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தொகையீடு: திருத்தங்களுக்கு இடையிலான வேறுபாடு

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Booradleyp (பேச்சு | பங்களிப்புகள்)
17,595 தொகுப்புகள்
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Booradleyp (பேச்சு | பங்களிப்புகள்)
17,595 தொகுப்புகள்
No edit summary
வரிசை 17:
 
மிக நுண்ணிய அகலம் கொண்ட எண்ணற்ற [[செவ்வகம்|செவ்வகங்களின்]] பரப்புகளின் கூடுதலாக வரையறுத்த தொகையீடு கருதப்பட்டது. தெளிவான வரையறையை [[ஜெர்மனி|ஜெர்மானியக்]] [[கணிதவியலாளர்]] ரீமான் அளித்தார். அவரது வரையறை, ஒரு வளைபரப்பை எண்ணற்ற மெல்லிய செவ்வக செங்குத்துப் பட்டைகளாகப் பிரித்து அவற்றின் பரப்புகளின் கூடுதலின் எல்லை மதிப்பாக வரையறுத்த தொகையீட்டைத் தந்தது. 19 ஆம் நூற்றாண்டின் தொடக்கதிலிருந்து தொகையீட்டின் மேம்பட்ட வரையறைகள் தோன்றத் தொடங்கின.
 
==குறிப்புகள்==
{{Reflist}}
 
==மேற்கோள்கள்==
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* {{Citation | last=Bourbaki| first=Nicolas | author-link=Nicolas Bourbaki | title=Integration I | year=2004 | publisher=[[Springer Science+Business Media|Springer Verlag]] | isbn=3-540-41129-1}}. In particular chapters III and IV.
* {{Citation | last=Burton | first=David M. | title=The History of Mathematics: An Introduction | edition=6th | year=2005<!--November 8--> | publisher=[[McGraw-Hill]] | isbn=978-0-07-305189-5 | page=359}}
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* {{Citation | last1=Dahlquist | first1=Germund | author1-link=Germund Dahlquist | last2=Björck | first2=Åke | title=Numerical Methods in Scientific Computing, Volume I | publisher=[[Society for Industrial and Applied Mathematics|SIAM]] | location=Philadelphia | year=2008 | url=http://www.mai.liu.se/~akbjo/NMbook.html | chapter=Chapter&nbsp;5: Numerical Integration}}
* {{Citation | last = Folland | first = Gerald B.| title=Real Analysis: Modern Techniques and Their Applications | edition=1st | publisher=[[John Wiley & Sons]] | year = 1984 | isbn=978-0-471-80958-6 }}
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>Available in translation as {{citation | last=Fourier | first=Joseph | title=The analytical theory of heat | year=1878<!--original 1822--> | publisher=[[Cambridge University Press]] | url=http://www.archive.org/details/analyticaltheory00fourrich | others=Freeman, Alexander (trans.) | pages=200–201}}
* {{Citation | editor-last=Heath | editor-first=T. L. | editor-link=T. L. Heath | title = The Works of Archimedes | year = 2002 | publisher = [[Dover Publications|Dover]] | isbn = 978-0-486-42084-4 | url = http://www.archive.org/details/worksofarchimede029517mbp }}<br/>(Originally published by [[Cambridge University Press]], 1897, based on J. L. Heiberg's Greek version.)
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* ''Der Briefwechsel von Gottfried Wilhelm Leibniz mit Mathematikern. Erster Band. Hrsg. von C. I. Gerhardt. Mit Unterstützung der Königl. Preussischen Akademie der Wissenschaften.''<br /
>Leibniz, Gottfried Wilhelm, Freiherr von, 1646–1716., Gerhardt, Karl Immanuel, ed. 1816–1899, Berlin: Mayer & Müller, 1899. [http://name.umdl.umich.edu/AAX2762.0001.001]
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==வெளி இணைப்புகள்==
{{Wikibooks|Calculus}}
* {{springer|title=Integral|id=p/i051340}}
* [http://mathworld.wolfram.com/RiemannSum.html Riemann Sum] by [[Wolfram Research]]
* [http://www.khanacademy.org/video/introduction-to-definite-integrals?playlist=Calculus Introduction to definite integrals] by [[Khan Academy]]
 
===இணைய நூல்கள்===
* Keisler, H. Jerome, [http://www.math.wisc.edu/~keisler/calc.html Elementary Calculus: An Approach Using Infinitesimals], University of Wisconsin
* Stroyan, K.D., [http://www.math.uiowa.edu/~stroyan/InfsmlCalculus/InfsmlCalc.htm A Brief Introduction to Infinitesimal Calculus], University of Iowa
* Mauch, Sean, [http://www.its.caltech.edu/~sean/book/unabridged.html ''Sean's Applied Math Book''], CIT, an online textbook that includes a complete introduction to calculus
* Crowell, Benjamin, [http://www.lightandmatter.com/calc/ ''Calculus''], Fullerton College, an online textbook
* Garrett, Paul, [http://www.math.umn.edu/~garrett/calculus/ Notes on First-Year Calculus]
* Hussain, Faraz, [http://www.understandingcalculus.com Understanding Calculus], an online textbook
* Kowalk, W.P., [http://einstein.informatik.uni-oldenburg.de/20910.html ''Integration Theory''], University of Oldenburg. A new concept to an old problem. Online textbook
* Sloughter, Dan, [http://math.furman.edu/~dcs/book Difference Equations to Differential Equations], an introduction to calculus
* [http://numericalmethods.eng.usf.edu/topics/integration.html Numerical Methods of Integration] at ''Holistic Numerical Methods Institute''
* P.S. Wang, [http://www.lcs.mit.edu/publications/specpub.php?id=660 Evaluation of Definite Integrals by Symbolic Manipulation] (1972)&nbsp;— a cookbook of definite integral techniques
 
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