An introduction to Riemann integration - Dr Joel Feinstein

This is the final lecture of the second-year module G12MAN Mathematical Analysis, as taught by Dr Joel Feinstein.

See also Dr Feinstein's blog http://explainingmaths.wordpress.com/

This lecture gives a brief introduction to Riemann integration. This material is motivated in terms of questions of antidifferentiation and area. The proofs of the lemmas and theorems are not included here (see books for details), but the main definitions are given in full, along with illustrative examples and diagrams, and the statements of the main theorems.

Material discussed includes partitions of intervals; Riemann lower and upper sums (approximation sing rectangles); the Riemann lower and upper integrals; Riemann integrability of functions, and the Riemann integral. Examples are given of functions which are/are not Riemann integrable in particular, continuous real-valued functions on closed intervals are Riemann integrable.

The lecture concludes with the statements of the (first) Fundamental Theorem of Calculus and the Mean Value Theorem of Integral Calculus.

Category:

Education

Tags:

• Mathematics
• integral_calculus
• Riemann_integral
• integration
• Riemann_integrable_functions
• antidifferentiation
• primitives

[LASATEAZUL]

Dear Doctor.. I want know if yoi have videos of the riemman sum of sen (x) i wanna proof that integration....

[JoelFeinstein]

@jazzguitar2010 Thanks! If I had another four or five lectures, I could give more examples and fill in the details of the omitted proofs. That would be good, I think.

[jazzguitar2010]

Excellent. 

[JoelFeinstein]

I have been asked about the acronym NEB. This stands for Not Examinable as Bookwork. I posted a note on my blog about this on January 3rd 2010 entitled "What does NEB stand for?".

Joel Feinstein