
3144:2015-11-15
3109:: 291â313.
3022:2015-11-15
2984:2015-11-15
2842:2015-11-15
2789:2015-07-31
2745:References
2676:Serge Lang
2436:, and the
2418:relativity
2305:computable
2158:See also:
2128:appear in
2102:algorithms
2040:measurable
2028:consistent
1700:continuous
1569:smoothness
1565:continuity
1360:See also:
958:, i.e., a
840:, and the
817:(called a
752:set theory
536:adequality
530:developed
499:arctangent
477:developed
426:arithmetic
401:Archimedes
345:Archimedes
177:Philosophy
120:Statistics
110:Set theory
6291:Sociology
6281:Chemistry
6077:Effective
6072:Conformal
6067:Classical
5939:Geometric
5912:Geometric
5309:Geometric
5299:Algebraic
5238:Euclidean
5213:Algebraic
5109:Universal
4905:Functions
4481:M. Dekker
4455:(1981) .
3081:144760421
2908:+ ... = â
2513:manifolds
2243:of basic
2237:functions
2227:functions
2051:σ
2024:countably
2020:empty set
1827:economics
1807:variables
1730:functions
1646:imaginary
1587:functions
1557:sequences
1545:sequences
1541:functions
1472:∞
1469:→
1388:countable
1327:≥
1214:≤
1074:≥
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987:→
981:×
975::
826:real line
770:to solve
669:continuum
638:Liouville
528:Descartes
430:geometric
347:used the
306:functions
182:Education
172:Economics
147:Chemistry
6395:Category
6366:Category
6015:analysis
5934:Exterior
5907:Exterior
5787:Analysis
5749:Discrete
5623:analysis
5530:Category
5286:Topology
5233:Discrete
5218:Analytic
5205:Geometry
5177:Discrete
5132:Calculus
5124:Analysis
5079:Abstract
5018:Glossary
5001:Timeline
4930:Infinity
4783:ordinary
4763:Calculus
4677:Archived
4613:(1987).
4587:(1976).
4491:(2002).
4429:(1974).
3640:(1974).
3617:Archived
3591:(2011).
3559:(1998).
3486:Archived
3464:(1994).
3428:(1991).
3394:(1979).
3337:(1976).
3298:(1997).
3251:Archived
3232:51861422
3138:Archived
3032:Archived
3016:Archived
2978:Archived
2927:(1958).
2836:Archived
2783:Archived
2682:See also
2291:rigorous
2223:calculus
2063:-algebra
2030:size to
2022:and be (
1950:interval
1803:function
1799:equation
1684:topology
1561:calculus
1520:Calculus
1514:Calculus
1429:) (with
1384:function
1376:elements
1356:Sequence
1184:symmetry
960:function
842:integers
836:, other
815:distance
782:created
756:Lebesgue
697:theorems
685:complete
677:Dedekind
566:ordinary
444:Medieval
395:such as
314:geometry
310:calculus
255:Analysis
96:Analysis
92:Calculus
82:Geometry
6376:outline
6307:Related
6276:Biology
6126:Bosonic
6087:Quantum
6037:physics
6003: (
5735:Solvers
5542:Commons
5324:Applied
5294:General
5071:Algebra
4996:History
4788:partial
4499:(ed.).
4036:. 1970.
4022:. 1955.
4008:. 1955.
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1372:members
764:Hilbert
732:measure
658:Riemann
642:Fourier
634:Poisson
554:Leibniz
495:tangent
422:Liu Hui
397:Eudoxus
368:Ancient
336:History
302:complex
279:measure
162:Biology
142:Physics
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5949:Vector
5944:Tensor
5922:Vector
5917:Tensor
5618:design
5243:Finite
5099:Linear
5006:Future
4982:Major
4925:Series
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1186:), and
936:metric
894:where
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819:metric
780:Banach
742:, and
736:Cantor
728:Jordan
722:, and
606:Cauchy
576:, and
550:Newton
524:Fermat
513:Modern
491:cosine
457:sphere
386:Zeno's
289:, and
287:series
267:limits
6082:Gauge
5470:lists
5013:Lists
4986:areas
4920:Limit
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744:Baire
594:Euler
361:limit
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4655:ISBN
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